T^B 

OF  THE 

UNIVERSITY 


EXPERIMENTAL  ENGINEERING 


AND 


MANUAL   FOR  TESTING. 


FOR   ENGINEERS    AND    FOR    STUDENTS   IN 
ENGINEERING    LA  BORA  TORIES. 


BY 

t? 

ROLLA   C.  CARPENTER,    M.S.,   C.E.,   M.M.E., 

n 

PROFESSOR  OF   EXPERIMENTAL    ENGINEERING,   SIBLEY   COLLEGE, 
CORNELL   UNIVERSITY. 


SIXTH  REVISED    AND    ENLARGED    EDITION. 
FIRST    THOUSAND. 


NEW    YORK  : 

JOHN    WILEY    &    SONS. 

LONDON:    CHAPMAN    &    HALL,    LIMITED, 

1906. 


COPYRIGHT,  1892,  1906, 

BY 

ROLLA   C.  CARPENTER. 


ROBERT   DRUMMOND,    HLECTROTYPEK    AND   PRINTER,   NKW   YORK. 


PREFACE  TO   THE   SIXTH    EDITION, 


THE  first  edition  of  the  present  work,  entitled  "Notes  to 
Mechanical  Laboratory  Practice,"  was  published  in  1890;  a 
second  edition  was  published  in  1891,  and- soon  exhausted  by  an 
unexpected  demand  from  engineering  schools  and  the  profession. 
The  two  early  editions  were  prepared  especially  for  the  use  of 
students  in  the  Laboratory  of  Experimental  Engineering,  Sibley 
College,  Cornell  University,  for  the  purpose  of  facilitating  in- 
vestigation of  engineering  subjects,  and  of  providing  a  systematic 
course  of  instruction  in  experimental  work. 

The  book  was  rewritten  and  much  enlarged  in  1892,  and  the 
title  changed  to  Experimental  Engineering.  Four  revised  editions, 
containing  a  total  of  nearly  ten  thousand  volumes,  have  been 
published  since  that  time,  in  which  various  errors  in  the  previous 
editions  have  been  eliminated  and  additions  made  as  required 
by  the  advance  in  the  engineering  art.  The  present,  or  sixth, 
edition  is  a  complete  revision  of  the  entire  book,  with  a  new 
index  and  more  than  100  pages  of  additional  matter,  including 
chapters  on  the  testing  of  the  Steam-turbine,  the  Air-compressor, 
and  the  Refrigerating-machine.  It  also  contains  much  new 
matter  relating  to  the  testing  of  the  Gas-engine. 

.  Respecting  the  field  of  the  book,  attention  is  called  to  the 
well-known  and  universally  acknowledged  fact  that  nearly  all 
the  recent  progress  in  the  engineering  art  is  due  to  experimental 
investigation  and  research.  Without  such  research  the  coefficients 
which  are  employed  in  making  practical  application  of  theoretical 
laws  would  not  have  been  known,  and  engineering  constructions 


IV  P  KEF  ACE    TO    THE    SIXTH  EDITION. 

and  machines  which  are  now  designed  with  confidence  to  pro- 
duce definite  results,  in  advance  of  actual  trial,  would  not  have 
been  possible.  Experimental  research  and  test  are  also  valuable 
in  discriminating  between  correct  and  false  theories,  since  it  is 
true  that  any  reliable  theory  will  be  verified  by  experiment,  whereas 
nd  theory  can  be  correct  which  does  not  accord  with  experimental 
results. 

On  the  other  hand,  experimental  results  may  lead  to  erroneous 
conclusions  if  the  fundamental  rational  theory  which  applies  is 
unknown,  and  it  is  for  this  reason  important  to  understand  the 
fundamental  theory,  if  any  exist,  in  advance  of  the  experimental 
work.  The  fact  should  be  noted  and  appreciated  that  without 
theory  all  engineering  knowledge  would  be  reduced  to  a  mere 
inventory  of  the  results  of  observations.  It  is  attempted  in  the 
work  on  Experimental  Engineering  to  point  out  the  relation 
between  the  fundamental  theory  and  the  experimental  results 
where  such  a  theory  exists,  and  for  other  cases  to  point  out  general 
methods  of  drawing  conclusions  from  the  observations  and  data 
obtained  in  performing  the  experiments. 

The  principal  object  of  the  present  edition  is  to  supply  a  text- 
book for  laboratory  use,  but  it  is  also  believed  that  the  volume  will 
not  be  without  value  as  a  reference-book  to  the  consulting  and 
practising  engineer,  since  it  contains  in  a  single  volume  the  prin- 
cipal standard  methods  which  have  been  from  time  to  time  adopted 
by  various  engineering  societies  for  the  testing  of  materials,  engines, 
and  machinery,  and  an  extensive  series  of  tables  useful  in  com- 
puting results.  It  also  contains  a  description  of  the  apparatus 
required  in  testing,  directions  for  taking  data  and  deducing  results 
in  engineering  experiments,  as  applied  in  nearly  every  branch  of 
the  art. 

The  book  is,  however,  intended  chiefly  for  use  in  engineering 
laboratories,  and  presents  information  which  the  experience  of 
the  author  has  shown  to  be  necessary  to  carry  out  experiments 
intelligently  and  without  great  loss  of  time  on  the  part  of  students. 
For  this  purpose  it  gives  a  brief  statement  of  the  theoretical  prin- 


PREFACE    TO    THE   SIXTH  EDITION.  V 

ciples  involved  in  connection  with  each  experiment,  with  references 
to  complete  demonstrations,  short  descriptions  of  the  various 
classes  of  engineering  apparatus  or  machinery,  a  full  statement 
of  methods  of  testing  and  of  preparing  reports.  For  a  few  cases 
where  references  cannot  readily  be  given,  demonstrations  of  the 
fundamental  principles  are  given  in  full. 

An  attempt  has  been  made,  by  dividing  the  book  into  several 
chapters  of  moderate  length,  by  making  the  paragraphs  short, 
and  by  placing  the  paragraph- numbers  at  the  top  of  the  page, 
to  make  references  to  the  book  easy  to  those  who  care  to  consult 
it.  References  which  will,  it  is  believed,  be  found  ample  for  all 
purposes  of  the  student  or  engineer  are  given,  where  needed,  to 
more  complete  treatises  on  the  various  subjects  discussed. 

The  importance  of  an  engineering  laboratory  is  now  so  fully 
recognized  in  colleges  of  engineering  that  it  is  hardly  necessary 
to  refer  to  the  advantages  which  it  confers.  If  devoted  to  educa- 
tional purposes,  it  should  afford  students  the  opportunity  of 
obtaining  practical  knowledge  of  the  application  and  limitation 
of  theoretical  principles  by  personal  investigation,  under  such 
direction  as  will  insure  systematic  methods  of  observation,  accurate 
use  of  apparatus,  and  the  proper  methods  of  drawing  conclu- 
sions and  of  making  reports.  If  of  an  advanced  character,  it 
should  also  provide  facilities  for  systematic  research  by  skilled 
observers,  for  the  purpose,  among  other  things,  of  discovering 
laws  or  coefficients  of  value  to  the  engineering  profession. 

This  work  deals  principally  with  the  educational  methods, 
the  use  of  apparatus,  and  the  preparation  required  for  making 
a  skilled  observer. 

In  an  engineering  laboratory  for  the  education  of  students, 
a  systematic  schedule  of  experiments  parallel  to  the  course  of 
instruction  in  theoretical  principles  is  recommended.  While  such 
a  laboratory  course  cannot  be  laid  down  here  as  applicable  to  all 
courses  of  instruction  in  engineering,  the  following  schedule  of 
studies  is  presented  for  consideration  as  one  which  has  been 
successfully  adopted  in  the  instruction  of  large  classes  in  Sibley 


vi  PREFACE    TO    THE  SIXTH  EDITION. 

College.  The  order  of  the  experiments  was  largely  determined 
by  the  previous  training  of  the  men,  and  by  the  attempt  to 
make  a  limited  amount  of  apparatus  do  maximum  duty.  The 
schedule  is  presented  more  as  an  illustration  of  one  that  has 
been  practically  tested,  and  for  which  the  work  on  Experimental 
Engineering  is  adapted,  than  as  a  model  for  other  institutions 
to  follow. 

COURSE    OF   EXPERIMENTS, 
SIBLEY  COLLEGE  ENGINEERING  LABORATORY. 

JUNIOR  YEAR. 
First  Term. 

Strength  of  Materials — Tensile  and  Transverse;  Calibration — Indicator- 
springs  and  Steam-gauges;  Weirs  and  Water-meters;  Mercurial  Thermom- 
eters; Pyrometers;  Transmission-dynamometers;  Slide-rule;  Calculating- 
machines;  Planimeters;  Calorimeter  and  Indicator-practice. 

Second  Term. 

Strength  of  Materials — Compression  and  Torsion;  Lubricants — Viscosity; 
Flash-test;  Coefficient  of  Friction;  Steam-engine — Valve-setting;  Flue-gas 
Analysis;  Temperature — Pyrometers,  Air- thermometers;  Calibration — Indi- 
cator-springs; Efficiency -tests — Steam-boiler;  Steam -pump;  Steam-engine; 
Hydraulic  Ram. 

SENIOR  YEAR. 
First  Term. 

Strength  of  Materials — Brick;  Stone;  Cement;  Efficiency-tests — Hot-air 
Engine  (2  tests);  Gas-engine  (3  tests) ;  Injector;  Centrifugal  Pump;  Hydrau- 
lic Motor;  Belting;  Steam  Boiler;  Compound  Engine;  Oil-engine  (2  tests); 
DeLaval  Steam  Turbine;  Parsons  Steam  Turbine. 

Second  Term. 

Strength  of  Materials  —  Springs;  Tension  test  on  Emery -machine; 
Efficiency -tests — Air-compressor;  Triple-expansion  Engine;  University  Elec- 
tric-lighting Plant;  Doble  Water-wheel;  Pelton  Wheel;  Refrigeration;  Com- 
pound and  Triple-expansion  Engine  by  Hirn's  Method;  Special  Research; 
Thesis  Work. 

The  work  required  of  each  student  per  week  is  substantially 
as  follows:  one  laboratory  exercise  three  hours  in  length,  one 


PREFACE    TO    THE   SIXTH  EDITION.  Vll 

recitation  one  hour  in  length,  and  the  computation  of  the  data 
and  the  preparation  of  a  report,  including  data,  results,  and  all 
necessary  curves.  The  report  is  required  to  be  full  and  com- 
plete, and  is  expected  to  train  the  young  man  in  methods  of  writing 
English  and  of  reporting  in  his  own  language  what  he  has  learned 
respecting  the  subject  under  investigation  in  the  laboratory  and 
in  the  references,  as  well  as  to  teach  him  method?  of  observing 
and  recording  the  data  and  of  computing  the  results  of  the  test. 
For  the  purpose  of  performing  the  experiments  the  students  are 
divided  into  groups  of  three,  and  the  experiments  are  usually 
arranged  as  to  require  three  observers  or  multiples  thereof.  The 
computation  of  results  is  made  by  all  the  members  of  the  group, 
but  each  man  is  required  to  write  an  individual  report  of  the  test. 
The  credit  given  is  the  same  as  for  a  recitation  course  requiring 
three  hours  per  week.  The  student's  work  is  performed  under 
the  personal  direction  of  a  competent  instructor,  who  has  charge 
usually  of  twelve  to  fourteen  men,  who  gives  such  detailed  instruc- 
tion as  is  required,  and  reads,  corrects,  and  grades  all  reports. 
The  student  is  required,  whenever  practicable  or  possible,  to 
operate  his  own  machine  or  apparatus  during  the  test,  in  order 
to  obtain  practical  skill  in  the  handling  and  operation  of  appara- 
tus, machines,  and  prime  movers,  which  is  believed  to  meet  an 
important  requirement  of  an  engineering  laboratory.  He  is  not 
expected  to  do  the  shop  work  required  for  construction  of  the 
apparatus,  or  that  required  for  the  preparation  of  the  experi- 
ment, as  the  time  at  his  command  is  not  sufficient  for  such  work; 
and  besides,  instruction  in  shop  work  is  given  in  a  different 
department  in  Sibley  College. 

The  full  list  of  subjects  treated  in  the  book  is  given  in  the 
table  of  contents  which  immediately  follows  the  preface.  Some 
of  the  more  important  divisions  of  the  work  are  as  follows  • 

Experimental  Methods  of  Investigation. 

Reduction  of  Experimental  Data  Analytically  and  Graphically. 
Apparatus  for  Reduction  of  Experimental  Data,  including  use  of  Slide-rule, 
Planimeter,  etc. 


viii  PREFACE    TO    THE   SIXTH  EDITION. 

Strength  01  Materials,  including  General  Formulae,  Description  of  Testing 

machines,  and  Methods  of  Testing. 
Cement-testing  Machines  and  Methods  of  Testing. 
Machines  and  Methods  for  Testing  Lubricants  and  Friction. 
Dynamometers  and  Machines  for  the  Measurement  of  Power. 
Hydraulics,  Hydraulic  Machinery,  and  Methods  of  Testing. 
Measurement  of  Pressure  and  Temperature. 
Measurement  of  Moisture  in  Steam  by  Calorimeters. 
Fuel-calorimeters  and  Flue-gas  Analysis. 
Tne  St2am-engine  and  Methods  of  Testing. 
The  Steam-boiler  and  Methods  of  Testing. 
The  Steam-turbine  and  Methods  of  Testing. 
Gas  and  Hot-air  Engines  and  Methods  of  Testing. 
The  Injector  and  Methods  of  Testing. 
Methods  of  Testing  Locomotives. 
Methods  of  Testing  Pumping-engines. 
Air-compressors  and  Methods  of  Testing. 
Refrigerating-machines  and  Methods  of  Testing. 

The  author  has  been  assisted  in  the  preparation  of  the  various 
editions  of  the  book  by  his  colleagues  and  assistants  in  Sibley 
College,  and  is  indebted  to  them  for  many  suggestions  and  a 
great  deal  of  valuable  information.  Ample  credit  is  given  authori- 
ties from  whom  information  has  been  obtained  in  the  body  of  the 
book  in  connection  with  the  matter  under  discussion.  In  the 
early  editions  of  the  work  the  writer  was  under  special  obligation 
to  the  late  Dr.  R.  H.  Thurston  and  to  Professor  C.  W.  Scribner; 
for  the  later  editions  to  Assistant .  Prof essor  H.  Diederichs,  and 
C.  Hirshfeldt,  and  to  Mr.  R.  L.  Shipman,  Mr.  W.  M.  Sawdon, 
and  Mr.  G.  B.  Upton. 


TABLE   OF   CONTENTS. 


INTRODUCTION. 

ARTICLE  PAGE 

1.  Objects  of  Engineering  Experiment i 

2.  Relation  of  Theory  to  Experiment 2 

3.  The  Method  of  Investigation 2 

4.  Classification  of  Experiments 3 

5.  Efficiency-tests 3 


CHAPTER  I. 

REDUCTION   OF  EXPERIMENTAL  DATA. 

6.  Classification  of  Errors 5 

7.  Probability  of  Errors 6 

8.  Errors  of  Simple  Observations 7 

10.  Combination  of  Errors 9 

i2.  Deduction  of  Empirical  Formulae 10 

15.  Rules  and  Formulae  for  Approximate  Calculation 15 

16.  Rejection  of  Doubtful  Observations 17 

1 7.  Errors  to  be  Neglected 18 

18.  Accuracy  of  Numerical  Calculations 19 

19.  Graphical  Representation  of  Experiments 20 

21.  Autographic  Diagrams 21 

22.  Construction  of  Diagrams 22 

CHAPTER  II. 

APPARATUS   FOR  REDUCTION  OF  EXPERIMENTAL  DATA. 

23.  The'  Slide-rule 24 

25.  The  Vernier 29 

26.  The  Polar  Planimeter 30 

30.  The  Suspended  Planimeter 41 

31.  The  Coffin  Planimeter 41 

ix 


TABLE   OF  CONTENTS. 


34.  The  Roller  Planimeter 45 

36.  Care  and  Adjustment  of  Planimeters 50 

37.  Directions  for  Use  of  Planimeters 51 

38.  Calibration  of  Planimeters 52 

39.  Errors  of  Planimeters 55 

40.  The  Vernier  Caliper.  .....: 57 

41.  The  Micrometer 58 

42.  The  Micrometer  Caliper 59 

43.  The  Cathetometer .' 62 

44.  Computation  Machines 64 


CHAPTER  III. 

STRENGTH  OF   MATERIALS — GENERAL  FORMULAE. 

45.  Definitions 67 

46.  Strain -diagrams 69 

47.  Viscosity 70 

48.  Notation 72 

49.  Tension. 72 

51.  Compression 73 

52.  Transverse . 76 

54.  Shearing  and  Torsion 81 

55.  Modulus  of  Rigidity 83 

58.  Combination  of  Two  Stresses 84 

60.  Thermodynamic  Relations 86 

CHAPTER  IV. 

STRENGTH  OF   MATERIALS— TESTING-MACHINES. 

61.  General  Description  of  Machines 88 

65.  Shackles  or  Holders 98 

66.  Emery  Testing-machine. IOo 

68.  Riehle  Bros.'  Testing-machine I07 

70.  Olsen  Testing-machine x  I0 

73.  Thurston's  Torsion  Machines 1 14 

75.  Richie's  and  Olsen's  Torsion  Machines u8 

76.  Impact  Testing-machine IZg 

77.  Cement-testing  Machines n^ 

Testing-machine  Accessories^ I2 


TABLE   OF  CONTENTS, 


XI 


ARTICLE  PAGE 

78  to  86.  Extensometers I24 

87.  Deflectometer 


CHAPTER  V. 

METHODS   OF   TESTING  MATERIALS   OF   CONSTRUCTION. 

88.  Form  of  Test-pieces I36 

93.  Elongation — Fracture I^ 

94.  Strain -diagrams I44 

95.  Tension  Tests I4^ 

99.  Compression  Tests I54 

TOO.  Transverse  Tests j^ 

102.  Elastic  Curve JCQ 

103.  Torsion  Test !6o 

105.  Impact  Test ^ 

107.  Special  Tests  of  Materials ^5 

109.  Method  of  Testing  Bridge  Materials 168 

1 10.  Admiralty  Tests !  72 

in.  Lloyd's  Tests  for  Steel  used  in  Ship-building 173 

112.  Tests  for  Cast-iron  Water-pipe 174 

114.  Testing  Stones 175 

115.  "       Bricks I78 

1 16.  "       Paving  Material , 1 79 

117.  M       Hydraulic  Cements 181 


CHAPTER  VI. 

FRICTION — TESTING  OF   LUBRICANTS. 

122.  Friction— Definitions— Useful  Formulae 196 

127.  Friction  of  Teeth IOQ 

128.  "        "  Cords  or  Belts 199 

129.  "        "Fluids - 200 

130.  "        "  Lubricated  Surfaces 201 

131.  Testing  of  Lubricants — Density 201 

i36-  "  Viscosity 209 

143-  "  Gumming 210 

144-  Flash-test 210 

147.  Testing  of  Lubricants— Cold  Test 213 

151.  Oil-testing  Machines— Rankine's 215 

152.  "  "          Thurston's 217 


Xii  TABLE   OF  CONTENTS. 

ARTICLE  PAGE 

155.  Coefficient  of  Friction 222 

157.  Richie's  Oil-testing  Machine 224 

158.  Durability  Test  of  Lubricants 226 

159.  Ashcroft's  Oil-testing  Machine 227 

160.  Boult's             "                ' '       227 

162.  Experiment  with  Limited  Feed 231 

163.  Forms  for  Report  of  Lubricant  Test 233 


CHAPTER  VII. 

MEASUREMENT  OF   POWER — BELT-TESTING. 

165.  Absorption  Dynamometer.     The  Prony  Brake 235 

173.  "  "    .  "    Alden  Brake 241 

178.  Practical  Directions  for  Use  of  Brake 244 

1 79.  Pump-brakes 245 

180.  Fan-brakes 245 

181.  Traction  Dynamometers 246 

182.  Transmission  Dynamometers — Morin 247 

186.  "  "  Steelyard 250 

187.  "  "  Pillow-block 252 

188.  "  "  Lewis 252 

189.  "  "  Differential 255 

192.  Emerson 259 

194.  "  "  Van  Winkle 261 

195-  "  Belt 263 

197.  Belt-testing  Machine,  with  Directions 264 

CHAPTER  VIII. 

MEASUREMENTS   OF   LIQUIDS   AND   GASES. 

200.  Theory  of  the  Flow  of  Water 270 

201.  Flow  of  Water  over  Weirs — Formulae 272 

203.      "      "      "      through  Nozzles — Formulas 275 

205.  ' c      "      ' '      under  Pressure — Formulae 276 

206.  "      "      "      in  Circular  Pipes 277 

207.  "      "      "      through  a  Diaphragm — Formulae 279 

209.  Method  of  Measuring  the  Flow  of  Water  by  Weirs 281 

213.        "       "  "      "      "       "     "  Meters 283 

217.        "       "  "      "      "       "      "  Nozzles 287 

219.  "       "  "          "      "      "       "      "Diaphragms.-. 288 

220.  "       "  "          "      "      "       "      ll   in  Streams. 28o 

222.        "       "  "      "      "       "     "  Pitot'sTube 292 


TABLE  OF  CONTENTS.  xiii 

ARTICLE  PAGE 

225.  Flow  of  Compressible  Fluids  through  an  Orifice 295 

229.  "     "             "               "       in  a  Pipe 299 

230.  "     "  Steam 300 

232.  Gas-meters 304 

233.  Anemometer 306 


CHAPTER  IX. 

HYDRAULIC   MACHINERY. 

235.  Classification. , 308 

239.  Water-pressure  Engines 309 

241.  Overshot  Water-wheels 311 

242.  Breast-wheels 313 

243.  Undershot  Wheels 313 

244.  Impulse-wheels ' , 314 

245.  Turbine 315 

248.  Reaction -wheels '. . .  317 

249.  The  Hydraulic  Ram 321 

250.  Methods  of  Testing  Water-motors 322 

253.  Pumps 327 

256.  Test  of  Pumps 330 

258.  Form  for  Data  and  Report  of  Pump-test 332 


CHAPTER  X. 

DEFINITIONS   OF   THERMODYNAMIC   TERMS. 

259.  Eooks  of  Reference 325 

260.  Units  of  Pressure 336 

261.  Heat  and  Temperature 337 

264.  Properties  of  Steam 340 

267.  Steam-tables 344 

CHAPTER  XI. 

MEASUREMENT   OF   PRESSURE. 

268.  Manometers 345 

271.  Mercury  Columns 349 

273.  Draught-gauges 351 


XIV  7 'ABLE   OF  CONTENTS. 


277.  Steam-gauges 357 

281.  Apparatus  for  Testing  Gauges 363 


CHAPTER  XII. 

MEASUREMENT   OF  TEMPERATURE. 


285.  Mercurial  Thermometers 369 

288.  Air-thermometers 371 

295.  Calibration  of  Thermometers .• 380 

296.  Metallic  Pyrometers 380 

298.  Air  and  Calorimetric  Pyrometers 381 

299.  Determination  of  Specific  Heat 382 

302.  Electric  Pyrometers 385 

303,  Optical  Pyrometers 386 


CHAPTER  XIII. 

METHODS   OF   MEASURING   MOISTURE   IN   STEAM. 

305.  Definitions 390 

307.  General  Methods 391 

314.  Errors  in  Calorimeters 396 

315.  Sampling  the  Steam 399 

317.  Water  Equivalent  of  Calorimeter 401 

318.  Barrel  Calorimeter 402 

321.  Hoadley  Calorimeter 407 

323.  Barrus  Continuous  Calorimeter 4II 

326.       * '      Superheating       "          4I6 

328.  Throttling  Calorimeter.*.  .' 4lg 

336.  Separator  430 

341.  Chemical  ' (         440 

CHAPTER  XIV. 

HEATING  VALUE   OF   COALS — FLUE -GAS   ANALYSIS. 

343.  Combustion— Definition  and  Table 443 

344.  Heat  of  Combustion 444 

345.  Determination  of  Heat  by  Welter's  Law .- 446 

346.  Temperature  produced  by  Combustion 448 


TABLE   OF  CONTENTS.  XV 

ARTICLE  PAGE 

347.  Composition  of  Fuels 4^0 

348.  Fuel-calorimeters — Principle 4^! 

352.  "  Favre  and  Silbermann's 453 

353-  Thompson's.  . 455 

354-  Berthkr 456 

355.  Berthelot  Bomb.  .  .  .  .- 459 

356.  Carpenter 463 

357.  Value  of  Fuel  by  Boiler-trial. 472 

358.  Analysis  of  the  Products  of  Combustion 473 

360.  Reagents  for  Flue-gas  Analysis 475 

363.  Elliot's  Flue-gas  Apparatus 479 

364.  Wilson's      "  "        481 

365.  Orsat's        "  " ; ..481 

366.  Hemple's     "  483 

367.  Deductions  from  Flue-gas  Analysis 486 


CHAPTER  XV. 

METHOD   OF  TESTING   STEAM-BOILERS. 

369.  Objects  of  Boiler-testing 492 

371.  Efficiency  of  a  Boiler 493 

375.  Standard  Method  of  Testing  Steam-boilers 495 

377.  Concise  Directions  for  Testing  Boilers. 513 


CHAPTER  XVI. 

THE   STEAM-ENGINE   INDICATOR. 

378.  Uses  of  the  Indicator c^cj 

380.  Early  Forms ^j 

381.  Richards ^xg 

382.  Thompson 519 

383.  Tabor 520 

384..  Crosby 52I 

385.  Indicators  with  External  Springs :' 523 

387.  Optical  Indicators 525 

390.  Reducing-motions 529 

393-  Calibration 535 

397.  Method  of  Attaching  to  the  Cylinder 543 

398.  Directions  for  Use 545 


xvi  TABLE   OF  CONTENTS. 


CHAPTER  XVII. 

THE  INDICATOR-DIAGRAM. 

ARTICLE  PAGE 

400.  Definitions 547 

401.  Measurement  of  Diagrams 551 

403.  Form  of  Diagram £53 

4c6.  Weight  of  Steam  from  the  Diagram 557 

407.  Clearance  from  the  Diagram 560 

408.  Cylinder-condensation  and  Re -evaporation 561 

409.  Discussion  of  Diagrams 562 

410.  Diagrams  from  Compound  Engines 565 

411.  Crank-shaft  and  Steam-chest  Diagrams 567 


CHAPTER  XVIII. 

METHODS   OF  TESTING  THE   STEAM-ENGINE. 

412.  Engine  Standards 569 

414.  Measurement  of  Speed 571 

417.  Surface  Condenser 576 

418.  Calibration  of  Apparatus 578 

419.  Preparations  for  Testing 581 

421.  Quantities  to  be  Observed 583 

422.  Preliminary  Indicator-practice 584 

423.  Valve-setting 586 

424.  Friction-test 589 

425.  Efficiency-test 589 

426.  Hirn's  Analysis 590 

430.      '  *  "       of  Compound  Engines 603 

CHAPTER  XIX. 

PUMPING-ENGINES   AND  LOCOMOTIVES. 

433.  Standard  Method  of  Testing  Pumping-engines 614 

434-  ' '       "        "       Locomotives 634 

435.  Experimental  Engines. ... 656 


TABLE    OF  CONTENTS.  xvii 


CHAPTER  XX. 

EXPERIMENTAL  DETERMINATION  OF  INERTIA. 

ARTICLE  PAGE 

436.  General  Effects  of  Inertia 660 

437.  The  Williams  Inertia-indicator 661 

438.  ' '    Inertia -diagram 664 


CHAPTER  XXI. 

THE   INJECTOR  AND  PULSOMETER. 

439.  Description  of  the  Injector 670 

440.  Theory 672 

442.  Limits  of 676 

443-5.  Directions  for  Testing 679 

446-7.  The  Pulsometer 683 

CHAPTER  XXII. 

THE   STEAM-TURBINE. 

448.  General  Principles 686 

449.  Impulse  Type  (De  Laval) 687 

450.  Reaction  Type  (Parsons) ' 689 

451.  Combined  Type  (Curtis) 690 

452.  Testing 691 

CHAPTER  XXIII. 

HOT-AIR  AND   GAS  ENGINES. 

454.  General  Principles 692 

455.  Ericsson  Hot-air  Engine 692 

456.  Rider  Hot-air  Engine 693 

457.  Theory 695 

458.  Method  of  Testing 095 

460.  The  Gas-engine , 701 

461.  Oil-engines 709 

462.  Theoretical  Formulae 711 

463.  Cycle  of  Operation 713 


xvin  TABLE    OF  CONTENTS. 


464.  Method  of  Testing 714 

465.  Data  and  Results  of  Test 717 


CHAPTER  XXIV. 

AIR -COMPRESSORS. 

466.  Types  of  Compressors 720 

467.  Piston  Air-compressor 720 

468.*  Rotary  Blowers 723 

469.  Centrifugal  Fans 724 

470.  Measurement  of  Pressure  and  Velocity 725 

471.  Clearance,  Effect  of.  .  .  . 728 

472.  Loss  of  Work  Due  to  Rise  of  Temperature 728 

473.  Centrifugal  Fan,  Theory  of 729 

474.  Test  of  Air-compressor  Data  Sheets 730 

475.  '  *    < '  Centrifugal  Blower 733 

CHAPTER  XXV. 

MECHANICAL  REFRIGERATION. 

476.  Systems  of  Mechanical  Refrigeration 734 

477.  Relation  of  Work  to  Heat  Transfer 735 

478.  Working  Fluids,  Properties  of 736 

479.  Efficiency  of  the  Refrigerating-machine 738 

480.  Heat  Losses 740 

481.  The  Air-refrigerating  Machine 741 

482.  The  Ammonia  Refrigerating-machine 742 

483.  Relations  of  Pressure  and  Volume 744 

484.  Absorption  System  of  Refrigeration 747 

Logs  and  Data  Sheets 749 


CHAPTER  XXVI. 

PRACTICAL     TABLES. 
TABLE 

I.  U.  S.  Standard  and  Metric  Measures 754 

II.  Numerical  Constants 756 

III.  Logarithms  of  Numbers 769 

IV.  Logarithmic  Functions  of  Angles , 77! 


TABLE   OF  CONTENTS.  xix 

TABLE  PAGE 

V.  Natural  Functions  of  Ang.es 777 

VI.  Coefficients  of  Strength  of  Materials 781 

VII.  Strength  of  Metals  at  Different  Temperatures 782 

VIII.  Important  Properties  of  Familiar  Substances 783 

IX.  Coefficient  of  Friction 784 

X.  Hyperbolic  Naperian  Logarithms 784 

XI.  Moisture  Absorbed  by  Air 785 

XII.  Relative  Humidity  of  the  Air 785 

XIII.  Table  for  Reducing  Beaume's  Scale-reading  to  Specific  Gravity  786 

XIV.  Composition  of  Fuels  of  U.  S 787 

XV.  Buel's  Steam-tables 788 

XVI.  Entropy  of  Water  and  Steam 794 

XVII.  Discharge  of  Steam:  Napier  Formula 795 

XVIII.  Water  in  Steam  by  Throttling  Calorimeter 795 

Diagram  for  Determining  Per  Cent  of  Moisture  in  Steam 796 

XIX.  Factors  of  Evaporation 797 

XX.  Dimensions  of  Wrought-iron  Pipe 798 

XXI.  Density  and  Weight  of  Water  per  Cubic  Foot 799 

XXII.  Horse -power  per  Pound  Mean  Pressure 800 

XXIII.  Water  Rate  Computation  Table  for  Engines 801 

XXIV.  Weirs  with  End  Contraction 803 

XXV.  Weirs  without  End  Contraction 803 

XXVI.  Horse-power  of  Shafting 804 

XXVII.  "  "  Belting 804 

Sampls-sheet  of  Cross-section  Paper 805 

IMPORTANT  TABLES  IN  BODY  OF  BOOK. 

Moments  of  Inertia 78 

Units  of  Pressure  Compared 336 

Thermometric  Scales 337 

Melting-points  and  Specific  Heats  of  Metals 383 

Maximum  Temperature  of  Combustion 450 

Average  Composition  of  Fuels 451 

Properties  of  Saturated  Ammonia 738 


INTRODUCTION. 


I.  Objects  of  Engineering  Experiments. — The  object  of 

experimental  work  in  an  engineering  course  of  study  may  be 
stated  under  the  following  heads :  firstly,  to  afford  a  practical 
illustration  of  the  principles  advanced  in  the  class-room  ;  sec- 
ondly,  to  become  familiar  with  the  methods  of  testing;  thirdly, 
to  ascertain  the  constants  and  coefficients  needed  in  engineer- 
ing  practice ;  fourthly,  to  obtain  experience  in  the  use  of  vari- 
ous types  of  engines  and  machines  ,  fifthly,  to  ascertain  the 
efficiency  of  these  various  engines  or  machines ;  sixthly,  to  de- 
duce general  laws  of  action  of  mechanical  forces  or  resistances, 
from  the  effects  or  results  as  shown  in  the  various  tests  made. 
The  especial  object  for  which  the  experiment  is  performed 
should  be  clearly  perceived  in  the  outset,  and  such  a  method 
of  testing  should  be  adopted  as  will  give  the  required  informa- 
tion. 

This  experimental  work  differs  from  that  in  the  physical 
laboratory  in  its  subject-matter  and  in  its  application,  but  the 
methods  of  investigation  are  to  a  great  extent  similar.  In  per- 
forming engineering  experiments  one  will  be  occupied  princi- 
pally in  finding  coefficients  relating  to  strength  of  materials  or 
efficiency  of  machines ;  these,  from  the  very  nature  of  the  ma- 
terial investigated,  cannot  have  a  constant  value  which  will  be 
exactly  repeated  in  each  experiment,  even  provided  no  error 
be  made.  The  object  will  then  be  to  find  average  values  of 
these  coefficients,  to  obtain  the  variation  in  each  specific  test 


2  EXPERIMENTAL  ENGINEERING.  [§  3- 

from  these  average  values,  and,  if  possible,  to  find  the  law  and 
cause  of  such  variation. 

The  results  are  usually  a  series  of  single  observations  on  a 
variable  quantity,  and  not  a  series  of  observations  on  a  con- 
stant quantity ;  so  that  the  method  of  finding  the  probable 
error,  by  the  method  of  least  squares,  is  not  often  applicable. 
This  method  of  reducing  and  correcting  observations  is,  how- 
ever, of  such  value  when  it  is  applicable,  that  it  should  be 
familiar  to  engineers,  and  should  be  applied  whenever  practi- 
cable. The  fact  that  single  observations  are  all  that  often  can 
be  secured  renders  it  necessary  in  this  work  to  take  more  than 
ordinary  precautions  that  such  observations  be  made  correctly 
and  with  accurate  instruments. 

2.  Relation  of  Theory  to  Experiment. — It  will  be  found 
in  general  better  to  understand  the  theoretical  laws,  as  given 
in  text-books,  relating  to  the  material  or  machine  under  inves- 
tigation, before  the  test  is  commenced ;  but  in  many  cases  this 
is  not  possible,  and  the  experiment  must  precede  a  study  of  the 
theory. 

It  requires  much  skill  and  experience  in  order  to  deduce 
general  laws  from  special  investigations,  and  there  is  always 
reason  to  doubt  the  validity  of  conclusions  obtained  from  such 
investigations  if  any  circumstances  are  contradictory,  or  if  any 
cases  remain  unexamined. 

On  the  other  hand,  theoretical  deductions  or  laws  must  be 
rejected  as  erroneous  if  they  indicate  results  which  are  con- 
tradictory  to  those  obtained  by  experiments  subject  to  condi- 
tions applicable  in  both  cases. 

3.  The  Method  of  Investigation   is  to  be  considered  as 
consisting  of  three  steps :  firstly,  to  standardize  or  calibrate  the 
apparatus  or  instruments  used  in  the  test ;  secondly,  to  make 
the  test  in  such  a  way  as  to  obtain  the  desired  information ; 
thirdly,  to  write  a  report  of  the  test,  which  is  to  include  a  full 
description  of  the  methods  of  calibration  and  of  the  results, 
which  in  many  cases  should  be  expressed  graphically. 

The  methods  of  standardizing  or  calibrating  will  in  gen- 
eral consist  of  a  comparison  with  standard  apparatus,  under 


§5-]  INTRODUCTION.  3 

conditions  as  nearly  as  possible  the  same  as  those  in  actual  prac- 
tice. These  methods  later  will  be  given  in  detail.  The  manner 
of  performing  the  test  will  depend  entirely  on  the  experiment. 

The  report  should  be  written  in  books  or  on  paper  of  a  pre- 
scribed form,  and  should  describe  clearly:  (i)  Object  of  the 
experiment;  (2)  Deduction  of  formulae  and  method  of  perform- 
ing the  experiment;  (3)  Description  of  apparatus  used,  with 
methods  of  calibrating;  (4)  Log  of  results,  which  must  include 
all  the  figures  taken  in  the  various  observations  of  the  calibra- 
tion as  well  as  in  the  experiment.  These  results  should  be 
arranged,  whenever  possible,  in  tabular  form;  (5)  Results  of 
the  experiment ;  these  should  be  expressed  numerically  and 
graphically,  as  explained  later;  (6)  Conclusions  deduced  from 
the  experiment,  and  comparison  of  the  results  with  those  given 
by  theory  or  other  experiments. 

4.  Classification   of    Experiments. — The  method  of  per- 
forming an  experiment  must  depend  largely  on  the  special  object 
of  the  test,  which  should  in  every  case  be  clearly  comprehended. 
The   following   subjects   are   considered   in   this   treatise,   under 
various  heads:    (i)  The  calibration  of  apparatus;    (2)  Tests  of 
the   strength   of   materials;     (3)    Measurements   of  liquids   and 
gases;     (4)   Tests   of   friction   and   lubrication;     (5)    Emciency- 
tests,  which  relate  to  (a)  belting  and  machinery  of  transmission, 
(b)  water-wheels,  pumps,  and  hydraulic  motors,  (c)  hot-air  and 
gas  engines,  (d)  air-compressors  and  compressed-air  machinery, 
(e)  steam-engines,  boilers,  injectors,  and  direct-acting  pumps. 

5.  Efficiency-tests. — Tests  may  be  made   for   various   ob- 
jects* the  most  important  being  probably  that  of  determining  the 
efficiency,  capacity,  or  strength. 

The  efficiency  of  a  machine  is  the  ratio  of  the  useful  work 
delivered  by  the  machine  to  the  whole  work  supplied  or  to  the 
whole  energy  received.  The  limit  to  the  efficiency  of  a  machine 
is  unity j  which  denotes  the  efficiency  of  a  perfect  machine. 

The  whole  work  performed  in  driving  a  machine  is  evidently 
equal  to  the  useful  work,  plus  the  work  lost  in  friction,  dissi- 
pated in  heat,  etc.  The  lost  work  of  a  machine  often  consists 


4  EXPERIMENTAL   ENGINEERING.  [§  5- 

of  a  constant  part,  and  in  addition  a -part  bearing  some  definite 
proportion  to  the  useful  work;  in  some  cases  all  the  lost  work 
is  constant. 

Efficiency-tests  are  made  to' determine  the  ratio  of  useful 
work  performed  to  total  energy  received,  and  require  the  deter- 
mination of,  first,  the  work  or  energy  received  by  the  machine; 
second,  the  useful  work  delivered  by  the  machine.  The  friction 
and  other  lost  work  is  the  difference  between  the  total  energy 
supplied  and  the  useful  work  delivered.  In  case  the  efficiency 
of  the  various  parts  of  the  machine  is  computed  separately,  the 
efficiency  of  the  whole  machine  is  equal  to  the  product  of  the 
efficiencies  of  the  various  component  parts  which  transmit  energy 
from  the  driving-point  to  the  working-point. 

The  work  done  or  energy  transmitted  is  usually  expressed 
in  foot-pounds  per  minute  of  time,  or  in  horse-power,  which  is 
equivalent  to  33,000  foot-pounds  per  minute,  or  550  foot-pounds 
per  second  of  time. 


EXPERIMENTAL    ENGINEERING. 


REDUCTION   OF  EXPERIMENTAL  DATA. 

METHOD  OF  LEAST  SQUARES— NUMERICAL  CALCULATIONS- 
GRAPHICAL  REPRESENTA  TION  OF  EXPERIMENT  J. 


CHAPTER   I. 
APPLICATION  OF  THE  METHOD  OF  LEAST  SQUARES. 

IN  the  following  articles  the  application  of  this  method  to 
reducing  observations  and  producing  equations  from  experi- 
mental data  is  quite  fully  set  forth.  The  theory  of  the 
Method  of  Least  Squares  is  not  given,  but  it  can  be  fully 
studied  in  the  work  by  Chauvenet  published  by  Lippincott  & 
Co.,  or  in  the  work  by  Merriman  published  by  John  Wiley  & 
Sons. 

6.  Classification  of  Errors. — The  errors  to  which  all  ob- 
servations are  subject  are  of  two  classes:  systematic  and  acci- 
dental. 

Systematic  errors  are  those  which  affect  the  same  quanti- 
ties in  the  same  way,  and  may  be  further  classified  as  instru- 
mental and  personal.  The  instrumental  errors  are  due  to 
imperfection  of  the  instruments  employed,  and  are  detected  by 
comparison  with  standard  instruments  or  by  special  methods 
of  calibration.  Personal  errors  are  due  to  a  peculiar  habit  of 
the  observer  tending  to  make  his  readings  preponderate  in 
a  certain  direction,  and  are  to  be  ascertained  by  comparison  of 

5 


6  EXPERIMENTAL   ENGINEERING.  [§  7- 

observations  :  first,  with  those  taken  automatically  ;  second, 
with  those  taken  by  a  large  number  of  observers  equally  skilled  ; 
third,  with  those  taken  by  an  observer  whose  personal  error  is 
known.  Systematic  errors  should  be  investigated  first  of  all, 
and  their  effects  eliminated. 

Accidental  errors  are  those  whose  presence  cannot  be  fore- 
seen nor  prevented;  they  may  be  due  to  a  multiplicity  of  causes, 
but  it  is  found,  if  the  number  of  observations  be  sufficiently 
great,  that  their  occurrence  can  be  predicted  by  the  law  of 
probability,  and  the  probable  value  of  these  errors  can  be  com- 
puted by  the  METHOD  OF  LEAST  SQUARES. 

Before  making  application  of  the  <4  Method  of  Least 
Squares,"  determine  the  value  of  the  systematic  errors,  elimi- 
nate them,  and  apply  the  method  of  least  squares  to  the  de- 
termination of  accidental  errors. 

7.  Probability  of  Errors.  —  The  following  propositions  are 
regarded  as  axioms,  and  are  the  fundamental  theorems  on 
which  the  Method  of  Least  Squares  is  based  : 

1st.  Small  errors  will  be  more  frequent  than  large  ones. 

2d.  Errors  of  excess  and  deficiency  (that  is,  results  greater 
or  less  than  the  true  value)  are  equally  probable  and  will  be 
equally  numerous. 

3d.  Large  errors,  beyond  a  certain  magnitude,  do  not  occur. 
That  is,  the  probability  of  a  very  large  error  is  zero. 

From  these  it  is  seen  that  the  probability  of  an  error  is  a 
function  of  the  magnitude  of  the  error.  Thus  let  x  represent 
any  error  and  y  its  probability,  then 


By  combination  of  the  principles  relating  to  the  probability 
of  any  event  Gauss  determined  that 

y  =  "-JV  .....   .  .   .   (i) 

in  which  c  and  h  are  constants,  and  e  the  base  of  the  Napierian 
system  of  logarithms. 


§  9-]    APPLICATION  OF  METHOD    OF  LEAST  SQUARES.          / 

8.  Errors  of  Simple  Observations. — It  can  be  shown  by 
calculation  that  the  most  probable  value  of  a  series  of  obser- 
vations made  on  the  same  quantity  is  the  arithmetical  mean,  and 
if  the  observations  were  infinite  in  number  the  mean  value  would 
be  the  true  value.  The  residual  is  the  difference  between  any 
observation  and  the  mean  of  all  the  observations.  The  mean 
error  of  a  single  observation  is  the  square  root  of  the  sum  of  the 
squares  of  the  residuals,  divided  by  one  less  than  the  number 
of  observations.  The  probable  error  is  0.6745  time  the  mean 
error.  The  error  oj  the  result  is  that  of  a  single  observation 
divided  by  the  square  root  of  their  number. 

Thus  let  n  represent  the  number  of  observations,  5  the  sum 
of  the  squares  of  the  residuals ;  let  e,  el ,  <?2 ,  etc.,  represent  the 
residual,  which  is  the  difference  between  any  observation  and 
the  mean  value '  let  2  denote  the  sum  of  the  quantities  indi- 
cated by  the  symbol  directly  following. 

Then  we  shall  have 


Mean  error  of  a  single  observation  ±  \/~  — •  •  •  (2) 
Probable  error  of  a  single  observation  ±  0.6745/1  /—£  —  .  (3) 
Mean  error  of  the  result  ±  A  /  ,  _  -r.  .  (4) 


Probable  error  of  the  result  ±  0.6745  \/  /tt(^_-\-  ($) 


In  every  case  5  = 

9.  Example.  —  The  following  example  illustrates  the  method 
of  correcting  observations  made  on  a  single  quantity: 

A  great  number  of  measurements  have  been  made  to 
determine  the  relation  of  the  British  standard  yard  to  the 


8 


EXPERIMENTAL  ENGINEERING. 


meter.  The  British  standard  of  length  is  the  distance,  on  a 
bar  of  Bailey's  bronze,  between  two  lines  drawn  on  plugs  at 
the  bottom  of  wells  sunk  to  half  the  depth  of  the  bar.  The 
marks  are  one  inch  from  each  end.  The  measure  is  standard 
at  72°  Fah.,  and  is  known  as  the  Imperial  Standard  Yard. 

The  meter  is  the  distance  between  the  ends  of  a  bar  of 
platinum,  the  bar  being  at  o°  Centigrade,  and  is  known  as  the 
Metre  des  Archives. 

The  following  are  some  of  these  determinations.  That 
made  by  Clarke  in  1866  is  most  generally  recognized  as  of 
the  greatest  weight. 

COMPARISON   OF   BRITISH   AND    FRENCH   MEASURES. 


Name  of  Observer. 

Date. 

Observed 
length  of  meter 
in  inches. 

Difference  from 
the  mean. 
ResiduaJ  =  e. 

Square  of  the 
Residuals. 
*'. 

Kater  

1821 

•an.  -57070 

—  o  001460 

Hassler  

1832 

3Q.^8lO^ 

-4-        8780 

o  0000770884 

Clarke  

1866 

•7Q.  7704.^2 

1818 

1884 

1Q  .  ^7OI  5 

2IOO 

Comstock  

188* 

•JQ     7608^ 

qo.q722:?O 

=  S  =  0.0000907024,     n  =  5,    n(n  —  i)  =  20. 


/—$- 
Mean  error  of  a  single  observation  =  ±  \  /     ___     =  0.00476* 


Probable  error  of  single  observation  =  ±  0.003 17. 


Mean  error  of  mean  value 


=  ± 


—=  0.0021$ 


Probable  error  of  mean  value  =  ±  0.00142. 


§11.]     APPLICATION   OF  METHOD   OF  LEAST  SQUARES.         9 

That  is,  considering  the  observations  of  equal  weight,  it 
would  be  an  even  chance  whether  the  error  of  a  single  obser- 
vation were  greater  or  less  than  0.00317  inch,  and  the  error 
of  the  mean  greater  or  less  than  0.00142. 

10.  Combination  of  Errors.  —  When  several  quantities  are 
involved  it  is  often  necessary  to  consider  how  the  errors  made 
upon  the  different  quantities  will  affect  the  result. 

Since  the  error  is  a  small  quantity  with  reference  to  the  re- 
sult, we  can  get  sufficient  accuracy  with  approximate  formulae. 

Thus  let  X  equal  the  calculated  or  observed  result,  F  the 
error  made  in  the  result  ;  let  x  equal  one  of  the  observed 
quantities,  and  /  its  error.  Then  will 


JV 

in  which  j-  is  the  partial  derivative  of  the  result  with  respect 

to  the  quantity  supposed  to  vary.  In  case  of  two  quantities 
in  which  the  errors  are  F,  Ff,  etc.,  the  probable  error  of  the 
result 


=  ±  VF*  +  F" (7) 

II.  As  an  example,  discuss  the  effect  of  errors  in  counting  the 
number  of  revolutions,  and  in  measurement  of  the  mean  effec- 
tive pressure,  acting  on  the  piston,  with  regard  to  the  power 
furnished  by  a  steam-engine.  Denote  the  number  of  revolu- 
tions by  n,  the  mean  pressure  by/,  the  length  of  stroke  in  feet 
by  /,  and  the  area  of  piston  in  square  inches  by  a\  the  work 
in  foot-pounds  done  on  one  side  of  the  piston  by  W.  Then 

W  —  plan,  F  =  lanft 

F      dW  _,  ,, 

J=-dp=lan>  F=plaf>. 

F'       dW 


*0  EXPERIMENTAL   ENGINEERING.  [§  I2' 

The  error/  in  the  mean  pressure  is  itself  a  complicated 
one,  since  /  is  measured  from  an  indicator-diagram  and  depends 
on  accuracy  of  the  indicator-springs,  accuracy  of  the  indicator- 
motion,  and  the  correct  measurement  of  the  indicator-diagram. 
These  errors  vary  with  different  conditions.  Suppose,  however, 
the  whole  error  to  be  that  of  measurement  of  the  indicator- 
diagram.  This  is  usually  measured  with  a  polar  planimeter,  of 
which  the  minimum  error  of  measurement  may  be  taken  as 
0.02  square  inch ;  with  an  indicator-diagram  three  inches  in 
length  this  corresponds  to  an  error  of  0.0067  of  an  inch  in  ordi- 
nate.  In  a  similar  manner  the  error  in  the  number  of  revolu- 
tions depends  on  the  method  of  counting:  with  a  hand-counter 
the  best  results  by  an  expert  probably  would  involve  an  error 
of  one  tenth  of  a  second ;  with  an  attached  chronograph  the 
error  would  be  less,  and  would  probably  depend  on  the  accu- 
racy with  which  the  results  could  be  read  from  the  chronograph- 
diagram.  The  ordinary  errors  are  fully  three  times  those 
given  here. 

Take  as  a  numerical  example,  a  =  100  square  inches, 
1  =  2  feet,  n  =  300,  /  =  50  pounds,  /=  0.335,  /'  =  0.5. 

F  =.  20,100,  F  =  5,ooo,  W  =  3,000,000. 


Probable  error  =  ±  VF*  +  F'*  =  20,712  ft.-lbs.,  which  in  this 
case  is  0.0069  of  the  work  done. 

12.  Deduction  of  Empirical  Formulae. — Observations  are 
frequently  made  to  determine  general  laws  which  govern 
phenomena,  and  in  such  cases  it  is  important  to  determine 
what  formula  will  express  with  least  error  the  relation  between 
the  observed  quantities. 

These  results  are  empirical  so  long  as  they  express  the  re- 
lation between  the  observed  quantities  only;  but  in  many  cases 
they  are  applicable  to  all  phenomena  of  the  same  class,  in 
which  case  they  express  engineering  or  physical  laws. 

In  all  these  cases  it  is  important  that  the  form  of  the  equa- 
tion be  known,  as  will  appear  from  the  examples  to  be  given 
later.  The  form  of  the  equation  is  often  known  from  the 


§  1 3.]       APPLICATION   OF  METHOD    OF  LEAST  SQUARES.    II 

general  physical  laws  applying  to  similar  cases,  or  it  may  be 
determined  by  an  inspection  of  the  curve  obtained  by  a 
graphical  representation  of  the  experiment.  A  very  large  class 
of  phenomena  may  be.  represented  by  the  equation 

y  =  A  -f  Bx  +  Cx*  +  Dx*  +  etc.  ....    (8) 

In  case  the  graphical  representation  of  the  curve  indicates  a 
parabolic  form,  or  one  in  which  the  curve  approaches  parallel- 
ism  with  the  axis  of  X,  the  empirical  formula  will  probably  be 
of  the  form 

jr  =  A  +  £x*  +  Cx?  +  £>J+etc.      ...     (9) 

In  case  the  observations  show  that,  with  increasing  values  of  xy 
y  passes  through  repeating  cycles,  as  in  the  case  of  a  pendulum, 
or  the  backward  and  forward  motion  of  an  engine,  the  charac- 
teristic curve  would  be  a  sinuous  line  with  repeated  changes 
in  the  direction  of  curvature  from  convex  to  concave.  The 
equation  would  be  of  the  form 


y  =  A  +  Bt  sin         x  +  £,  cos       -x  +  C,  sin 


m  m  m 

360° 


•fete.  .    .    .    (10) 

m 

Still  another  form  which  is  occasionally  used  is 

y  =  A  +B  sin  mx -\-  Cs\tfmx-\-  etc,      .     .    (il) 

13.  General  Methods. — A  method  of  deducing  the  em- 
pirical formula  is  illustrated  by  the  following  general  case: 

In  a  series  of  observations  or  experiments  let  us  suppose 
that  the  errors  (residuals)  committed  are  denoted  by  e,  e',  e"9 


12  EXPERIMENTAL   ENGINEERING.  L§  J3- 

etc.,  and  suppose  that  by  means  of  the  observations  we  have 
deduced  the  general  equations  of  conditions  as  follows: 

e     =  h     +  ax     -f-  by     +  cz, 
e'    =  h'    +  a'x    +  b'y    +c'*, 
e"  =  k"  +  a"x  +  b"y  +  c"  z 
e'"  =  k'"  +  a'"x  +  b'"y  +  c'" 
etc.  etc.         etc. 

Let  it  be  required  to  find  such  values  of  x,  y,  z,  etc.,  that  the 
values  of  the  residuals  e,  ef,  e" ,  e'",  etc.,  shall  be  the  least  pos- 
sible, with  reference  to  all  the  observations. 

If  we  square  both  members  of  each  equation  in  the  above 
group  and  add  them  together,  member  to  member,  we  shall 
have 

^  +  </»  4.  e"*  +  e'"*  +  etc.  =  x\c?  +  a">  +  a"*  +  etc.) 

+  2x{(ak  +  a'ti  +  a"h"  +  etc.)+  a(fy  +  cz  +  etc.) 
+  a'(b'y  +  c'z  +  etc.)  +  etc. }  +  tf  +  k'*  +  etc. 

This  equation  may  be  arranged  with  reference  to  x  as 
follows  : 

u  =  ^  +  J*  +  e"*  +  etc.  =  Px*  +  zQx  +  R  +  etc. ; 

in  which  the  various  coefficients  of  the  different  powers  of  x 
are  denoted  by  the  symbols  P,  Q,  R,  etc. 

Now  in  order  that  these  various  errors  may  be  a  minimum, 
^a+  ^/a  +  e"*  +  etc-  ==  u  must  be  a  minimum,  in  which  case 
its  partial  derivative,  taken  with  respect  to  each  variable  in 
succession,  should  be  separately  equal  to  zero.  Hence 


or,  substituting  the  values  of  P  and  Q, 

x(a?  +  a'*  +  etc.)  +  ah  +  ah'  +  etc.  +  a  (by  +  cz  +  etc.) 

+  a'(b'y  +  ^  +  etc.)  +  etc.  =  o. 
Similar  equations  are  to  be  formed  for  each  variable. 


§  1 4.]        APPLICATION   OF  METHOD   OF  LEAST  SQUARES.    13 


From  the  form  of  these  equations  we  deduce  the  principle 
that  in  order  to  find  an  equation  of  condition  for  the  minimum 
error  with  respect  to  one  of  the  unknown  quantities,  as  x  for 
example,  we  have  simply  to  multiply  the  second  member  of  each 
of  the  equations  of  condition  by  the  coefficient  of  the  unknown 
quantity  in  that  equation,  take  the  sum  of  the  products,  and  place 
the  result  equal  to  zero.  Proceed  in  this  manner  for  each  of  the 
unknown  quantities,  and  there  will  result  as  many  equations  as 
there  are  unknown  quantities,  from  which  the  required  values 
of  the  unknown  quantities  may  be  found  by  the  ordinary 
methods  of  solving  equations. 

14.  Example. — As  an  illustration,  suppose  that  we  require 
the  equation  of  condition  which  shall  express  the  relation  be- 
tween the  number  of  revolutions  and  the  pressure  expressed 
in  inches  of  water,  of  a  pressure-blower  delivering  air  into  a 
closed  pipe.  Let  m  represent  the  reading  of  the  water-column, 
and  n  the  corresponding  number  of  revolutions.  Suppose 
that  the  observations  give 

for  m  =  24  inches,    n  =  297  revolutions  • 
"   m  =  32      "         n  =  340          " 

"   "*  =  33      "         »  =  355         " 
«    m  =  35      "         n  =  376 

Average  values  for  m  =  31  inches,  n  —  342  revolutions. 
Arranging  the  results  in  the  following  form,  we  have : 


Water-column. 

Revolutions. 

Observations. 

Residuals. 

Observations. 

Residuals. 

24 
32 
33 
35 

il 

+  4 

297 

340 
355 
376 

-45 
—     2 

+  13 

+  34 

Assume  that  the  equation  of  condition  is  of  the  form 


EXPERIMENTAL  ENGINEERING. 


[§'4- 


To  find  those  values  of  A,  B,  and  C  which  will  most 
nearly  satisfy  the  equation,  as  shown  in  the  experiment: 
Taking  the  values  of  x,  as  the  residual  or  difference  between 
the  mean  and  any  observation  in  height  of  water-column,  and 
the  value  of  y  as  the  corresponding  residual  in  number  of 
revolutions,  we  have  the  following  equations  of  condition : 


=  -45, 
A+  £  +  C=-  2, 
A-\-2B-{-  4£7=  +  i3, 


Multiplying   each   equation   by  the   coefficient  of  A   in  that 
equation,  we  have 


A  —  7B  +  4gC  =  -45, 
A+  B  +  C=  -  2, 
A  +  2B+  46"=  +  13, 
48+  i6C  =  +  34. 


A 


II. 


Equations  of  minimum  condi- 
tion of  error  with  respect  to  A. 


4A  +0,5  +  706'=          o.    III.  Sum  of  equations  in  group  II. 

Multiplying  each  equation  in  group  I  by  the  coefficient  of 
B  in  that  equation,  we  have 


A+ 
2A+  4B+ 


=      315 
C=-      2 

C  =        26 
=       136 


Equations    of    minimum 
>-  IV.     condition  of  error  with 
respect  to  B. 


oA  +  708  —  2JQC  =      475      Sum  of  equations  in  group  IV. 

Multiplying  each  equation  in  group  I  by  the  Coefficient  of 
C  in  that  equation,  we  have 


Equations  of    minimum 
-  V.     condition  of  error  with 
respect  to  C. 


—  343^  +  2401 C  =  —  2205 
A+       £+         C=-       2 
4A+     SB+      i6C=          52 
64^+   256(7=        544 


70A  —  26SB  +  2674(7  =  —  161 1      Sum  of  equations  in  group  V. 


§  I5-J     APPLICATION  OF  METHOD   OF  LEAST  SQUARES.       1 5 

The  sums  of  these  various  equations  of  minimum  condition  are 
the  same  in  number  as  the  unknown  quantities,  and  by  com- 
bining  them  the  various  values  of  A,  B,  C,  etc.,  can  be  deter- 
mined. We  have,  in  the  following  case : 


4A  + 

oA  +   7oB  -    2706"  =        475  \  VI. 
70^4  -  268£  +  2674(7  =  —  161 1  ) 

Solving  the  above, 

A  =  1.608 ;        B  =  7.140 ;        C  =  —  0.0919. 
Substituting  in  the  original  equation  of  condition, 
y  =  1. 608  +  7.140*  —  0.09 1 9*a. 

To  reduce  this  form  to  an  equation  expressing  the  probable 
relation  of  the  number  of  revolutions  to  the  height  of  the  water- 
column,  we  must  substitute  for  y  its  value,  n  —  342 ;  and  for  x 
its  value,  m  —  31.  In  this  case  we  shall  have 

*  -  342  =  i .608  +  7-i40»  -  31)  -  0.0919(02  -  3i)a; 

which  reduced  gives  the  following  equation  as  the  most  proba- 
ble value  in  accordance  with  the  observations : 

n  =  34.952  -f-  13.0202  —  0.091902*; 

which  is  the  empirical  equation  sought. 

15.  Rules  and  Formulae  for  Approximate  Calculation. — 

When  in  a  mathematical  expression  some  numbers  occur  which 
are  very  small  with  respect  to  certain  other  numbers,  and  which 
are  therefore  reckoned  as  corrections,  they  may  often  be  ex 
pressed  with  sufficient  accuracy  by  an  approximate  formula, 
which  will  largely  reduce  the  labor  of  computation. 


1 6  EXPERIMENTAL  ENGINEERING.  [§  !  5- 

On  the  principle  that  the  higher  powers  of  very  small  quan- 
tities may  be  neglected  with  reference  to  the  numbers  them- 
selves, we  can  form  a  series  by  expansion  by  the  binomial 
formula,  or  by  division,  in  which,  if  we  neglect  the  higher 
powers  of  the  smaller  quantities,  the  resulting  formulae  become 
much  more  simple,  and  are  usually  of  sufficient  accuracy. 

Thus,  for  instance,  let  d  equal  a  very  small  fraction  ;  then 
the  expression 

(a  +  S)m  =  am-{-  mam-ld  4-  nr     ~  l^am~1d2  -f  etc., 

will  become  am  +  mam~*8,  if  the  higher  powers  of  d  be  neglected. 
If  d  is  equal  to  y^Vir  Part  °f  ^>  tne  error  which  results  from 
omitting  the  remaining  terms  of  the  series  becomes  very 
small,  as  in  this  case  the  value  of  tf2  =  -Y-Q-Q-Q-Q-Q^M' 

The  following  table  of  approximate  formulae  presents  several 
cases  which  can  often  be  applied  with  the  effect  of  materially 
reducing  the  work  of  computation,  without  any  sensible  effect 
on  the  accuracy : 

I  +  mdt         (l-6)m=l-md;      .     .    .     .     (12) 


(i  +  tf)3  =1  +  3*,       (i-tf)3  =1-3*; (15) 

_L_     TS^         _L_     =I  +  d; (I6) 

l-2*>       n~r*v  =  I  +  ^;  •   ....   (17) 


(19) 
(20) 


I  1 6.]        APPLICATION  OF  METHOD   OF  LEAST  SQUARES.    I/ 
(I  ±  <?)(!  ±  C)  -  _ 


±  e)(l  ± 


(22) 


sin  (>  +  d)  =  sin  ^r  -J-  d  cos  # ; (24) 

cos  (x  -f-  <?)  =  cos  x — tfsin^;; .    (25) 

d 

tan  (#  +  #)  =  tan  #  + -^5-^  =  tan  * -f  #  see9  # ;     .    .    (26) 

sin  (#  —  #)  =  sin  x  —  3  cos  ^r ; (27) 

cos  (^r  —  <J)  =  cos  x  +  tf  sin  x. (28) 

16.  The  Rejection  of  Doubtful  Observations.* — It  often 
happens  that  in  a  set  of  observations  there  are  certain  values 
which  are  so  much  at  variance  with  the  majority  that  the  ob- 
server rejects  them  in  adjusting  the  results.  This  might  be 
done  by  application  of  Rule  3,  Article  7,  provided  the  magni- 
tude of  the  errors  which  could  not  occur  were  definitely  deter- 
mined ;  but  to  reject  such  observations  without  proper  rules  is 
a  dangerous  practice,  and  not  to  be  recommended. 

This  brings  into  sight  a  class  of  errors  which  we  may  term 
mistakes,  and  which  are  in  no  sense  errors  of  observation,  such 
as  we  have  been  considering.  Mistakes  may  result  from  vari- 
ous causes,  as  a  misunderstanding  of  the  readings,  or  from  re- 
cording the  wrong  numbers,  inverting  the  numbers,  etc. ;  and 
when  it  is  certainly  shown  that  a  mistake  has  occurred,  if  it 
cannot  be  corrected  with  certainty,  the  observations  should 
be  rejected.  After  making  allowance  for  all  constant  errors,  no 
results  except  those  which  are  unquestionably  mistakes  should  be 
rejected. 

The  remaining  discrepancies  will  then  fall  under  the  head 

*  See  Adjustment  of  Observations,  by  T.   W.   Wright.      N.  Y.,   D.  Van 
Nostrand. 


1 8  EXPERIMENTAL  ENGINEERING.  [§  17- 

of  irregular  or  accidental  errors,  and  are  to  be  corrected  as  ex- 
plained in  the  preceding  articles ;  the  effect  of  a  large  error  is 
largely  or  wholly  compensated  for  by  the  greater  frequency  of 
the  smaller  errors. 

17.  When  to  Neglect  Errors. — Nearly  all  the  observa- 
tions taken  on  any  experimental  work  are  combined  with 
observations  of  some  other  quantity  in  order  to  obtain  the 
desired  result.  Thus,  for  example,  in  the  test  of  a  steam- 
engine,  observations  of  the  number  of  revolutions  and  of  the 
mean  effective  pressure  acting  on  the  piston  are  combined  with 
the  constants  giving  the  length  of  stroke  and  area  of  piston. 
The  product  of  these  various  quantities  gives  the  work  done 
per  unit  of  time. 

All  of  these  quantities  are  subject  to  correction,  and  it  is 
often  important  to  allow  for  such  correction  in  the  result.  Just 
how  important  these  corrections  may  be  depends  on  the  degree 
of  accuracy  which  is  sought. 

As  the  degree  of  accuracy  increases,  the  number  of  influenc- 
ing circumstances  increases  as  well  as  the  difficulty  of  eliminat- 
ing them  ;  hence  this  part  of  the  work  is  often  the  most  difficult 
and  sometimes  the  most  important.  To  what  limit  these  cor- 
rections may  be  carried  depends  on  our  knowledge  of  the  laws 
which  govern  the  experiments  in  question,  as  well  as  the 
accuracy  with  which  the  observations  may  be  taken.  It  is 
evidently  unnecessary  to  correct  by  abstruse  and  difficult  cal- 
culation for  influences  which  make  less  difference  than  the 
least  possible  unit  to  be  determined  by  observation,  and  this 
consideration  should  no  doubt  determine  whether  or  not  correc- 
tions should  be  taken  into  account  or  neglected. 

Thus,  in  the  case  of  the  test  of  a  steam-engine,  we  have 
errors  made  in  obtaining  the  engine  constants,  i.e.,  length  of 
stroke  and  area  of  piston.  These  errors  may  be  simply  of 
measurement,  or  they  may  be  due  to  changes  in  the  tempera- 
ture of  the  body  measured.  The  errors  of  measurement  depend 
on  accuracy  of  the  scale  used,  care  with  which  the  observations 
are  made,  and  can  be  discussed  as  direct  observations  on  a  single 
quantity.  The  errors  due  to  change  of  temperature  can  be  cal- 


§  IS.]        APPLICATION  OF  METHOD   OF  LEAST  SQUARES.  '19 

culated  if  observations  showing  the  temperature  are  taken,  an<? 
if  the  coefficient  of  expansion  is  known.  A  calculation  will,  in 
case  of  the  steam-engine  constants  referred  to  above,  show  that 
in  general  the  probable  error  of  observation  is  many  times  in 
excess  of  any  change  due  to  expansion,  and  hence  the  latter 
may  be  neglected.  The  effect  of  errors  in  the  other  quantities 
has  already  been  discussed  in  Article  II. 

It  is  to  be  remembered  that  the  method  of  correction 
outlined  in  the  "  Method  of  Least  Squares"  applies  only  to 
those  accidental  and  irregular  errors  which  cannot  be  directly 
accounted  for  by  any  imperfection  in  instruments  or  peculiar 
habit  of  the  observer;  usually  the  correction  for  instrumental 
and  personal  errors  is  to  be  made  to  the  observations  them- 
selves,  before  computing  the  probable  error. 

18.  Accuracy  of  Numerical  Calculations. — The  results  of 
all  experiments  are  expressed  in  figures  which  show  at  best 
only  an  approximation  to  the  truth,  and  this  accuracy  of  ex- 
pression is  increased  by  extending  the  number  of  decimal  figures. 
It  is,  however,  evidently  true  that  the  mere  statement  of  an  ex- 
periment, with  the  results  expressed  in  figures  of  many  decimal 
places,  does  not  of  necessity  indicate  accurate  or  reliable  ex- 
periments. The  accuracy  depends  not  on  the  number  oi 
decimal  places  in  the  result,  but  on  the  least  errors  made  in 
the  observations  themselves. 

It  is  generally  well  to  keep  to  the  rule  that  the  result  is  to 
be  brought  out  to  one  more  place  than  the  errors  of  observa- 
tion would  indicate  as  accurate :  that  is,  the  last  decimal  place 
should  make  no  pretensions  of  accuracy;  the  one  preceding 
should  be  pretty  nearly  accurate.  In  doubtful  cases  have  one 
place  too  many  rather  than  too  few.  No  mistake,  however, 
should  be  made  in  the  numerical  calculations ;  and  these,  to 
insure  accuracy,  should  be  carried  for  one  place  more  than  is 
to  be  given  in  the  result,  otherwise  an  error  may  be  made  that 
will  affect  the  last  figure  in  the  result.  The  extra  place  is  dis. 
carded  if  less  than  5  ;  but  if  5  or  more  it  is  considered  as  10,  and 
the  extra  place  but  one  increased  by  I. 

In  performing  numerical   calculations,  it  will   be   entirely 


20  EXPERIMENTAL  ENGINEERING.  [§  T9- 

unnecessary  to  attempt  greater  accuracy  of  computation  than 
can  be  carried  out  by  a  four-place  table  of  logarithms,  except  in 
cases  where  the  units  of  measurement  are  very  small  and  the 
numbers  correspondingly  great.  In  general,  sufficient  accuracy 
can  be  secured  by  the  use  of  the  pocket  slide-rule,  the  readings 
of  which  are  hardly  as  accurate  as  a  three-place  table  of  loga- 
rithms. The  slide-rule  will  be  found  of  great  convenience  in 
facilitating  numerical  computations,  and  its  use  is  earnestly 
advised. 

19.  Methods  of  representing  Experiments  Graphically. 
—Nearly  all  experiments  are  undertaken  for  the  purpose  of 
ascertaining  the  relation  that  one  variable  condition  bears  to 
another,  or  to  the  result.  All  such  experiments  can  be  repre- 
sented graphically  by  using  paper  divided  into  squares.  The 
result  of  the  experiment  is  represented  by  a  curve,  drawn  as 
follows:  Lay  off  in  a  horizontal  direction,  using  one  or  more 
squares  as  a  scale,  distances  corresponding  with  the  record  values 
of  one  of  the  various  observations,  and  in  a  similar  manner, 
using  any  convenient  scale,  lay  off,  in  a  vertical  direction  from 
the  points  already  fixed,  distances  proportional  to  the  results 
obtained.  A  line  connecting  these  various  points  often  will  be 
more  or  less  irregular,  but  will  represent  by  its  direction  the 
relation  of  the  results  to  any  one  class  or  set  of  observations. 
A  connecting  line  may  form  a  smooth  curve,  but  if,  as  is  usually 
the  case,  the  line  is  irregular  and  broken,  a  smooth  curve  should 
be  drawn  in  a  position  representing  the  average  value  of  the  ob- 
servations. The  points  of  observation,  located  on  the  squared 
paper  as  described,  should  be  distinctly  marked  by  a  cross,  or  a 
point  surrounded  with  a  circle,  triangle,  or  square;  and  farther, 
all  observations  of  the  same  class  should  be  denoted  by  the  same 
mark;  so  that  the  relation  of  the  curve  to  the  observations  can 
be  perceived  at  any  time. 

The  value  of  the  graphical  method  over  the  numerical  one 
depends  largely  on  the  well-known  fact  that  the  mind  is  more 
sensitive  to  form,  as  perceived  by  the  eye,  than  to  large  num- 
bers obtained  by  computation.  Indeed,  when  numbers  are 


§  21.]     APPLICATION  OF  METHOD   OF  LEAST  SQUARES.       21 

used,  the  averages  of  a  series  of  observations  are  all  that  can 
be  considered,  and  the  effect  of  a  gradual  change,  and  the 
relation  of  that  change  to  the  result,  which  is  often  more  im- 
portant than  any  numerical  determination,  is  entirely  disre- 
garded, and  often  not  perceived. 

Every  experiment  should  be  expressed  graphically,  and  stu- 
dents should  become  expert  in  interpreting  the  various  curves 
produced.  A  sample  of  paper  well  suited  for  representing 
experiments  is  bound  in  the  back  portion  of  the  present  work. 

All  important  tests  should  also  be  accompanied  by  a 
graphical  log ;  in  this  case  time  is  taken  as  the  abscissa,  and  the 
various  observations  corresponding  to  the  time  are  plotted  at 
convenient  heights.  The  variation  of  these  quantities  from  a 
horizontal  line  shows  in  a  striking  way  irregularities  which 
occur  during  the  test,  a  horizontal  line  indicating  uniform  con- 
ditions. 

20.  Area  of  the  Diagram  represents   Work  "done.— 
In  case  the  horizontal  distances  or  abscissae  represent  space 
passed  through,  and  the  vertical  distances  or  ordinates  represent 
the  force  acting,  then  will  the  area  included  between  this  curve 
and  the  initial  lines,  represent  the  product  of  the  mean  force 
into  the  space  passed  through, — or,  in  other  words,  the  work 
done.     The    units  in  which  the  work  will  be  expressed  will 
depend  on  the  scales  adopted.     If  the  unit  of  space  represent 
feet,  the  unit  of  force  pounds,  the  results  will  be  in  foot-pounds. 
The  initial  lines  in  each  case  must  be  drawn  at  distances  corre- 
sponding to  the  scales  adopted,  and  must  represent,  respectively, 
zero-force  and  zero-space. 

21.  Autographic  Diagrams. — In  various  instruments  used 
in  testing,  a  diagram  is  drawn  automatically,  in  which  the  ab- 
scissa corresponds  to  the  space  passed  through,  the  ordinate 
to    the   force   exerted,  and   the  area  to  the  work   done.     A 
familiar  illustration  is  the  steam-engine  indicator-diagram,  in 
which   horizontal  distance  corresponds  to  the  stroke  of   the 
piston  of  the  engine,  and  vertical  distance  or  ordinates  to  the 
pressure   acting   on   the   piston    at  any  point.     The  absolute 
amount  of  the  pressures  may  be  determined  by  reference  to  the 


22  EXPERIMENTAL   ENGINEERING.  [§  22. 

atmospheric  line.  The  distance  vertically  between  the  lines 
drawn  on  the  forward  and  back  strokes  of  the  engine  is  the 
effective  pressure  acting  on  the  piston  at  the  given  position  of 
its  stroke ;  the  mean  length  of  all  such  lines  is  the  mean 
effective  pressure  utilized  in  work.  The  vertical  distance  from 
any  point  on  the  atmospheric  line  to  the  curve  drawn  while  the 
piston  is  on  its  forward  stroke  is  the  forward  pressure,  the 
corresponding  distance  to  the  back-pressure  line  is  the  back 
pressure,  and  the  areas  between  these  respective  curves  give 
effective  or  total  work  per  revolution. 

An  autographic  device  is  put  on  many  testing-machines  :  in 
this  case  the  ordinates  of  the  diagram  drawn  represent  pres- 
sure applied  to  the  test  specimen,  and  abscissae  represent  the 
stretch  of  the  specimen.  This  latter  corresponds  to  the  space 
passed  through  by  the  force,  so  that  the  area  of  the  diagram 
included  between  the  curve  and  line  of  no  pressure  represents 
the  work  done, — at  least  so  far  as  the  resistance  of  the  test- 
piece  is  equal  to  the  pull  exerted,  which  is  the  case  within  the 
elastic  limit  only. 

Various  dynamometers  construct  autographic  diagrams,  in 
which  ordinates  are  proportional  to  the  force  exerted  and  ab- 
scissae to  the  space  passed  through,  so  that  the  area  is  propor- 
tional to  the  work  done.  The  diagram  so  drawn  would  repre- 
sent the  work  done  equally  well  were  ordinates  proportional 
to  space  passed  through,  and  abscissae  to  the  force  exerted,  but 
such  diagrams  are  not  often  used. 

22.  Reduction  of  Diagrams. — In  the  reduction  of  auto- 
graphic diagrams  the  process  is  reversed  as  compared  with  the 
construction  of  the  diagram.  The  important  data  required  are, 
first,  the  position  of  initial  lines  of  force  and  of  space ;  second, 
the  respective  scales  of  force  and  of  space.  In  computing  the 
work,  it  is  usually  customary  to  find  the  mean  pressure  from 
the  diagram,  and  multiply  this  result  by  the  space  through 
which  the  body  actually  moves,  instead  of  multiplying  by  the 
length  of  the  diagram. 

To  find  the  length  of  the  mean  ordinate,  from  which  the 
mean  pressure  is  easily  obtained,  vertical  lines  are  drawn  so 


§  22.]     APPLICATION   OF  METHOD    OF  LEAST  SQUARES.       2$ 

close  together  that  the  portion  of  the  curve  included  between 
them  is  sensibly  straight ;  the  sum  of  these  lines,  which  may 
be  expeditiously  taken  by  transferring  them  successively  to  a 
strip  of  paper  and  measuring  the  total  length,  is  found ;  and 
this  result  divided  by  the  number  gives  the  length  of  the  mean 
ordinate.  This  length  multiplied  by  the  scale  gives  the  pres- 
sure. An  integrating  instrument,  the  planimeter,  is  more 
frequently  used  for  this  purpose,  and  gives  more  accurate 
results.  The  theory  of  the  instrument  and  method  of  using  is 
of  great  importance  to  engineers,  and  is  given  in  full  in.  the 
following  chapter. 

Logarithmic  Cross-section  Paper  is  very  convenient  for 
the  reduction  of  certain  forms  of  curves  to  algebraic  or 
analytic  equations.  The  rulings  of  this  paper  are  made  at 
distances  proportional  to  the  logarithms  of  the  numbers  which 
represent  the  ordinates  and  abscissae.  Any  curve  which  may 
be  represented  by  a  simple  logarithmic  or  exponential  equa- 
tion would  be  represented  on  paper  ruled  in  this  way  by  a 
straight  line.  Thus,  an  equation  of  the  general  form  y  = 
Bxn  can  be  reduced  so  that  logy  =  log  B  +  n  log  x,  which 
is  the  equation  of  a  straight  line  in  logirithmic  units.  In 
this  equation  n  is  the  tangent  of  the  angle  which  the  line 
makes  with  the  axis  of  abscissae,  and  B  is  the  intercept  on  this 
axis  from  the  origin.  Paper  ruled  in  this  manner  can  be  ob- 
tained from  most  dealers  in  technical  supplies.  In  case  it 
cannot  be  obtained,  ordinary  cross-section  paper,  as  shown  in 
the  Appendix  to  this  book,  may  be  used  by  numbering  the 
graduations  on  the  axes  of  abscissae  and  ordinates  as  propor- 
tional to  the  logarithms  of  the  distances  from  the  origin. 


CHAPTER    II. 

APPARATUS  FOR  REDUCTION  OF   EXPERIMENTAL  DATA 
AND  FOR  ACCURATE  MEASUREMENT. 

23.The  Slide-rule. — The  slide-rule  is  made  in  several  forms, 
but  it  consists  in  every  case  of  a  sliding  scale,  in  which  the 
distance  between  the  divisions,  instead  of  corresponding  to  the 
numbers  marked  en  the  scale,  corresponds  to  the  logarithms  of 
these  numbers.  This  scale  can  be  made  to  slide  past  another 
logarithmic  scale,  so  that  by  placing  them  in  proper  positions 
there  may  be  shown  the  sum  or  difference  of  these  scales,  and 
the  number  corresponding.  As  these  scales  are  logarithmic,  the 
number  corresponding  to  the  sum  is  the  product,  that  corre- 
sponding to  the  difference  is  the  quotient.  Operations  involv- 
ing involution  and  evolution  can  also  be  performed.  Scales 
showing  the  logarithmic  functions  of  angles  are  also  usually 
supplied. 


FIG.  i.— THE  SLIDE-RULE. 

.  The  usual  form  of  the  slide-rule  is  shown  in  Fig.  I.  This 
form  carries  four  logarithmic  scales,  one  on  either  edge  of  the 
slide,  and  one  above  and  one  below.  Either  scale  can  be  used; 
that  above  is  generally  to  one  half  the  scale  of  the  lower,  and 
while  not  quite  as  accurate,  is  more  convenient  than  the  one 
below.  The  trigonometrical  scales  are  on  the  back  of  the  slide. 

24 


§24.]  APPARATUS.  2$ 

The  principal  use  to  the  computer  is  the  solution  of  problems 
in  multiplication  and  division. 

The  following  directions  for  use  of  the  plain  slide-rule, 
which  is  ordinarily  employed,  give  a  simple  practical  method 
of  multiplying  or  dividing  by  the  slide-rule,  experience 
having  shown  that  when  these  processes  are  fully  understood 
the  others  are  mastered  without  instruction. 

Suppose  that  a  student  has  a  slide-rule  of  the  straight  kind, 
and  similar  to  the  one  in  Fig.  I,  which  consists  of  a  stationary 
scale,  a  sliding-scale,  and  a  sliding  pointer  or  runner.  These 
parts  we  will  term,  respectively,  the  "  scale,"  the  slide,  and  the 
runner. 

24.  Directions  for  using  the  Slide-rule. — Holding  the 
rule  so  that  the  figures  are  right  side  up,  four  graduated  edges 
will  be  seen,  of  which  only  the  upper  two  are  used  in  the 
problem  we  are  about  to  describe.  (The  method  of  using  the 
two  lower  scales  would  be  exactly  the  same,  the  difference 
being,  that  they  are  twice  as  long,  and  that  the  slide  is  above 
instead  of  below  the  scale.) 

Move  the  slide  to  such  a  position  that  the  graduations 
agree  throughout  the  length  of  the  scale,  and  place  the  runner 
at  a  division  marked  I,  and  the  rule  is  ready  for  use.  Arrange 
the  factors  to  be  dealt  with  in  the  form  of  a  fraction,  with  one 
more  factor  in  numerator  than  in  denominator,  units  being  in- 
troduced if  necessary  to  make  up  deficiencies  in  the  factors. 

Thus,  to  multiply  6  by  7  by  3  and  divide  by  8  times  2, 
arrange  the  factors  as  follows  : 

6X7X3 
8X2 

The  factors  in  the  numerator  show  the  successive  positions 
which  the  runner  must  take ;  those  in  the  denominator  the 
positions  of  the  slide.  Thus,  to  solve  above  example,  start  (i) 
with  runner  at  6  on  the  scale,  always  reading  from  same  side  of 
runner ;  (2)  bring  figure  8  on  slide  to  runner ;  (3)  move  runner 
to  7  on  slide:  the  result  can  now  be  read  on  the  scale;  (4) 


26  EXPERIMENTAL  ENGINEERING.  [§  24. 

bring  2  on  slide  to  runner ;  (5)  move  runner  to  3  on  slide.  The 
result  is  read  directly  on  the  scale  at  position  of  runner. 

Another  example  :  Multiply  11  by  6  by  7  by  8,  and  divide 

by  31- 

In  this  case  arrange  the  factors 

j 

ii  X  6  X  7  X  8 

i  X  i  X  31 

Start  with  runner  at  1 1  on  scale,  move  I  on  slide  to  runner,- 
move  runner  to  6  on  slide,  move  I  on  slide  to  runner,  runner 
to  7  on  slide,  move  31  on  slide  to  runner,  runner  to  8  on  slide: 
read  result  on  scale  at  runner. 

The  numbers  on  the  slide-rule  are  to  be  considered  signifi- 
cant figures,  and  to  be  used  without  regard  to  the  decimal 
point.  Thus  the  number  on  the  rule  for  8  is  to  be  used  as  .8 
or  80  or  800,  as  may  be  desired,  even  in  the  same  problem. 
The  significant  figures  in  the  result  are  readily  determined  by 
a  rough  computation.  In  case  the  slide  projects  so  much 
beyond  the  scale,  that  the  runner  cannot  be  set  at  the  required 
figure  on  the  slide,  bring  the  runner  to  I  on  the  slide,  then 
move  the  slide  its  full  length,  until  the  other  I  comes  under 
the  runner.  Then  proceed  according  to  directions  above ;  i.e., 
move  runner  to  number  on  slide,  and  read  results  on  the  scale  : 


6  X  25  x  3-5  X  7  X  7  X  31  _? 
n  X  426  X  9H  X  i  X  i 


Begin  with  the  first  factor  in  the  numerator,  and  multiply 
and  divide  alternately,  — 

X  6,     -T-  7t,     X  25,     -^  426,     X  3-5>     -*-  9i4>     etc.,— 

until  all  the  factors  have  been  used,  checking  them  off  as  they 
are  used,  to  guard  against  skipping  any  or  using  one  twice. 


§24.]  APPARATUS.  2/ 

To  multiply,  move  the  runner;  to  divide,  move  the  slide:  in 
either  case  see  that  the  runner  points  to  a  graduation  on  the 
slide  corresponding  to  the  factor.  The  result  at  the  end  or  at 
any  stage  of  the  process  is  given  by  the  runner  on  the  station- 
ary scale.  Or,  to  be  more  exact,  the  significant  figures  of  the 
result  are  given,  for  in  no  case  does  the  slide-rule  show  where 
to  place  the  decimal  point.  If  the  decimal  point  cannot  be 
located  by  inspection  of  the  factors,  make  a  rough  cancel- 
lation. 

Involution  and  evolution  are  readily  mastered  by 
simple  practice.  Slide-rules  working  on  the  same  prin- 
ciple are  frequently  made  with  circular  or  cylindrical  scales, 
which  in  the  Thacher  and  Fuller  instruments  are  of  great 
length. 

Thacher's  calculating  instrument  consists  of  a  cylinder  4 
inches  in  diameter  and  18  inches  long,  working  within  a  frame- 
work of  triangular  bars.  Both  the  cylinders  and  bars  are  grad- 


FIG.  2. — THACHER'S  CALCULATING  INSTRUMENT. 

uated  with  a  double  set  of  logarithmic  scales,  and  results  in 
multiplication  or  division  can  be  obtained  from  one  setting  of 
the  instrument,  hence  it  is  especially  convenient  when  a  series 
of  numbers  are  to  be  multiplied  by  a  common  factor.  The 
scales  in  this  instrument  are  about  50  feet  in  length,  and  results 
can  be  read  usually  to  five  places. 

The  instrument  is  similar  to  the  straight  slide-rule  previously 
described,  the  scale  on  the  triangular  bars  corresponding  to  the 
stationary  scale,  that  on  the  cylinder  to  the  sliding  scale,  and  a 
triangular  index  /  to  the  sliding  pointer  or  runner.  The  method 
of  using  is  essentially  similar  to  that  of  the  plain  slide-rule  ; 


28 


EXPERIMEN TA  L   ENGINEERING. 


[ 


thus,  to  solve  an  example  of  the  form  a/b,  put  the  runner  /  on 
the  triangular  scale  at  the  number  corresponding  to  a,  bring 
the  number  corresponding  to  b  on  the  cylindrical  scale  to 
register  with  a  on  the  triangular  scale ;  the  respective  numbers 
on  the  trianglar  scale  and  cylinder  will  in  this  position  all  be  in 
the  ratio  of  a  to  b\  and  the  quotient  will  be  read  by  noting  that 
number  on  the  triangular  scale  which  registers  with  I  on  the 
cylindrical  scale.  The  product  of  this  quotient  by  any  other 
number  will  be  obtained  by  reading  the  number  on  the  trian- 
gular scale  registering  with  the  required  multiplier  on  the  cylin- 
drical scale. 

Fuller's  slide-rule  consists  of  a  cylinder  C  which  can  be 
moved  up  or  down  and  turned  around  a  sleeve  which  is  attached 
to  the  handle  H.  A  single  logarithmic  scale,  42  feet  in  length, 


FIG.  3. — THE  FULLER  SLIDE-RULE. 

is  graduated  around  the  cylinder  spirally,  and  the  readings  are 
obtained  by  means  of  two  pointers  or  indices,  one  of  which,  A, 
is  attached  to  the  handle,  and  the  other,  B,  to  an  axis  which 
slides  in  the  sleeve.  This  instrument  is  not  well  adapted  for 
multiplying  or  dividing  a  series  of  numbers  by  a  constant,  since 
the  cylinder  must  be  moved  for  every  result.  The  instrument 
is,  however,  very  convenient  for  ordinary  mathematical  com- 
putations, and  the  results  may  be  read  accurately  to  four  deci- 
mal places. 

The  method  of  using  the  instrument  is  as  follows  :  Call  the 
pointer^,  fixed  to  the  handle,  \hz  fixed  pointer,  the  other  BB' , 
which  may  be  moved  independently  as  the  movable  index. 
To  use  the  instrument,  as  for  example  in  performing  the  oper- 
ation indicated  by  (a  X  b)  -f-  c,  set  the  fixed  pointer  A  to  the 
first  number  in  the  numerator,  then  bring  the  movable  index 


§25.]  APPARATUS.  29 

B  to  the  first  figure  in  the  denominator ;  then  move  the  cy« 
linder  C  until  the  second  figure  in  the  numerator  appears  under 
the  movable  index,  finally  read  the  answer  on  the  cylinder  C 
underneath  the  fixed  pointer  A. 

In  general,  to  divide  with  this  instrument  move  the  index 
B\  to  multiply,  move  the  cylinder  C\  read  results  under  the 
fixed  pointer  A.  The  movable  index  BB'  has  two  marks, 
one  at  the  middle,  the  other  near  the  end  of  the  pointer,  either 
of  which  may  be  used  for  reading,  as  convenient,  their  distance 
apart  corresponding  to  the  entire  length  of  the  scale  on  the 
cylinder  C. 

25.  The  Vernier. — The  vernier  is  used  to  obtain  finer  sub- 
divisions than  is  possible  by  directly  dividing  the  main  scale, 
which  in  this  discussion  we  will  term  the  limb. 

The  vernier  is  a  scale  which  may  be  moved  with  reference 
to  the  main  scale  or  limb,  or,  vice  versa,  the  vernier  is  fixed 
and  the  limb  made  to  move  past  it. 

The  vernier  has  usually  one  more  subdivision  for  the  same 
distance  than  the  limb,  but  it  may  have  one  less.  The 
theory  of  the  vernier  is  readily  perceived  by  the  following 
discussion.  Let  d  equal  the  value  of  the  least  subdivision 
of  the  limb;  let  n  equal  the  number  of  subdivisions  of 
the  vernier  which  are  equal  to  n  —  I  on  the  limb.  Then  the 

(72  j\ 
). 
;/     / 

The  difference  in  length  of  one  subdivision  on  the  limb  and 
one  on  the  vernier  is 


In  -  i\        d 

d  —  d\ )  =  -, 

\     n    i       n 


which  evidently  will  equal  the  least  reading  of  the  vernier,  and 
indicates  the  distance  to  be  moved  to  bring  the  first  line  of 
the  vernier  to  coincide  with  one  on  the  limb.  In  case  there  is 
one  more  subdivision  on  the  limb  than  on  the  vernier  for  the 
same  distance,  the  interval  between  the  graduations  on 'the 
vernier  is  greater  than  on  the  limb,  and  the  vernier  must  be 


30  EXPERIMENTAL   ENGINEERING.  [§  26. 

behind  its  zero-point  with  reference  to  its  motion,  and  hence  is 
termed  retrograde.     The  formula  for  this  case,  using  the  same 

ifi  _j_  i  \  d 

notation  as  before,  gives  d\ — — j  —d=-ior  the  least  reading. 

The  following  method  will  enable  one  to  readily  read  any 
vernier:  i.  Find  the  value  of  the  least  subdivision  of  the  limb. 
2.  Find  the  number  of  divisions  of  the  vernier  which  corre- 
sponds to  a  number  one  less  or  one  greater  than  that  on  the 
limb:  the  quotient  obtained  by  dividing  the  least  subdivision 
of  the  limb  by  this  number  is  the  value  of  the  least  reading  of 
the  vernier.  The  following  rules  for  reading  should  be  care- 
fully observed : 

Firstly.  Read  the  last  subdivision  of  the  limb  passed  over  by 
the  zero  of  the  vernier  on  the  scale  of  the  limb  as  the  reading  of 
the  limb. 

Secondly.  Look  along  the  vernier  until  a  line  is  found  which 
coincides  with  some  line  on  the  limb.  Read  the  number  of  this 
line  from  the  scale  of  the  vernier.  This  number  multiplied  by 
the  least  reading  of  the  vernier  is  the  reading  of  the  vernier. 

Thirdly.  The  sum  of  these  readings  is  the  one  sought. 

Thus,  in  Fig.  5,  page  31,  (i)  the  reading  of  the  limb  hs  4.70 
-at  a;  (2)  that  of  the  vernier  is  0.03  ;  (3)  the  sum  is  4.73. 

26.  The  Polar  Planimeter. — The  planimeter  is  an  instru- 
ment for  evaluating  the  areas  of  irregular  figures,  and  in  some 
one  of  its  numerous  forms  is  extensively  used  for  rinding  the 
areas  of  indicator  and  dynamometer  diagrams. 

The  principal  instrument  now  in  use  for  this  purpose  was 
invented  by  Amskr  and  exhibited  at  the  Paris  Exposition  in 
1867.  This  form  is  now  generally  known  as  Amsler's  Polar 
Planimeter;  as  most  of  the  other  instruments  are  modifications 
of  this  one,  it  is  important  that  it  be  thoroughly  understood. 

The  general  appearance  of  the  instrument  is  shown  in  Fig. 
4,  from  which  it  is  seen  that  it  consists  of  two  simple  arms  PK 
and  FK,  pivoted  together  at  the  point  K.  The  arm  PAT  during 
-use  is  free  to  rotate  around  the  point  P9  and  is  held  in  place  by 
a  weight.  The  arm  KF  carries  at  one  end  a  tracing-point, 
which  is  passed  around  the  borders  of  the  area  to  be  integrated 


§26.] 


APPARA  TUS. 


It  also  carries  a  wheel,  whose  axis  is  in  the  same  vertical  plane 
with  the  arm  KF,  and  which  may  be  located  indifferently  be- 
tween AT  and  F,  or  in  KF  produced.  It  is  usually  located  in  KFy 
produced  as  at  D.  The  rim  of  this  wheel  is  in  contact  with 
the  paper,  and  any  motion  of  the  arm,  except  in  the  direction 
of  its  axis,  will  cause  it  to  revolve.  A  graduated  scale  with  a 
vernier  denotes  the  amount  of  lineal  travel  of  its  circumference. 
This  wheel  is  termed  the  record-wheel. 


FIG.  4.— AMSLER'S  POLAR  PLANIMETER. 


The  detailed  construction  of  the  record-wheel,  and  the  ar- 
rangement of  the  counter  G,  showing  the  number  of  revolutions, 


FIG.  5.— THE  RECORD-WHEEL.    AMSLER'S  POLAR  PLANIMBTER. 

is  shown  in  Fig.  5.  The  wheel  D  is  subdivided  into  a  given 
number  of  parts,  usually  TOO  ;  the  value  of  one  of  these  parts  is 
to  be  obtained  by  dividing  the  circumference  of  the  rim  of  the 
wheel  which  is  in  contact  with  the  paper  by  the  number  of 


32  EXPERIMENTAL  ENGINEERING.  [§  27- 

divisions.  This  result  will  give  the  value  of  the  least  division  on 
the  limb;  this  is  subdivided  by  an  attached  vernier,  in  this  par- 
ticular case  to  tenths  of  the  reading  of  the  limb,  so  that  the  least 
reading  of  the  vernier  is  one  thousandth  of  that  of  one  revolution. 

27.  Theory  of  the  Instrument.  (See  Fig.  9.) — The  Zero- 
circle. — If  the  two  arms  be  clamped  so  that  the  plane  of  the  record- 
wheel  intersects  the  centre  P,  and  be  revolved  around  P,  the 
graduated  circle  will  be  continually  travelling  in  the  direction  of 
its  axis,  and  will  evidently  not  revolve.  A  circle  generated  under 
such  a  condition  around  P  as  a  centre  is  termed  the  zero-circle. 
If  the  instrument  be  undamped  and  the  tracing-point  be  moved 
around  an  area  in  the  direction  of  the  hands  of  a  watch  outside 
the  zero-circle,  the  registering  wheel  will  give  a  positive  record; 
while  if  it  be  moved  in  the  same  direction  around  an  area  inside 
the  zero- circle,  it  will  give  a  negative  record.  This  fact  makes  it 
necessary,  in  evaluating  areas  that  are  very  large  and  have  to  be 
measured  by  swinging  the  instrument  completely  around  P  as  a 
centre,  to  know  the  area  of  this  zero-circle,  which  must  be  added 
to  the  determination  given  by  the  instrument,  since  for  such  cases 
that  circumference  is  the  initial  point  for  measurement. 

Geometrical  and  Analytical  Demonstration. — If  a  straight  line 
mn  move  in  a  plane,  it  will  generate  an  area.  This  area  may  be 
considered  positive  or  negative  according  to  the  direction  of 
motion  of  the  line.  In  Fig.  6,  let  the  paths  of  the  ends  m  and  n 
of  the  line  be  the  perimeters  of  the  areas  A  and  B  respectively; 
then  it  is  at  once  apparent  that  the  net  area  generated  is  A  +  C  — 
C—B  or  A—  B.  The  immediate  corollary  to  this  is  that  if  the 
area  B  be  reduced  in  width  to  zero,  i.e.,  become  aline  along  which 
n  travels  back  and  forth,  the  area  swept  over  will  be  A,  around 
which  m  is  carried. 

Analyzing  a  differential  motion  of  the  line  from  mn  to  m'nf 
(Fig.  8),  it  may  be  broken  up  into  three  parts:  a  movement  per- 
pendicular to  the  line,  giving  area  ldp\  a  movement  in  the  direc- 
tion of  the  length  of  the  line,  giving  no  area;  and  a  movement 
of  rotation  about  one  end,  giving  as  area  %l2dd.  The  total  differ- 
ential of  area  is  then  dA=ldp  +  %l2d6.  I  is  always  a  constant 


§2/.]  APPARATUS.  33 

during  the  operation  of  a  planimeter,  so  that  A=fdA=lfdp  + 


The  common  use  of  a  planimeter  is  that  typified  in  Fig.  7, 
where  the  tracing-point  is  carried  around  the  area  to  be  meas- 
ured, while  the  other  end  of  the  tracing-arm  is  guided  back  and 
forth  along  some  line.  The  guide-line  is  usually  either  a  straight 
line  or  an  arc  of  a  circle.  When  the  tracing-point  has  returned 
to  its  initial  position  the  net  angle  turned  through  by  the  tracing- 

arm,  or  J  dd,  is  zero.  Hence  A  =  IJ  dp  simply.  But  J  dp  is 
the  net  distance  the  arm  has  moved  perpendicular  to  itself. 
Call  this  R,  and  there  results  the  equation  of  the  planimeter 
A=l-R. 


FIG.  6.  FIG.  7. 


If  the  polar  planimeter  is  so  used  as  to  bring  in  the  zero- circle, 
the  case  is  that  of  Fig.  6,  each  end  of  the  line  describing  an  area. 
The  tracing-arm  sweeps  over  the  difference  between  the  area 
described  by  T  (Fig.  9)  and  the  circle  made  by  G  about  P  as 
centre.  This  difference-area  is  not,  however,  recorded  by  the 

planimeter  because  the  J  dd  is  now  2n  instead  of  zero,  T  making 
a  complete  revolution  about  G.  The  linear  turning  of  the  edge 
of  the  recording- wheel  is  jdp  —  2nn,  where  n  is  the  distance  from 

guided  point  G  to  the  plane  of  the  wheel.  The  effect  on  the 
reading  is  the  same  as  if  the  radius  PG  were  increased.  The 


34  EXPERIMENTAL  ENGINEERING.  [§  2? 

zero-circle  is  traced  by  T  when  the  plane  of  W  passes  through 
P.     Then  fdp  =  2nn,  and  the  wheel  records  zero. 

In  practice  the  area  described  by  the  tracing-point  is  found 
by  adding  to  the  area  of  the  zero-circle  the  area  recorded  by  the 
wheel,  taking  account  of  the  algebraic  sign  of  the  latter. 


ap 


FIG.  8.  FIG.  9. 

The  following  demonstration  is  of  German  origin  and, 
although  less  general  in  its  nature,  is  retained  for  the  reason 
that  it  is  more  satisfactory  to  some  minds  than  the  one  given 
above. 

Movement  of  the  Record-wheel.  (Fig.  10.) — From  the  preced- 
ing discussion  it  is  seen  that  the  record-wheel  does  not  register, 
so  long  as  its  plane  is  radial,  or  so  long  as  angle  EDfF"  =  cp°. 
The  amount  of  rotation  due  to  variation  in  the  angle  EJD 
between  the  arms  is,  if  an  area  be  completely  circum- 
scribed, equal  in  opposite  directions,  and  hence  does  not 
affect  the  result,  so  that  it  is  necessary  to  discuss  merely  the 
case  of  motion  around  the  pole  E,  with  the  angle  EJD  fixed. 
Thus,  for  instance,  suppose  angle  EJD  to  remain  constant,  and 
the  tracing-point  to  swing  through  the  infinitesimal  angle  F"EF, 
designated  by  dd,  the  record-wheel  would  move  near  the  path 
DD'  more  or  less  irregularly,  but  subtending  an  equal  angle 
DED'.  The  component  of  this  motion  which  constitutes  the 
record  is  OD',  designated  by  dR,  which  is  the  projection  of 


§  2/.]  APPARATUS.  35; 

this  path  on  a  perpendicular  to  JF.     Since  DED'  is  infinitesi- 
mal, and  dB  —  tan  ^6>,  we  have 


DD'  =  DEdQ  ;     also     dR  =  OD'  =  DD'  cos  ED'D  ; 
but  ED'  D  =  £/?<9  from  similar  triangles.     Hence 
dR  =  ED  cos  EDOdQ. 

Denote  the  length  of  arm  EJ  by  m,  the  length  of  arm  JF  from 
pivot  to  tracing-point  by  /,  the  distance  JD  from  pivot  to  record- 
wheel  by  n,  the  angle  EJD  by  B.  Let  fall  a  perpendicular 
from  E  on  ^P/?,  or  FD  produced  at  O.  Then  we  have 


ED  cos  EDO  =  OD~JO  —  JD  = 
Hence 


dR  =  (m  cos  B  —  n)d()  .......     (i) 


Second,  the  infinitesimal  area  FtF"t  ',  /j/zVz^  adjacent  to  the 
zero-circle.  —  Let  EF  =  r,  let  EF"  =  r',  the  radius  of  the 
zero-circle.  Let  dA  =  the  area  sought.  Let  dO  =  FEt. 
Then 

area  FEt  =  £rV0, 
and 

area  F"£/' 
Then 


From  the  oblique  triangle 


36  EXPERIMENTAL   ENGINEERING. 

From  the  right  triangle  ED'F", 


[§  27- 


(4) 


Substituting  the  values  of  r2  and  r/2  in  equation  (2),  we  have 

dA  =  l(mcosB-  n)dd.  .     .....     (5) 

By  comparing  equation  (5),  the  differential  equation  for  the 
area,  with  equation  (i),  the  corresponding   equation  for  the 


FIG.  io. — POLAR  PLANIMETER. 


record,  we  see  that 


(6) 


dA  = 
or  by  integration  between  limits  o  and  R,  since  /  is  a  constant, 

A  =  IR (7) 

This   shows   that   the  area  is  equal  to  the  length  of  arm 
from  pivot  to  the  tracing-point ^  multipliea  by  the  space  registered 


§  28.]  APPARA  TUS.  37 

on  the  circumference  of  the  record-wheel,  and  is  independent  of 
the  other  dimensions  of  the  instrument. 

That  this  is  true  for  areas  not  adjacent  to  the  zero-circle, 
or  for  areas  partly  inside  and  out,  can  readily  be  proved  by 
subtracting  the  areas  between  the  zero-circle  and  the  given 
area,  or  by  a  similar  process.  Hence  the  demonstration  is 
general. 

The  Amsler  instrument  is  usually  constructed  so  that  the 
arm  /  is  adjustable  in  length,  and  consequently  it  may  be 
made  available  for  any  scale  or  for  various  units.  Gradua- 
tions are  engraved  on  the  arm  which  show  the  length  required 
to  give  a  record  in  a  given  scale  or  for  given  units. 

The  area  of  the  zero-circle  is  usually  engraved  on  the  top 
•of  the  arm  /.  In  case  it  is  not  given,  it  may  be  found  by 
evaluating  the  areas  of  two  circles  of  known  area,  each  greater 
than  the  area  of  the  zero-circle  nr'*.  Let  the  areas  of  such 
circles  be  respectively  C  and  C't  and  the  corresponding  read- 
ings of  the  record-wheel  R  and  R',  in  proper  units.  Then  we 
have 

C  =  nr'*  +  R  and  C  =  nr'*  +  R, 
from  which 

(8) 


Having  found  r'2,  we  can  compute  n,  since  r'a  =  m*  -f-  /2  -\-  2nlt 
and  m  and  /  can  both  be  obtained  from  measurement. 

28.  Forms  of  Polar  Planimeters.  —  Polar  planimeters  are 
made  in  two  forms  :  I.  With  the  pivot/,  Fig.  10,  fixed.  2.  With 
pivot  /  movable,  so  that  the  arm  /  between  pivot  and  tracing- 
point  may  be  varied  in  length.  Since  the  area  is  in  each  case 
equal  to  the  length  of  this  arm,  multiplied  by  the  lineal  space 
R  moved  through  by  the  record-wheel,  we  have  in  the  first 
case,  since  /  is  not  adjustable,  the  result  always  in  the  same 
unit,  as  square  inches  or  square  centimeters.  In  this  case  it  is 


38  EXPERIMENTAL  ENGINEERING.  2& 

customary  to  fix  the  circumference  of  the  record-wheel  and 
compute  the  arm  /  so  as  to  give  the  desired  units. 

For  example,  the  circumference  of  the  record-wheel  is 
assumed  as  equal  to  100  divisions,  each  one-fortieth  of  an  inch,, 
thus  giving  us  a  distance  of  2.5  inches  traversed  in  one  revolu- 
tion. The  diameter  corresponding  to  this  circumference  is 
0.796  inch,  which  is  equal  to  2.025  centimeters.  The  distance 
from  pivot  to  tracing-point  can  be  taken  any  convenient  dis- 
tance :  thus,  if  the  diameter  of  the  record-wheel  is  as  above,, 
and  the  length  of  the  arm  be  taken  as  4  inches,  the  area 
described  by  a  single  revolution  of  the  register-wheel  will  be 
2.5  x  4  =  10.0  square  inches. 

Since  there  were  100  divisions  in  the  wheel,  the  value  of 
one  of  these  would  be  in  this  case  o.i  square  inch.  This  would 
be  subdivided  by  the  attached  vernier  into  ten  parts,  giving  as 
the  least  reading  one  one-hundredth  of  a  square  inch.  By  mak- 
ing the  arm  larger  and  the  wheel  smaller,  readings  giving  the 
same  units  could  be  obtained. 

The  formula  expressing  this  reduction  is  as  follows :  Let  d 
equal  the  value  of  one  division  on  the  record-wheel ;  let  /  equal 
the  length  of  the  arm  from  pivot  to  tracing-point ;  let  A  equal 
the  area,  which  must  evidently  be  either  i,  10,  or  100  in  order 
that  the  value  of  the  readings  in  lineal  measures  on  the  record- 
wheel  shall  correspond  with  the  results  in  square  measures. 
Then  by  equation  (7)  we  shall  have,  supposing  100  divisions, 


100  dl=A\ (8) 


If  A  =  10  square  inches  and  d  =  -fa  inch, 


§  29.1  APPARA  TUB.  39 

If  -^  =  10  square  inches  and  d  =  -^  inch, 


The  length  of  the  arm  from  centre  to  the  pivot  has  no  effect 
on  the  result  unless  the  instrument  makes  a  complete  revolu- 
tion around  the  fixed  point  E,  in  which  case  the  area  of  the 
zero-circle  must  be  considered.  It  is  evident,  however,  that 
this  arm  must  be  taken  sufficiently  long  to  permit  free  motion 
•of  the  tracing-point  around  the  area  to  be  evaluated. 

The  second  class  of  instruments,  shown  in  Fig.  £L  are 
arranged  so  that  the  pivot  can  be  moved  to  any  desirea  posi- 
tion on  the  tracing-arm  KF,  or,  in  other  words,  the  length  can 
be  changed  to  give  readings  in  various  units.  The  effect  of 
such  a  change  will  be  readily  understood  from  the  preceding 
discussion. 

29.  The  Mean  Ordinate  by  the  Polar  Planimeter.  — 
If  we  let/  equal  the  length  of  the  mean  ordinate,  and  let  L 
equal  the  length  of  the  diagram,  then  the  area  A  =  Lp,  but 
the  area  A  =  IR  [eq.  (7)].  Therefore  Lp  =  IR,  from  which 


(10) 


In  an  instrument  in  which  /  is  adjustable,  it  may  be  made 
the  length  of  the  area  to  be  evaluated.  Now  if  /  be  made 
equal  L,  p  =  R.  That  is,  if  the  adjustable  arm  be  made  equal 
to  the  length  of  the  diagram^  the  mean  ordinate  is  equal  to  the 
reading  of  the  record-wheel,  to  a  scale  to  be  determined. 

The  method  of  making  the  adjustable  arm  the  length  of 
the  diagram  is  facilitated  by  placing  a  point  U  on  the  back  of 
the  planimeter  at  a  convenient  distance  back  of  the  tracing- 
point  Fand  mounting  a  similar  point  Fat  the  same  distance 
back  of  the  pivot  C\  then  in  all  cases  the  distance  UV  'will  be 
equal  to  the  length  of  the  adjustable  arm  /.  The  instrument  is 
readily  set  by  loosening  the  set-screw  5  and  sliding  the  frame 


40  EXPERIMENTAL   ENGINEERING.  |_§  2 9, 

carrying  the  pivot  and  record-wheel  until  the  points  C/Fare  at 
the  respective  ends  of  the  diagram  to  be  traced,  as  shown  in 
Fig.  ii. 

In  the  absence  of  the  points  U  and  V  the  length  of  the 
diagram  can  be  obtained  by  a  pair  of  dividers,  and  the  distance 
of  the  pivot  C  from  the  tracing-point  F  made  equal  to  'the 
length  of  the  diagram. 

In  this  position,  if  the  tracing-point  be  carried  around  the 
diagram,  the  reading  will  be  the  mean  ordinate  of  the  diagram 


FIG.  ii.— METHOD  OF  SETTING  THE  PLANIMETER  FOR  FINDING  THE  MEAN  ORDINATE. 

expressed  in  the  same  units  as  the  subdivisions  of  the  record- 
wheel  ;  thus  if  the  subdivisions  of  this  wheel  are  fortieths  of 
one  inch,  the  result  will  be  the  length  of  the  mean  ordinate  in 
fortieths.  This  distance,  which  we  term  the  scale  of  the  record- 
wheel,  is  not  the  distance  between  the  marks  on  the  graduated 
scale,  but  is  the  corresponding  distance  on  the  edge  of  the 
wheel  which  comes  in  contact  with  the  paper. 

The  scale  of  the  record-ivheel  evidently  corresponds  to  a 
linear  distance,  and  it  should  be  obtained  by  measurement  or 
computation.  It  is  evidently  equal  to  the  number  of  divisions 
in  the  circumference  divided  by  nd,  in  which  d  is  the  diameter, 
or  it  can  be  obtained  by  measuring  a  rectangular  diagram  with 
a  length  equal  to  /,  and  a  mean  ordinate  equal  to  one-inch,  in 
which  case  the  reading  of  the  record-wheel  will  give  the  num- 
ber of  divisions  per  inch.  A  diameter  of  0.795  inch,  which 
corresponds  to  a  radius  of  one  centimeter,  with  a  hundred  sub- 


§  32-]  APPARA  rus.  41 

divisions  of  the  circumference,  corresponds  almost  exactly  to 
a  scale  of  forty  subdivisions  to  the  inch,  and  is  the  dimension 
usually  adopted  on  foreign-made  instruments. 

30.  The  Suspended  Planimeter.— In  the  Amsler  sus- 
pended planimeter  as  shown  in  Fig.  12,  pure  rolling  motion 
without  slipping  is  assumed  to  take  place.  The  motion  of  the 
record-wheel,  not  clearly  shown  in  the  figure,  is  produced  by 
the  rotation  of  the  cylinder  c  in  contact  with  the  spherical 


FIG.  12.— SUSPENDED  PLAWIMETER. 


segment  K.  The  rotation  of  the  segment  is  due  to  angular 
motion  around  the  pole  O,  that  of  the  cylinder  c  to  its  posi- 
tion with  reference  to  the  axis  of  the  segment.  This  position 
depends  on  the  angle  that  the  tracing  arm,  ks,  makes  with  the 
radial  arm,  BB.  The  area  in  each  case  being,  as  with  the 
polar  planimeter,  equal  to  the  product  of  the  length  of  tracing 
arm  from  pivot  to  tracing  point  multiplied  by  a  constant 
factor. 

31.  The  Coffin  Planimeter  and  Averaging  Instrument. 
— This  instrument   is  shown  in  Fig.  13,  from  which  it  is  seen 
that  it  consists  of  an  arm  supporting  a  record-wheel  whose  axis 
is  parallel  to  the  line  joining  the  extremities  of  the  arm.     This 
instrument  was  invented  by  the  late  John  Coffin,  of  Johnstown, 
in  1874.     The  record-wheel  travels  over  a  special  surface;  one 
end  of  the  arm  travels  in  a  slide,  the  other  end  passes  around 
the  diagram. 

32.  Theory  of  the  Coffin  Instrument. — This  planimeter 
may  be  considered  a  special  form  of  the  Amsler,  in  which  the 
point  P,  see  Fig.  14,  page  43,  moves  in  a  right  line  instead  of 


EXPERIMEN  TA  L  ENGINEERING. 


[§32. 


swinging  in  an  arc  of  a  circle,  and  the  angle  CPT,  correspond- 
ing to  B  in  eq.  (i),  is  a  fixed  right  angle.  The  differential 
equation  for  area  therefore  is 

dA=lndV,     .......     (u) 


FIG.  13.  —  THE  COFFIN  AVERAGING  INSTRUMENT. 

and  the  differential  equation  of  the  register  becomes 


Hence,  as  in  equation  (7), 


A  = 


(13) 


§  32.]  APPARA  TUS.  43 

That  is,  the  area  is  equal  to  the  space  registered  by  the  record- 
wheel  multiplied  by  the  length  of  the  planimeter  arm. 

This  instrument  may  be  made  to  give  a  line  equivalent  to 
the  mean    ordinate  (M.  O  )   by  placing  the  diagram   so  that 


FIG.  14. — COFFIN  AVERAGING  INSTRUMENT. 

one  edge  is  in  line  with  the  guide  for  the  arm ;  starting  at  the 
farthest  portion  of  the  diagram,  run  the  tracing-point  around 
in  the  usual  manner  to  the  point  of  starting,  after  which  run 
the  tracing-point  perpendicular  to  the  base  along  a  special 
guide  provided  for  that  purpose  until  the  record-wheel  reads 
as  at  the  beginning.  This  latter  distance  is  the  mean 
ordinate. 


44  EXPERIMENTAL  ENGINEERING.  [§  33- 

To  prove,  take  as  in  Art.  29  the  M.  O.  =  /,  the  length 
of  diagram  =  Z,  the  perpendicular  distance  =  5.     Then 

A  =pL=lR  .....     ...     (14) 

Let  C  be  the  angle,  EPT,  that  the  arm  makes  with  the  guide, 
Fig.  8.  In  moving  over  a  vertical  line  this  angle  will  remain 
constant,  and  the  record  will  be 

R=  Ss'm  C.   .     .  ;  .     ....     (15) 

For  the  position  at  the  end  of  the  diagram 

sin  C  =  L  -r-  1  ; 
therefore 


Substituting  this  in  equation  (14), 


Hence/  =  5  (150),  which  was  to  be  proved. 

From  the  above  discussion  it  is  evident  that  areas  will  be 
measured  accurately  in  all  positions,  but  that  to  get  the 
M.  O.  the  base  of  the  diagram  must  be  placed  perpendicular 
to  the  guide,  and  with  one  end  in  line  of  the  guide  pro- 
duced. 

•  It  is  also  to  be  noticed  that  the  record-wheel  may  be  placed 
in  any  position  with  reference  to  the  arm,  but  that  it  must  have 
its  axis  parallel  to  it,  and  that  it  registers  only  the  perpen- 
dicular distance  moved  by  the  arm. 

33.  The  Willis  Planim  eter.  —  This  planimeter  is  of  the 
same  general  type  as  the  Amsler  Polar,  but  in  place  of  the  record  - 
wheel  for  recording-  arm;  it  employs  a  disk  or  sharp-edged  wheel 
free  to  slide  on  an  axis  perpendicular  to  the  tracing-  arm.  The 
distance  moved  perpendicular  to  this  arm  is  read  on  the  graduated 


§34-]  APPARATUS.  45 

edge  of  a  triangular  scale  which  is  supported  in  an  ingenious  man- 
ner, as  shown  in  the  accompanying  figure.  The  planimeter-arm 
can  be  adjusted  as  in  the  Amsler  Planimeter  so  as  to  read  the 
M.  E.  P.  direct.  An  adjustable  pin,  E,  is  employed  for  the 
purpose  of  setting  off  the  length  of  the  diagram. 

The  mathematical  demonstration  is  exactly  as  for  the  Amsler 
Planimeter,  but  in  this  case  it  is  evident  that  the  perpendicular 
distance  which  is  registered  on  the  scale  is  independent  of  the 


FIG.  140. — THE  WILLIS    PLANIMETER. 

A 

circumference  of  the  wheel.  The  only  conditions  of  accuracy 
are,  that  the  axis  of  the  scale  shall  be  at  right  angles  to  the 
arm  of  the  planimeter,  and  that  its  graduations  shall  be 
equal  to  the  area  to  be  measured  divided  by  the  length  of  the 
arm. 

34.  The  Roller-planimeter. — This  is  the  most  accurate  of 
the  instruments  for  integrating  plane  areas,  and  is  capable  of 
measuring  the  area  of  a  surface  of  indefinite  length  and  of  lim- 
ited breadth.  This  instrument  was  designed  by  Herr  Corradi  of 
Zurich,  and  is  manufactured  in  this  country  by  Fauth  &  Com- 
pany of  Washington,  D.  C. 

A  view  of  the  instrument  is  shown  in  Fig.  15.  The  features 
of  this  instrument  are:  firstly,  the  unit  of  the  vernier  is  so 
small  that  surfaces  of  quite  diminutive  size  may  be  determined 
with  accuracy;  secondly,  the  space  that  can  be  encompassed 
bv  one  fixing  of  the  instrument  is  very  large;  thirdly,  the 


46 


EXPERIMEN  TA  L  ENGINEERING. 


[§34- 


results  need  not  be  affected  by  the  surface  of  the  paper  on 
which  the  diagram  is  drawn  ;  and,  fourthly,  the  arrangement  of 
its  working  parts  admit  of  being  kept  in  good  order  a  long 
time. 

The  frame  B  is  supported  by  the  shaft  of  the  two  rollers 
Rfi^ ,  the  surfaces  of  which  are  fluted.  To  the  frame  B  are 
fitted  the  disk  A,  and  the  axis  of  the  tracing-arm  F.  The  whole 
apparatus  is  moved  in  a  straight  line  to  any  desired  length 
upon  the  two  rollers  resting  on  the  paper,  while  the  tracing- 
point  travels  around  the  diagram  to  be  integrated.  Upon  the 
shaft  that  forms  the  axis  of  the  two  rollers  RlRl  a  minutely 


C    Ci 


FlG.  15.— ROLLBR-PLANIMETER, 


divided  mitre-wheel  R^  is  fixed,  which  gears  into  a  pinion 
R9.  This  pinion,  being  fixed  upon  the  same  spindle  as  the 
disk  A,  causes  the  disk  to  revolve,  and  thereby  induces  the  roll- 
ing motion  of  the  entire  apparatus. 

The  measuring-roller  E,  resting  upon  the  disk  A,  travels 
thereon  to  and  fro,  in  sympathy  with  the  motion  of  the  tracing- 
arm  F,  this  measuring-roller  being  actuated  by  another  arm 
fixed  at  right  angles  to  the  tracing-arm  and  moving  freely 
between  pivots.  The  axis  of  the  measuring-roller  is  parallel  to 
the  tracing-arm  F.  The  top  end  of  the  spindle  upon  which 


§35-]  APPARATUS.  47 

the  disk  A  is  fixed  pivots  on  a  radial  steel  bar  CCt ,  fixed  upon 
the  frame  B. 

35.  Theory. — The  following  theory  of  the  roller-planim- 
eter  is  partly  translated  from  an  article  by  F.  H.  Reitz,  in  the 
Zeitschrift fur  Vermessungs-Wesen,  1884. 

According  to  the  general  theory  of  planimeters  furnished 
with  measuring-rollers,  it  is  immaterial  what  line  the  free  end 
of  the  tracing-arm  travels  over  ;  nevertheless  there  is  some 
practical  advantage  in  the  construction  of  the  apparatus  to  be 
obtained  from  causing  that  end  to  travel  as  nearly  as  possible 
in  a  straight  line.  Still  it  is  obvious  that  a  slight  deviation 
from  the  straight  line  would  not  involve  any  inaccuracy  in  the 
result. 

Seeing  that  the  fulcrum  of  the  tracing-arm  keeps  travelling 
in  a  straight  line,  it  appears  advisable,  in  evolving  the  theory 
of  the  apparatus,  to  assume  a  rectangular  system  of  co-ordinates, 
and  fix  upon  the  line  along  which  that  fulcrum  travels  as  the 
axis  of  abscissae. 

The  passage  of  the  tracing-point  around  the  perimeter  of  a 
diagram  maybe  looked  upon  as  being  made  up  of  two  motions 
— one  parallel  to  the  axis  of  abscissae  and  the  other  at  right 
angles  to  that  axis.  Inasmuch  as  the  latter  of  these  two 
motions,  in  the  direction  of  the  axis  of  ordinates,  is  after  all 
but  an  alternate  motion  of  the  tracing-point  which  takes  place 
in  an  equal  ratio  until  the  tracing-point  has  returned  to  its 
starting-point,  no  one  point  of  the  circumference  of  the  measur- 
ing-roller is  continuously  moved  forward  in  consequence  of  this 
motion.  Therefore  it  is  only  necessary  to  take  the  differential 
motion  of  the  tracing-point  in  the  direction  of  the  axis  of 
abscissae  into  consideration. 

In  Fig.  16  the  same  letters  of  reference  denote  identical  parts 
or  organs  as  in  Fig.  15  and  the  position  of  the  parts  in  the  two 
figures  correspond  exactly,  the  letter  D  denoting  the  distance 
between  the  fulcrum  of  the  tracing-arm  and  the  axis  of  the 
disk  A.  The  amount  of  motion  of  a  point  on  the  record- 
wheel  E,  while  the  tracing-point  travels  to  the  extent  of  dx> 
must  be  determined.  If  the  construction  of  the  planimeter  is 


EXPERIMEN  TA  L   ENGINEERING. 


[§35. 


correct,  this  quantity  must  be  the  product  of  a  constant  derived 
from  the  instrument,  multiplied  by  the  differential  expression 
for  the  surface.  This  latter  quantity  with  reference  to  rectan- 
gular co-ordinates  is  ydx. 

It  is  readily  seen  that  as  the  tracing-point  moves  an  amount 
equal  to  dx,  a  point  in  the  circumference  of  the  rollers  R^ 
must  be  shifted  the  same  amount,  since  the  axes  of  these  rollers 
are  parallel  to  the  ordinate  y. 

Any  point  in  the  pitch-line  of  the  mitre-wheel  R^  must  move 

r> 

an  amount  equal  to  ~£dx. 


FIG.  16. 


Suppose  that  while  the  tracing-point  moves  a  distance  dx^ 
the  disk  A  moves  a  distance  ab,  Fig.  10,  since  this  disk  is  turned 
by  the  mitre-wheel  whose  pitch-circle  is  Rt ,  and  ad  is  the  dis- 
tance from  record-wheel  to  the  axis  of  this  wheel,  we  must 
have 


(16) 


£  35-]  APPARA  TUS.  49 

Because  of  the  position  of  the  axis  of  the  record-wheel  Ey  the 
motion  of  the  disk  A  to  the  extent  of  ab  produces  a  shifting 
of  a  point  in  the  circumference  of  E  equal  to  cby  while  the 
record-wheel  slips  a  distance  ac.  The  distance  cb  is  the  reading 
of  the  record-wheel  and  is  the  quantity  required.  We  have 
dab  =  90°,  cag  =  90°  ;  hence  caf  =  a,  and  fab  =  ft,  and  cab 
=  a  -[-  ft.  So  that  since  acb  =  90°, 


cb  =  ab  sin  («  +  /?)  =  ab  (sin  a  cos  /?  +  c°s  «  sin 
But  it  is  seen  that 


Hence 

cos  a  — 


~V ' - 


~^d~ 


Substitute  these  values  in  equation  (17): 


.  US) 

ff\aa/  _  raa 

Substitute  the  value  of  ab  in  (16), 

ct=z  -^nrrdx  =  (constant)  ydx,  .    .    .    .    (19) 

«VH^ 

which  was  to  be  proved. 


50  EXPERIMENTAL   ENGINEERING.  [§  36, 

The  differential  distance  cb  is  the  reading  of  the  record  wheel  . 

D  /? 
let  this  be  represented  by  dr,  denote  by  C  the  constant 


then 


dr  =  Cydx ;        ydx  =  ~  ; 


This  expression  integrated  gives 

I  ,  v       xiJ\.,J\.n. 

Area  =  ^(r1-ra)  =  --^-(r1~r1);      .     •    \2O) 

in  which  r,  and  r,  are  the  initial  and  final  readings  of  the 
record-wheel. 

In  the  construction  of  the  instrument  Rlt  R3,  D>  and  R^  are 
fixed  quantities,  but  the  length  of  the  tracing-arm  F  can  be 
varied,  with  a  corresponding  variation  in  the  unit  of  measure- 
ment. 

36.  Care  and  Adjustment  of  Planimeters.— From  the 
preceding  discussion  it  is  seen  that  the  area  in  every  case  is 
the  product  of  the  distance  actually  moved  by  the  circum- 
ference of  the  record-wheel  into  the  length  of  the  arm  from 
the  tracing-point  to  the  pivot,  into  a  constant  which  may  be 
and  is,  in  the  polar  planimeter,  equal  to  one.  It  is  also  to  be 
noticed  that  the  record-wheel  is  so  arranged  as  to  register  the 
distance  moved  by  a  point  in  a  direction  perpendicular  to  that 
.of  the  tracing-arm,  and  that  for  other  directions  it  slips.  This 
indicates  that  any  change  whatever  in  the  diameter  of  the 
record-wheel  or  gear-wheels,  due  to  wear  or  dirt,  will  require  a 
corresponding  change  in  the  length  of  tracing-arm  ;  and  further, 
any  irregularities  in  the  edge  of  this  wheel  will  make  the  rela- 
tive amounts  of  slipping  and  rolling  motion  uncertain,  and  con- 
sequently  impair  its  accuracy. 

Again,  the  plane  of  the  record-wheel  must  be  perpendicular 
to  the  tracing-arm,  otherwise  an  error  will  result. 

In  the  planimeter  the  moving  parts  usually  have  pivot- 


§3/0  APPARATUS.  51 

bearings  which  can  be  loosened  or  tightened  as  required.  The 
revolving  parts  should  spin  around  easily  but  at  the  same  time 
accurately,  and  the  various  arms  should  swing  easily  and  show 
no  lost  motion.  The  pitch-line  of  the  record-wheel  should  be 
as  close  as  possible  to  the  vernier,  but  yet  must  not  touch  it; 
the  counting-wheel  must  work  smoothly,  but  in  no  way  inter- 
fere  with  the  motion  of  the  record-wheel. 

37.  Directions  for  Use. — i.  Oil  occasionally  with  a  few 
drops  of  watch  or  nut  oil. 

2.  Keep  the  rim  of  the  record-wheel  clean  and  free  from 
rust.     Wipe  with  a  soft  rag  if  it  is  touched  with  the  fingers. 

3.  Prepare  a  smooth  level  surface,  and  cover  it  with  heavy 
drawing-paper,  for  the  record-wheel  to  move  over.     Stretch 
the  diagram  to  be  evaluated  smooth. 

4.  Handle  the  instrument  with  the  greatest  care,  as  the 
least  injury  may  ruin  it.     Select  a  pole-point  so  that  the  instru- 
ment will  in  its  initial  position  have  the  tracing-arm  perpen- 
dicular either  to  the  pole-arm   or  to  the  axis  of   the  fluted 
rollers,  as  the  case  may  be ;  for  in  this  position  only  is  the 
error  neutralized,  which  arises  from  the  fact  that  the  tracer  is 
not  returned  to  its  exact  starting-point.     Then  marking  some 
starting-point,  trace  the  outline  of  the  area  to  be  measured  in 
the  direction  of  the  hands  of  a  watch,  slowly  and  carefully, 
noting  the  reading  of  the  record-wheel  at  the  instant  of  start- 
ing and  stopping.     It  is  generally  more  accurate  to  note  the 
initial  reading  of  the  record-wheel  than  to  try  and  set  it  at  zero. 

5.  Special  Directions. — To  obtain  the  mean  ordinate  with 
the  polar  planimeter,  make  the  length  of  the  adjustable  arm 
equal  to  the  length  of  the  diagram,  as  explained  in  Art.  28, 
page  38,  and  follow  directions  for  use  as  before. 

6.  In  using  the  Coffin  planimeter,  the  grooved  metal  plate  / 
is  first  attached  to   the  board,  upon  which  the  apparatus  is 
mounted  as  shown  in  the  cut,  page  42,  being  held  in  place  by 
a  thumb-screw  applied  to  the  back  side. 

The  diagram  will  be  held  securely  in  place  by  the  spring-clips 
adjacent,  A  and  C,  Fig.  13.  The  area  may  be  found  by  running 
the  tracing-point  around  the  diagram,  as  described  for  the 


52  EXPERIMENTAL  ENGINEERING.  [§  38- 

polar  planimeter,  for  any  position  within  the  limits  of  the  arm. 
The  mean  ordinate  may  be  found  by  locating  the  diagram  as 
shown  in  the  cut,  with  one  extreme  point  in  the  line  of  the 
metal  groove  produced,  and  the  dimension  representing  the 
length  of  the  diagram  perpendicular  to  this  groove.  Start  to 
trace  the  area  at  the  farthest  distance  of  the  diagram  from  the 
metal  guide  produced,  as  shown  in  Fig.  13  ;  pass  around  in  the 
direction  of  the  motion  of  the  hands  of  a  watch  to  the  point 
of  beginning ;  then  carry  the  tracing-point  along  the  straight- 
edge, AK,  which  is  parallel  to  the  metal  groove,  until  the  record- 
wheel  shows  the  same  reading  as  at  the  instant  of  starting : 
this  latter  distance  is  the  length  of  the  mean  ordinate. 

38.  Calibration  of  the  Planimeter. — In  order  to  ascertain 
whether  the  instrument  is  accurate  and  graduated  correctly,  it 
is  necessary  to  resort  to  actual  tests  to  determine  the  character 
and  amount  of  error. 

It  is  necessary  to  ascertain:  I.  If  the  same  readings  are 
given  by  different  portions  of  the  record-wheel.  2.  Whether 
the  position  of  the  vernier  is  correct,  and  agrees  with  the  con- 
stants  tabulated  or  marked  on  the  tracing-arm.  3.  Whether 
the  scale  of  the  record-wheel  is  correct,  and  agrees  with  the 
constants  marked  on  the  tracing-arm. 

These  tests  are  all  made  by  comparing  the  readings  of  the 
instrument  with  a  definite  and  known  area.  To  obtain  a  defi- 
nite area,  a  small  brass  or  German-silver  rule,  shown  at  Z,  Fig. 
n,  is  used;  this  rule  has  a  small  needle-point  near  one  end, 
and  a  series  of  small  holes  at  exact  distances  of  one  inch  or 
one  centimeter  from  the  needle-point.  To  use  the  rule  the 
needle-point  is  fixed  on  a  smooth  surface  covered  with  paper, 
the  planimeter  is  set  with  its  tracing-point  in  one  of  the  holes 
of  the  rule,  and  the  pole-point  fixed  as  required  for  actual  use. 
With  the  tracing-point  in  the  rule  describe  a  circle,  as  shown 
by  the  dotted  lines  (Fig.  17)  around  the  needle-point  as  a 
centre.  Since  the  radius  of  this  circle  is  known,  its  area  is 
known ;  and  as  the  tracing-point  of  the  planimeter  is  guided  in 
the  circumference,  the  reading  of  the  record-wheel  should  give 
the  correct  area. 


§38.] 


APPARATUS 


53 


The  method  of  testing  is  illustrated  in  Figs.  17,  18,  19,  and 
20.  Figs.  17  and  18  show  the  method  with  reference  to  the 
polar  planimeter;  Figs.  19  and  20  show  the  corresponding 
methods  of  testing  the  rolling-planimeter.  In  Figs.  17  and  19 
P  is  the  position  of  the  pole,  B  the  pole-arm,  and  A  the  tracing- 
arm.  In  Figs.  1 8  and  20  B  is  the  axis  of  the  rollers  and  A  is 
the  tracing- arm. 

First  Test.  This  operation,  see  Figs.  17  and  18,  consists 
in  locating  the  planimeters  as  shown,  and  then  slowly  and 


FIG.  17. 


FIG. 18. 


caretfulty  revolving  so  as  to  swing  the  check-rule  as  shown 
by  the  arrow.  Take  readings  of  the  vernier  at  initial  point, 
and  again  on  returning  to  the  starting-point :  the  difference  of 
these  readings  should  give  the  area.  Repeat  this  operation 
several  times. 

The  instrument  is  now  placed  in  the  position  shown  in 
Figs.  19  and  20  when  the  circle  K  appears  on  the  rz^l-hand 
side  of  the  tracing-arm  A,  and  the  passage  of  the  tracer  takes 
place  in  exactly  the  same  way. 

If  the  results  obtained  right  and  left  of  the  tracing-arm  be 
equal  to  one  another,  it  is  clear  that  the  axis  ab  of  the  measur- 
ing-wheel is  parallel  to  the  tracing-arm,  and,  this  being  so,  the 
second  test  may  now  be  applied.  But  if  the  result  be  greater 
in  the  first  case,  that  is  to  say,  when  the  circle  lies  to  the  left 


54 


EXPERIMENTAL  ENGINEERING. 


[§38. 


of  the  tracing-arm,  the  extremity  a  of  the  axis  of  the  measur- 
ing-wheel must  be  further  removed  from  the  tracing-arm  ;  if  it 
be  less,  that  extremity  must  be  brought  nearer  to  the  tracing. 


arm. 


Second  Test.  The  tracing-arm  is  adjusted  by  means  of  the 
vernier  on  the  guide  and  by  means  of  the  micrometer-screw, 
in  accordance  with  the  formulae  for  different  areas ;  it  then  is 
fixed  within  the  guide  by  means  of  the  binding-screw.  The 
circumference  of  circles  of  various  sizes  are  then  travelled  over 


1     , 

b 

\*          I 

1 

n 

a 

A 

J 

r 

o 

FIG.  19. 


FIG.  20. 


with  the  check-rule,  and  the  results  thus  obtained  are  multi- 
plied into  the  unit  of  the  vernier  corresponding  to  the  area 
given  for  that  particular  adjustment  by  the  formula.  The  fig- 
ures thus  obtained  ought  to  be  equal  to  the  calculated  area  of 
the  circles  included  by  the  circumferences.  If  the  results  ob- 
tained with  the  planimeter  fall  short  of  the  calculated  areas  to 

the  extent  of  —  of  those  areas,  the  length  of  the  tracing-arm, 
that  is  to  say,  the  distance  between  the  tracer  and  the  fulcrum 

of  the  tracing-arm,  must  be  reduced  to  the  extent  of  -  of  that 

n 

length ;  in  the  opposite  case  it  must  be  increased  in  the  same 
proportion.  The  vernier  on  the  guide-piece  of  the  tracing-arm 
shows  the  length  thus  defined  with  sufficient  accuracy,  usually 


§39-] 


APPARA  TUS. 


55 


in  half-millimeters,  or  about  fiftieths  of  an  inch,  on  the  gauged 
portion  of  the  arm. 

In  order  to  test  the  accuracy  of  the  readings  according  to 
the  two  methods  just  described,  some  prefer  the  use  of  a 
check-plate  in  lieu  of  the  check-rule.  The  check-plate  is  a  cir- 
cular brass  disk  upon  which  are  engraved  circles  with  known 
radii. 

It  is  advisable  to  apply  the  second  test  also  to  a  large  dia- 
gram drawn  on  paper  and  having  a  known  area. 

The  instrument  having  been  found  correct  or  its  errors  de- 
termined, it  may  now  be  used  with  confidence. 

The  following  form  is  used  to  record  the  results  of  the  test : 

Calibration  of Planimeter 189. , 

by  Dia.  register-wheel,  in. . . » 

Formula  of  Instrument Length  of  arms,  pole  to  pivot,  in. ... 

Pivot  to  register-wheel,  in. ...  Pivot  to  tracing-point,  in. ... 
In  Roller  Pla.  radius  roller,  in. ...  Pitch  radius  Gears,  No.  I. . .  .No.  II 


COMPARISON  WITH  STANDARD. 


AREA. 

MEAN  ORDINATK. 

No. 

Inst.  Reading. 

0 

Difference  from 
Mean. 
e 

e* 

Inst.  Reading. 

0 

Difference  from 
Mean. 

e 

<* 

Mean 

Mean  error  of  one  observation,  ± 
Mean  error  of  result,  ± 

Probable  error  of  one  obs.,  ±  0.67 
Probable  error  of  result,       ±0.67 


(«  —  i)  in  area. . . .,  in  ordinate. .  .in. 


«(«  —  i)  in  area. . .,  in  ordinate. .  .in, 
—  i)  in  area. ...» in  ordinate ...  in. 


-*-»(«—  i)  in  area.  .  .  .  ,  in  ordinate.  .  .in. 


39.  Errors  of  Different  Planimeters.—  Professor  Lorber, 
of  the  Royal  Mining  Academy  of  Loeben,  in  Austria,  made 


EXPERIMENTAL  ENGINEERING. 


[§39 


extensive  experiments  on  various  planimeters,  with  the  results 
shown  in  the  following  table : 


The  error  in  one  passage  of  the  tracer  amounts  on  an  average  to 
the  following  fraction  of  the  area  measured  by  — 

AREA  IN— 

The  ordinary 
Polar  Plan- 

Stark's Linear 
Planimeter 

Suspended 
Planimeter 

Rolling  Planimeter— 

imeter  Unit 
of  Vernier: 

Unit  of  Ver- 
nier: 

Unit  of  Ver- 
nier: 

Unit  of  Ver- 
nier: 

Unit  of  Ver- 
nier  : 

Square 
cm. 

Square 
inches. 

to  sq.  mm.  = 
.015  sq.  in. 

i  sq.  mm.  = 
.015  sq.  in. 

i  sq.  mm.  = 
.0015  sq.  in. 

i  sq.  mm.  = 
.0015  sq.  in. 

.1  sq.  mm.  = 
.0001  sq.  in. 

10 

1-55 

TV 

i 

TTFIT 

vfr 

TUITo" 

20 

3-10 

riff 

ToVo" 

unnr 

50 

7«75 

•STF 

Tm 

'S'SWO 

2TT5T5" 

3  00  "6 

100 

15.50 

tfis 

ssW 

5'dW 

200 

31.00 

iisW 

T1T5T 

TTilF 

SJ'FS 

TlSl 

300 

46.50 

.... 



Wnr 

W&TT 

Toool) 

The  absolute  amount  of  error  increases  much  less  than  the 
size  of  the  area  to  be  measured,  and  with  the  ordinary  polar 
planimeter  is  nearly  a  constant  amount. 

The  following  table  is  deduced  from  the  foregoing,  and 
shows  the  error  per  single  revolution  in  square  inches: 


AREA  IN— 

Error  in  one  passage  of  the  tracer  in  square  inches- 

Polar  Planim- 
eter Unit  of 
Vernier: 
10  sq.  mm.  = 
.015  sq.  inches. 

Suspended  Plan- 
imeter Unit  of 
Vernier: 
i  sq.  mm.  = 
.0015  sq.  inches. 

Rolling  Planimeter— 

Unit  of  Vernier: 
i  sq.  mm.  = 
.0015  sq.  inches. 

Unit  of  Vernier: 
.1  sq.  mm.  = 
.0001  sq.  inches. 

Square 
cm. 

Square 
inches. 

10 
20 

50 
100 
200 
300 

1-55 
3.10 
7-75 
I5-50 
31.00 
46.50 

0.0207 
O.O2O6 
0.0221 
O.O227 
0.0243 

O.OO25 
0.0028 
0.0031 
0.0035 
0.0043 
0.0049 

0.0025 
0.0031 
0.0038 
0.0043 
0.0060 
0.0058 

0.00155 
0.00158 
0.00258 
0.00310 
0.00403 
0.00465 

These  errors  were  expressed  in  the  form  of  equations,  as 
follows,  by  Professor  Lorber.     Let  /  equal  the   area  corre- 


§40.] 


APPARATUS. 


57 


spending  to  one  complete  revolution  of  the  record-wheel ;  let 
dF  be  the  error  in  area  due  to  use  of  the  planimeter.  Then 
for  the  different  planimeters  we  have  the  following  equations : 


Lineal  planimeter, 
Polar  planimeter, 
Precision  polar  planimeter, 
Suspended  planimeter, 
Rolling  planimeter, 


dF  —  0.0008 1/ +  0.00087  VTf\ 

dF  =  O.OOI26/-)-  O.O0022  tfFf\ 

dF  =  o.ooo6o/  +  0.000 1 8  \'Ty ; 
dF=o.ooo6f  +  0.00026  VFf. 
^F=o.oooo/  +0.0006  VTf. 


40.  Moment  Planimeters  much  more  complicated  than  those 
described  have  been  made  for  special  purposes,  of  which  we 
may  mention  Amsler's  mechanical  integrator  for  rinding  the 
moment  of  inertia,  and  "Coradi's"  mechanical  integraph  for 
drawing  the  derivity  of  any  curve,  the  principal  curve  being 
known,  thus  giving  a  graphic  representation  of  moment. 


FIG  21. — VERNIER  CAU 


40.  Vernier  Caliper. — This  instrument  consists  of  a  slid- 
ing-jaw,  which  carries  a  vernier,  and  may  be  moved  over  * 
fixed  scale.  The  form  shown  in  Fig.  21  gives  readings  to  /tf 
inch  on  the  limb,  and  ^  this  amount  or  to  one-thousandth  of 


58  EXPERIMENTAL   ENGINEERING.  [§  4: 

an  inch  on  the  vernier.  The  reading  of  the  vernier  as  it  is 
shown  in  the  figure  is  1.650  from  the  scale,  and  0.002  on  the 
vernier,  making  the  total  reading  1.652  inches.  This  instru- 
ment is  useful  for  accurate  measurements  of  great  variety ;  the 
especial  form  shown  in  the  cut  has  a  heavy  base,  so  that  it  will 
stand  in  a  vertical  position  and  may  be  used  as  a  height-gauge. 
To  use  it  as  a  caliper,  the  specimen  to  be  measured  is  placed 
between  the  sliding-jaw  and  the  base ;  the  reading  of  the  vernier 
will  give  the  required  diameter. 

41.  The  Micrometer. — This  instrument  is  used  to  meas- 
ure small  subdivisions.  It  consists  of  a  finely  cut  screw,  one 
revolution  of  which  will  advance  the  point  an  amount  equal  to 
the  pitch  of  the  screw.  The  screw  is  provided  with  a  gradu- 
ated head,  so  that  it  can  be  turned  a  very  small  and  definite 
portion  of  a  revolution.  Thus  a  screw  with  forty  threads  to 
the  inch  will  advance  for  one  complete  revolution  -^  of  an 
inch,  or  25  thousandths.  If  this  be  provided  with  a  head  sub- 
divided to  250  parts,  the  point  would  be  advanced  one  ten- 
thousandth  of  an  inch  by  the  motion  sufficient  to  carry  the 
head  past  one  subdivision. 

The  micrometer  is  often  used  in  connection  with  a  micro- 
scope having  cross-hairs,  and  in  such  a  case  represents  the 
most  accurate  instrument  known  for  obtaining  the  value  of 
minute  subdivisions;  it  is  also  often  used  in  connection  with 
the  vernier.  The  value  of  the  least  reading  is  determined  by 
ascertaining  the  advance  due  to  one  complete  revolution,  and 
dividing  by  the  number  of  subdivisions.  The  total  advance  of 
he  screw  is  equal  to  the  advance  for  one  revolution  multiplied 
>y  the  number  of  revolutions  plus  the  number  of  subdivisions 
multiplied  by  the  corresponding  advance  for  each. 

The  accuracy  of  the  micrometer  depends  entirely  on  the 
screw  which  is  used. 

Accuracy  of  Micrometer-screws. — The  accuracy  attained  in 
cutting  screws  is  discussed  at  length  by  Prof.  Rogers  in  Vol.  V. 
of  Transactions  of  American  Society  of  Mechanical  Engineers, 
from  which  it  is  seen  that  while  no  screw  is  perfectly  accurate, 
still  great  accuracy  is  attained.  The  following  errors  are  those 


§42.] 


APPARA  TUS. 


59 


in  one  of  the  best  screws  in  the  United  States,  expressed  in 
hundred-thousandths  of  an  inch,  for  each  half-inch  space, 
reckoned  from  one  end. 


CORNELL  UNIVERSITY  SCREW. 

TOTAL  ERRORS  IN  HUNDRED-THOUSANDTHS  OF  AN  INCH. 


No.  of  Space. 

Total  Error. 

No.  of  Space. 

Total  Error. 

No.  of  Space. 

Total  Error. 

0 

0 

12 

-    4 

24 

-8 

I 

~f~  6 

13 

-    7 

25 

—  7 

2 

_j_  8 

14 

-    9 

26 

—  7 

3 

+  9 

15 

-    7 

27 

~  9 

4 

+  7 

16 

—  10 

28 

-9 

5 

+  9 

17 

—  ii 

29 

—  7 

6 

+  7 

18 

—  ii 

30 

—  7 

7 

+  4 

19 

—  10 

31 

-6 

8 

+  5 

20 

—  IO 

32 

-7 

9 

0 

21 

-    9 

33 

-7 

10 

—  i 

22 

—  ii 

34 

-3 

ii 

-  2 

23 

—  10 

It 

—  2 
0 

A  recent  investigation  made  by  the  author  of  the  errors  in 
the  ordinary  Brown  and  Sharpe  micrometer-screw,  failed  to 
detect  any  errors  except  those  of  observation,  which  were 
found  to  be  about  4  hundred-thousandths  of  an  inch  for  a 
distance  equal  to  three-fourths  its  length.  The  errors  in  the 
remaining  portion  of  the  screw  were  greater ;  the  total  error 
in  the  whole  screw  being  12  hundred-thousandths  of  an  inch. 
As  the  least  reading  was  one  ten-thousandth,  the  screw  was  in 
error  but  slightly  in  excess  of  the  value  of  its  least  subdivision. 
In  another  screw  of  the  same  make  the  error  was  three  times 
that  of  the  one  described. 

42.  Micrometer  Caliper  consists  of  a  micrometer-screw 
shown  in  Fig.  22,  which  may  be  rotated  through  a  fixed  nut. 
To  the  screw  is  attached  an  external  part  or  thimble,  which 
has  a  graduated  edge  subdivided  into  25  parts.  The  fixed  nut 
is  prolonged  and  carries  a  cylinder,  termed  the  barrel,  on  which 
are  cut  concentric  circles,  corresponding  to  a  scale  of  equal  parts, 
and  a  series  of  parallel  lines,  which  form  a  vernier  with  refer- 


6o 


EXPERIMENTAL  ENGINEERING. 


[§42. 


ence  to  the  scale  on  the  thimble,  the  least  reading  of  which  is 
one  tenth  that  on  the  thimble.  If  the  screw  be  cut  40  threads 
per  inch,  one  revolution  will  advance  the  point  0.025  inch  ;  and 
if  the  thimble  carry  25  subdivisions,  the  least  reading  past 
any  fixed  mark  on  the  barrel  would  be  one  thousandth  of  an 
inch. 

By  means  of  the  vernier  the  advance  of  the  point  can  be 
read  to  ten-thousandths  of  an  inch.     Thus  in  the  sketches  of 


64  tltS. 

I  .0156 
3    .0468 
5    .0781 
7     .1093 
9     .1406 

II  .1718 
13  .2031 


63  .9343 
61  .9531 
59  .9218 
57  .8906 
55  .8593 
53  .8231 
51  .7968 
_  -7856 
*'  .734., 


19   .2968 

81    .3281  39     6093 

83   .3593       Pat.^pr.211878.      37     5731 

85  .3906    Hu.Jan.22.1884.  35    .5468 

27   .4218  33  .5156 

29    .4531  31    .4843 


THIMBLE 
BARREL 


Mill 
i'o^ — *Js 

THIMBLE 

FIG.  22.— MICROMETER  CALIPBR. 

the  oarrel  and  thimble  scales  in  Fig.  16  the  zero  of  the  vernier 
coincides  in  the  upper  sketch  with  No.  7  on  the  thimble ;  but 
in  the  lower  figure  the  zero  of  the  vernier  has  passed  beyond  7, 
and  by  looking  on  the  vernier  we  see  that  the  3d  mark  coincides 
with  one  on  the  thimble,  so  that  the  total  reading  is  0.007  + 
0.0003,  which  equals  0.0073  inch. 

This  number  must  be  added  to  the  scale-reading  cut  on  the 
barrel  to  show  the  complete  reading.  The  principal  use  of  the 
instrument  is  for  measuring  external  diameters  less  than  the 
travel  of  the  micrometer-screw. 

The  Sweet  Measuring-machine. — The  Sweet  measuring- 
machine  is  a  micrometer  caliper,  arranged  for  measuring  larger 
diameters  than  the  one  previously  described.  The  general 


§42.] 


APPARATUS. 


6l 


form  of  the  instrument  is  shown  in  Fig.  23.  The  micrometer- 
screw  has  a  limited  range  of  motion,  but  the  instrument  is  fur- 
nished  with  an  adjustable  tail  spindle,  which  is  set  at  each 


FiG.  23;  —SWEET'S  MEASURING-MACHINE. 

observation  for  distances  in  even  inches,  and  the  micrometer, 
screw  is  used  only  to  measure  the  fractional  or  decimal  parts 
of  an  inch.  The  instrument  is  furnished  with  an  external 


FIG. 


scale,  graduated  on  the  upper  edge  to  read  in  binary  fractions 
of  an  inch,  and  on  the  lower  edge  to  read  in  decimals  of  an 
inch ;  this  scale  can  be  set  at  a  slight  angle  with  the  axis  to 
correct  for  any  error  in  the  pitch  of  the  micrometer-screw- 


62  EXPERIMENTAL   ENGINEERING.  |_§  43- 

The  graduated  disk  is  doubly  graduated  ;  the  right-hand  grad- 
uations corresponding  to  those  on  the  lower  side  of  the  scale. 
The  scale  and  graduated  disk  is  shown  in  Fig.  24,  and  the  read- 
ings corresponding  to  the  positions  shown  in  the  figure  are 
0.6822,  the  last-number  being  estimated. 

The  back  or  upper  side  of  the  scale,  and  the  left-hand  disk, 
are  for  binary  fractions,  the  figures  indicating  32ds.  Fig.  25 
shows  the  arrangement  of  the  figures. 
Beginning  at  o  and  following  the  line  of 
chords  to  the  right,  the  numbers  are  in 
regular  order,  every  fifth  one  being  counted, 
and  coming  back  to  o  after  five  circuits. 
This  is  done  to  eliminate  the  factor  five 
from  the  ten-thread  screw.  In  Fig.  24  the 
portion  to  the  left  of  o  in  Fig.  25  is  seen. 
The  back  side  of  the  index-bar  is  divided  only  to  i6ths,  the 
odd  32ds  being  easily  estimated,  as  this  scale  is  simply  used  for 
a  4<  finder ;"  thus :  In  the  figure  the  reading  line  is  very  near 
the  \\  mark,  or  six  32ds  beyond  the  half-inch.  This  shows 
that  6  is  the  significant  figure  upon  this  thread  of  the  screw. 
The  other  figures  belong  to  other  threads.  The  figure  6  is 
brought  to  view  when  the  reading  line  comes  near  this  division 
of  the  scale.  Bring  the  6  to  the  front  edge  of  the  index-bar, 
and  the  measurement  is  exactly  \%  ivithout  any  calculation. 
Thus  every  32d  may  be  read,  and  for  64ths  and  other  binary 
fractions  take  the  nearest  32d  below  and  set  by  the  interme- 
diate divisions,  always  remembering  that  it  requires  five  spaces 
to  count  one. 

43.  The  Cathetometer. — This  instrument  is  used  exten- 
sively to  measure  differences  of  levels  and  changes  from  a 
horizontal  line.  Primarily  it  consists  of  one  or  more  telescopes 
sliding  over  a  vertical  scale,  with  means  for  clamping  the  tele- 
scope in  various  positions  and  of  reading  minute  distances. 
The  one  shown  in  the  engraving  (Fig.  26)  consists  of  a  solid 
brass  tripod  or  base  supporting  a  standard  of  the  same  metal, 
the  cross-section  of  which  is  shown  at  different  points  by  the 
small  figures  on  the  left.  A  sliding-carriage  upon  which  is 


§  43-]  APPARA  TVS.  63 

secured  the  small  levelling  instrument,  and  whic    has  also  a 
vernier  scale  as  shown,  is  balanced  by  heavy  lead  weights,  sus- 


FIG.  26.— THE  CATHETOMETER. 


pended  within  the  brass  tubes  on  either  side  by  cords  attached 
to  the  upper  end  of  the  carriage,  and  passing  over  the  pulleys 


64  EXPERIMENTAL   ENGINEERING.  L§  43- 

shown  at  the  top  of  the  column.  The  column  is  made  ver- 
tical by  reference  to  the  attached  plumb-line. 

The  movable  clamping-piece  below  the  carriage  is  fixed  at 
any  point  required,  by  the  screw,  shewn  at  its  side,  after  which 
the  telescope  can  be  raised  or  lowered  by  rotating  the  micro- 
meter-screw attached  to  the  clamp.  The  telescope  is  provided 
with  cross-hairs,  which  can  be  adjusted  by  reversing  in  the 
wyes  and  turning  180  degrees  in  azimuth.  The  vertical  scale 
is  provided  with  vernier  and  reading-microscope. 

Aids  to  Computation — Graphical  methods  for  multiply- 
ing or  dividing  are  usually  given  in  treatises  on  geometry  and 
ate  often  sufficiently  accurate  for  the  required  results.  Tables 
of  logarithms  anti  of  products  often  save  much  labor.  The 
Rechentafeln  by  A.  L.  Crelle  of  Berlin  gives  one  million 
products  and  will  be  found  of  much  value  in  multiplication 
and  division.  A  very  excellent  logarithmic  table  has  recently 
been  issued  by  Prof.  G.  W.  Jones,  Ithaca,  N.  Y. 

Computation  Machines Several  very  excellent  ma- 
chines for  multiplying  and  dividing  are  now  made,  which 
give  accurate  results  to  from  14  to  17  places.  Of  these  we  may 
mention,  as  moderate  in  price  and  of  perfect  accuracy,  the 
calculating  machine  of  George  B.  Grant  of  Boston ;  the 
Brunsvega  by  Grimme-Natlis  &  Co..  Brunswick,  Germany, 
and  the  Comptometer,  made  by  the  Comptometer  Co.  of 
Chicago.  Slide-rules  of  compact  form  but  with  with  scales 
40  feet  in  length,  as  designed  by  Thatcher  or  Fuller,  can  also 
be  obtained  of  the  principal  stationers. 

The  processes  of  arithmetical  calculation  are  almost  entirely 
mechanical  and  involve  no  reasoning  powers,  yet  they  are  of 
utmost  importance  in  connection  with  experimental  work. 
Unless  the  observations  of  the  experiment  are  correctly 
recorded  and  the  necessary  calculations  for  expressing  the 
result  made  accurately,  the  experimental  work  will  either  be  of 
no  value,  or,  what  is  worse,  positively  misleading.  For  these 
reasons  mechanical  methods  of  computation,  which  involve  at 
best  small  errors  of  known  magnitude,  are  to  be  adopted  when- 
ever possible  in  reducing  engineering  experiments. 


§43-]  APPARATUS.  65 

The  calculating  machine  is  of  especial  value,  since  if  the 
mechanical  processes  are  correctly  performed  the  results  will 
be  given  with  accuracy  for  the  number  of  places  within  limits 
of  the  machine.  Numerous  calculating  machines  have  been 
designed,  the  most  noted  of  which  is  the  "  difference  engine" 
designed  by  Babbage  in  1822  and  on  which  the  English  Govern- 
ment expended  more  than  $85,000  without  bringing  it  to  per- 
fection. The  first  practical  machine  which  accomplished  any- 
thing worthy  of  permanent  record  was  invented  by  Thomas  de 
Colmar  in  1850,  and  since  that  time  numerous  others,  designed 
on  similar  lines,  have  appeared,  of  which  should  be  mentioned 
those  invented  by  Tate,  Burkhardt,  Grant,  Baldwin,  and 
Odhner.  The  Grant  machine,  developed  from  1874  to  1896, 
has  now  reached  a  high  degree  of  perfection,  and  its  price  is 
within  the  reach  of  any  engineering  laboratory.  The  Odhner 
or  Brunsvega,  referred  to  above,  was  shown  at  the  World's  Fair 
in  1893,  and  differs  from  the  Grant  principally  in  the  arrange- 
ment of  parts,  in  the  fact  that,  as  now  sold,  it  possesses  an 
index  or  counter  to  register  the  multiplier  during  the  process 
of  multiplication.  The  Grant  machine  will  on  special  order  be 
fitted  with  this  appliance  ;  its  mechanism  is  much  superior  to 
that  of  the  foreign  instrument,  and  it  is  operated  with  less  labor 
and  noise. 

In  both  machines,  the  result  is  read  on  a  series  of  wheels 
arranged  on  the  same  axis  and  so  connected  that  ten  revolu- 
tions of  one  of  lower  denomination  are  required  for  one  of  the 
next  higher,  etc.,  these  wheels  being  readily  and  simultaneously 
set  at  zero.  The  numbers  to  be  united  are  engraved  on  a  key- 
board. By  setting  a  lever  opposite  any  number  and  turning  a 
crank  once,  the  sum  will  appear  on  the  result-wheels  ;  by  turning 
the  crank  twice,  the  result-wheels  will  show  twice  the  sum,  etc. 
The  number  keyboard  can  be  shifted  several  places,  so  that  it 
is  possible  to  multiply  by  numbers  of  any  denomination,  by 
less  than  ten  revolutions  of  the  crank.  Subtraction  is  per- 
formed by  starting  with  the  larger  number  on  the  result-wheel 
and  the  smaller  number  on  the  keyboard  and  revolving  the 
crank  in  the  opposite  direction  from  that  required  for  addition. 


66  EXPERIMENTAL   ENGINEERING.  [§  43* 

Division  is  computed  as  a  sort  of  continued  subtraction,  and  is 
a  complicated  operation.  The  machine  is  readily  worked  as  a 
difference  engine,  thus  permitting  its  use  for  computing  com- 
plicated tables. 

A  trial  made  in  the  U.  S.  Coast  Survey  of  the  relative  ra- 
pidity and  accuracy  of  the  Grant  calculating  machine  and  a 
seven-place  table  of  logarithms,  in  multiplying  seven  figures  by 
seven  figures  and  retaining  seven  figures  in  the  result,  showed  the 
average  time  of  multiplication  with  the  machine  as  56  seconds, 
and  with  logarithms  157  seconds;  the  number  of  errors  in  100 
trials,  with  the  machine  7,  with  logarithms  12.  A  trial  made 
at  Sibley  College  showed  more  favorable  for  the  machine, 
probably  because  the  observers  were  not  as  expert  with  loga- 
rithms. 


STRENGTH  OF  MATERIALS. 


CHAPTER   III. 
GENERAL  FORMULAE. 

IN  this  chapter  a  statement  is  made  of  the  principal  for- 
mulae  required  for  the  experimental  work  in  "  Strength  of 
Materials."  The  full  demonstration  of  these  formulae  is  to  be 
found  in  "Mechanics  of  Engineering,"  by  I.  P.  Church; 
"  Strength  of  Materials,"  by  D.  V.  Wood  ;  "  Materials  of  Con- 
struction," by  R.  H.  Thurston:  N.  Y.,  J.  Wiley  &  Sons. 

44.  Object  of  Experiments. — The  object  of  experiments 
relating  to  the  "  Strength  of  Materials  "  is  to  ascertain,  firstly, 
the  resistance  of  various  materials  to  strains  of  different  char- 
acter;     secondly,  the    characteristics    which    distinguish   the 
different  qualities,  i.e.,  the  good  from  the  bad ;  thirdly,  experi- 
mental   proof   of   the  laws    deduced    theoretically ;    fourthly, 
general  laws  of  variation,  as  dependent  on  form,  material,  or 
quality. 

The  following  methods  of  testing  are  ordinarily  employed : 
(i)  by  tension  or  pulling ;  (2)  by  compression  ;  (3)  by  trans- 
verse loading ;  (4)  by  torsion  ;  (5)  by  impact ;  (6)  by  repeated 
loading  and  unloading,  or  fatigue. 

45.  Definitions. — Stress  is  the  distributed  force  applied  to 
the  material ;  it  may  be  internal  or  external. 

Stress  is  of  two  kinds,  normal  or  direct,  and  shearing  or 
tangential,  the  latter  force  acting  at  right  angles  to  the  first. 
A  direct  stress  on  an  element  is  always  accompanied  by  a 
shearing  stress,  which  tends  to  move  the  particles  at  rfght 

67 


68  EXPERIMENTAL   ENGINEERING.  L§  45- 

angles  to  the  line  of  action  of  the  force.  This  is  well  shown  in 
the  simple  break  by  tension,  in  which  case  the  particles  are  not 
only  pulled  apart,  but  they  are  moved  laterally,  since  the  break 
is  accompanied  with  an  elongation  of  the  original  specimen, 
and  a  corresponding  reduction  in  area  of  the  cross-section. 

Strain  is  the  distortion  of  the  material  due  to  the  action  of 
the  force,  and  within  the  limits  of  elasticity  is  proportional  to 
the  stress. 

Each  stress  produces  a  corresponding  strain. 

Elasticity  is  the  property  that  most  materials  have  of  re- 
gaining their  original  form  when  the  forces  acting  on  them  are 
removed.  This  property  is  possessed  only  to  a  limited  extent, 
and  if  the  deformation  or  strain  exceeds  a  certain  amount,  the 
material  will  not  regain  its  original  form. 

The  critical  condition  beyond  which  the  body  cannot  be 
strained  without  a  permanent  distortion  or  set  is  termed  the 
elastic  limit ;  this  point  is  gradually  reached  in  most  materials, 
and  is  indicated  by  an  increase  in  the  increment  of  strain  due 
to  a  constant  increment  of  stress. 

Rigidity  or  stiffness  is  the  property  by  means  of  which 
bodies  resist  change  of  form. 

The  coefficient  of  ultimate  strength  is  the  number  of  pounds 
per  square  inch  required  for  rupture,  and  is  obtained  by  calcu- 
lation from  the  known  area  and  actual  breaking-load.  The  co- 
efficient of  strength  at  the  elastic  limit  is  the  number  of  pounds 
per  unit  of  are^  acting  upon  the  material  when  a  failing  in 
strength  is  shown  by  an  increased  increment  of  distortion  for 
an  equal  increment  of  load. 

The  resilience  is  the  potential  energy  stored  in  the  body, 
and  is  the  amount  of  work  the  material  would  do  on  being  re- 
lieved from  a  state  of  stress.  Within  the  elastic  limit,  it  is  the 
work  done  by  the  force  acting  on  the  body,  and  is  evidently 
equal  at  any  point  to  the  product  of  one  half  the  load,  into  the 
distortion  of  the  piece,  this  latter  being  the  space  passed 
through.  The  elongation  is  the  total  relative  strain ;  it  is 
usually  expressed  in  percentage  of  the  full  length,  and  is 
calculated  for  the  point;  of  rupture.  In  connection  with 


§  46-]  STRENGTH  OF  MATERIALS— GENERAL  FORMULAE.    69 

this  should  be  measured  the  reduction  of  area  of  cross-sec- 
tion. The  modulus  of  elasticity  is  the  ratio  of  the  stress  per 
unit  of  area  to  the  deformation  per  unit  of  length.  The 
modulus  of  rigidity  is  the  amount  of  tangential  stress  per 
unit  of  area,  divided  by  the  deformation  it  produces,  expressed 
in  angular  or  n  measure.  The  maximum  load  is  usually  greater 
than  the  load  at  rupture. 

The  safe  load  must  always  be  less  than  the.  load  at  the 
elastic  limit,  and  is  usually  taken  as  a  certain  portion  of  the 
ultimate  or  breaking  load.  The  ratio  of  the  breaking-load  to 
the  safe  load  is  termed  a  factor  of  safety. 

The  different  kinds  of  stress,  consequently  the  different 
kinds  of  strain  produced,  are :  Longitudinal,  divided  into  tension 
and  compression  ;  Transverse,  ipto  shearing  and  bending ;  and 
Twisting  or  Torsional. 

46.  Strain-diagrams  are  diagrams  which  show  the  rela- 
tions which  the  increments  of  strain  bear  to  the  stress.  If  the 
strain-diagrams  of  several  specimens  be  drawn  on  the  same 
sheet,  the  relative  values  of  stress  and  of  strain  at  elastic  limit 
and  at  breaking  can  be  determined  by  inspection.  Within 
the  elastic  limit  the  diagram  will  be  a  straight  line. 

Strain-diagrams  are  constructed  (see  Article  19,  p.  20)  by  lay- 
ing off  the  strain  on  the  horizontal  axis  to-a  scale  that  is  readily 
apparent  to  the  eye,  and  the  corresponding  loads  as  ordinater 
to  a  convenient  scale,  as  3000  or  5000  pounds  per  inch  :  a  curve 
drawn  through  the  extremities  of  these  various  ordinates  will 
be  the  strain-diagram.  When  no  part  is  perfectly  elastic,  as  in 
cast-iron  or  rubber,  no  portion  of  the  curve  will  be  straight. 

The  general  form  of  the  strain-diagram,  as  drawn  auto- 
graphically,  is  shown  in  Fig.  27.  In  this  diagram  the  strain  is 
represented  by  distances  parallel  to  OX,  the  stress  as  a  certain 
number  of  pounds  per  inch  parallel  to  OY.  For  a  short  dis- 
tance from  O  to  A  the  diagram  is  a  straight  line,  showing  that 
the  increments  of  strain  and  stress  are  uniform ;  at  A  there  is 
a  sudden  increase  in  the  strain,  without  a  marked  increase  in 
load,  shown  by  the  curved  line  A  to  B.  The  point  A  is  often 
spoken  of  as  the  yield-point.  In  most  of  the  ductile  materials 


EXPERIMENTAL  ENGINEERING. 


[§47- 


this  sudden  increase  of  strain  is  accompanied  with  an  apparent 
reduction  of  stress,  as  shown  by  the  curve  from  B  to  C.  This 
reverse  curvature  is  often  well  marked  on  curves  taken  auto- 
matically, and  is  probably  due  to  the  fact  that  the  increase  in 


FIG.  27. —  THE  STRAIN-DIAGRAM. 

strain  is  so  great  that  the  scale-beam  of  the  machine  falls  until 
the  stress  is  increased.  The  curve  then  continues  to  rise,  reach- 
ing its  maximum  position  at  Z>,  and  falling  soon  after  when 
the  specimen  breaks,  as  shown  at  E. 

47.  Viscosity  or  Plasticity. — This  is  the  term  applied  to 
denote  the  change  of  form  or  flow  that  results  from  the  appli- 
cation of  stress  for  a  long  time.  It  is  the  result  of  internal 
molecular  friction,  and  the  resistance  exerted  is  proportioned 
to  the  rapidity  of  the  change.  The  definition  of  viscosity  is 
given  by  Maxwell  (see  Theory  of  Heat)  as  follows :  "  The  vis- 
cosity of  a  substance  is  measured  by  the  tangential  or  shearir  g 


§  47-]  STRENGTH  OF  MATERIALS— GENERAL  FORMULAE.     J  I 

force  on  the  unit  of  area  of  either  of  two  horizontal  planes  at 
the  unit  of  distance  apart,  one  of  which  is  fixed,  while  the 
other  moves  with  the  unit  of  velocity,  the  space  between  being 
filled  with  the  viscous  substance." 

Let  the  substance  be  in  contact  with  one  fixed  plane  and 
with  OIK  plane  moving  with  the  velocity^;  denote  the  dis- 
tance between  the  planes  by  c.  Let  F  be  the  coefficient  of 
shearing-force,  or  the  force  per  unit  of  area  tending  to  move 
the  substance  parallel  to  either  plane.  Let  /*  be  the  coefficient 
of  viscosity. 

Then  we  have 


If  we  let  b  =  the  breadth  and  a  the  length  of  the  plane 
and  R  the  total  force  acting, 

R  =  abF. 
Hence 

"  v  '~  vab* 
When  c,  a,  and  b  each  equal  unity, 


If  R  is  the  moving  force  that  would  generate  a  certain  velocity 
*  in  the  mass  M  in  time  t,  R  will  equal  Mv  -*-  /;  from  which 


Mvc 


of  which  quantities  may  be  determined  by  experiment. 


EXPERIMENTAL   ENGINEERING. 


[§  49- 


48.  Notation. — The  notation  used  is  the  same  as  that  in 
Church's  "  Mechanics  of  Engineering,"  and  is  as  follows : 


Quantity. 

Symbol. 

Maximum 
Load. 

'Breaking- 
Load. 

Elastic 
Limit. 

Safe 
Limit. 

P,n 

i 

Cm 

sm 

lm 

AXm 

€m 
Um 

Mm 

wm 

Jm 

P 

PT 
C 
S 
A 

AX 

€ 

U 
M 
d 
W 
J 

P" 
£,', 

C" 
S" 
A" 
AK' 
e" 
U" 
M" 
d" 
W" 
J" 

P' 

Pr 

C 

s! 

A' 
4X 

e' 
U' 
M' 
d' 
W 
J' 

Load  per  square  inch     •.«•  

"       "  compression             

"        "    shearing   

Increment  of  elongation.  ...      .  .    .  . 

Tension.        Compression.       Shearing. 
Modulus  of  Elasticity..                                         ..Et                  E,                  JS* 

Area  sq.  inches p 

Length,        "      / 

Factor  of  safety n 

Ordinary  moment  of  inertia / 

Polar  moment  of  inertia fp 

Maximum  fibre-distance , ^ 

49.  Formulae  for  Tensile  Strength.  (Church's  Mechanics, 
pp.  207-221.)— Since  in  tension  the  stress  is  uniformly  distrib- 
uted, we  have 

P=FT;   .    . (2) 

P=?> (3) 


(4) 


The  modulus  of  elasticity  by  definition  equals  the  load  per 
square  inch  divided  by  the  strain  per  inch  of  length,  within  the 
elastic  limit.  Hence 


§  51-]  STRENGTH  OF  MATERIALS— GENERAL   FORMULA.      73 

Resilience  U  =  mean  force  X  total  space  =  \P"\"  = 
\F'e"l  =  \T'e"FL  But  Fl  equals  the  volume  V. 

.-.     {7=ir'6"P=iP"6"/.      ....    (6) 

50.  Modulus  of  Elasticity  from  Sound  emitted  by  a 

Wire. — Let  /  equal  the  length  of  the  wire,  d  equal  its  specific 
gravity,  n  equal  the  number  of  vibrations  per  second,  v  equal 
the  velocity  in  feet  per  second. 

Determine  the  number  of  vibrations  by  comparing  the 
sound  emitted,  caused  by  rubbing  longitudinally,  with  that 
made  by  the  vibration  of  a  tuning-fork.  In  this  manner  de- 
termine the  note  emitted.  The  number  of  vibrations  per 
second  can  be  found  by  consulting  any  text-book  devoted  to 
acoustics. 

We  shall  have  finally 

v  =  2nl\ 
also 


from  which 

&d 


This  result  usually  gives  a  larger  value  by  one  or  two  per 
cent  than  that  obtained  by  tension-tests,  owing  to  the  viscosity 
of  the  body. 

51.  Formulae  for  Compression-tests.— The  compression- 
tests  are  of  value  in  determining  the  safe  dimensions  of  mate- 
rial subject  in  use  to  a  crushing  or  compressive  stress.  Nearly 


74  EXPERIMENTAL   ENGINEERING.  [§  51. 

all  bearings  in  machinery,  a  portion  of  the  framework,  the 
connecting-rod  of  an  engine,  during  some  portion  of  a  revo- 
lution, are  illustrations  of  common  occurrence,  of  members 
strained  by  compression.  Columns  and  piers  of  buildings, 
masonry-walls,  are  familiar  illustrations  in  structures. 

The  subject  is  naturally  divided  into  two  heads,  the  strength 
of  short  specimens  and  the  strength  of  long  specimens,  since 
the  strain  is  manifestly  different  in  each  case. 

Short  Pieces,  or  those  in  which  the  length  is  not  more  than 
four  diameters,  yield  by  crushing,  and  the  force  acts  uniformly 
over  each  square  inch  of  area,  so  that  formulae  similar  to  those 
used  in  tension  apply.  (For  notation  see  article  48,  page  62.) 
We  have 

P.  =  FC;    /=£ (8) 


Resilience     Uc  =  ±P'W  =  ±P  fe"l  =  %C"e"Fl.      .     .    (11) 

The  compression-strain  is  accompanied  with  a  shearing- 
strain  acting  at  right  angles  to  the  specimen  equal  to  P  sin  a 
cos  or,  being  a  maximum  when  a  =  45°.  Hence,  brittle 
materials  tend  to  fly  to  pieces  at  that  angle,  leaving  two  pyra- 
mids with  facing  points. 

Long  Pieces,  in  which  the  length  equals  ten  or  twenty  diam- 
eters, yield  by  bending  on  the  side  of  least  resistance. 

Rankine's  formula  is  most  used  for  this  case  (Church's 
Mechanics,  page  374). 

Breaking-load  for  flat  ends, 


(12) 


§  51-]  STRENGTH  OF  MATERIALS—  GENERAL   FORMULA,     75 

Breaking-load  for  round-ended  or  two-pin  column, 


Breaking-load  for  one  round  end  and  one  square  end  or  pin 
and  square  end, 


[126) 


VALUE  OF  COEFFICIENTS  AS  GIVEN  BY  RANKINE. 


Coefficients. 

Cast-iron. 

Wrought-iron. 

Timber. 

C  in  pounds  per  so    inch     •    .  .  . 

8OOOO 

36000 

72OO 

I  -T-  6400 

I  -s-  36000 

I  -T-  3OOO 

Notation  in  above  Formulas. 
,     F  =  area  in  square  inches. 
/  =  length  in  inches. 
K  =  radius  of  gyration. 
K*  —  /  -T-  F.     See  page  78  for  values  of  /. 
In  case  the  modulus  of  elasticity  is  required,  Ruler's  for- 
mula  should  be  used  ;  in  this 

P."  =  EIn*  ~  /'"' 
for  round-ended  columns,  in  which  I"  =  /  —  \9 


For  a  column  with  flat  ends, 


For  a  column  with  one  pin  or  round  end  and  the  other  end 

square, 


Ruler's  formula  has  only  been  approximately  verified  by 
experiment. 


;6  EXPERIMENTAL   ENGINEERING.  [§  52. 

52.  Transverse  Stress. —  Theory. — In  case  of  transverse 
stress  the  force,  or  a  component  of  the  force,  is  applied  at  right 
angles  to  the  principal  dimensions  of  the  material.  The 
material  is  generally  in  the  form  of  a  beam,  and  the  strains 
produced  make  the  beam  assume  a  concave  form  with  refer- 
ence to  the  direction  of  the  force  applied.  The  result  of  this 
is  a  compression  of  the  fibres  nearest  the  force,  and  a  corre- 
sponding elongation  of  those  farthest  away.  The  fibres  of 
the  beam  not  strained  or  deformed  by  any  longitudinal  force 
lie.  in  what  is  called  the  neiitral  axis.  The  curve  which  the 
neutral  axis  assumes  due  to  the  forces  acting  is  termed  the 
elastic  curve. 

The  weight  carried  tends  to  rupture  the  beam  at  right 
angles  to  the  neutral  axis  ;  this  stress  is  equal  to  the  resultant 
force  acting  at  any  point,  and  is  termed  the  transverse  shear. 
In  addition  to  this  there  is  a  shearing-force  tending  to  move  the 
fibres  of  the  beam  with  reference  to  each  other  in  a  longitudi- 
nal direction,  which  is  termed  parallel  shear;  this  force  is  a 
small  one  compared  with  the  other  forces,  and  for  that  reason 
is  difficult  to  measure  experimentally. 

Formula. — In  this  case  the  external  load  is  applied  with  an 
arm,  and  tends  to  produce  rotation  ;  the  result  is  termed  the 
Moment  of  Flexure  or  Bending-moment,  which  is  denoted  by  M. 

The  internal  moment  of  resistance  is  equal  to  //-f-  e,  in 
which  p  equals  the  intensity  of  strain  on  the  outermost  fibre 
of  the  piece,  /  equals  the  moment  of  inertia,  e  equals  the 
distance  of  the  outermost  fibre  to  the  neutral  axis.  Since 
these  moments  must  be  equal,  we  have 

M  —  pI-±e, (14) 

which  formula  may  be  used  for  strength.  We  also  have 

EI~p  =  M,  .......     (15) 

which  may  be  used  for  flexural  stiffness  (Church's  Mechanics, 

//a/ii 

page    250),    in    which    p  =  radius    of    curvature  =  I  -f-  -f^ 
(approximately). 


§  52.]  STRENGTH  OF  MATERIALS—  GENERAL  FORMULA.     77 

Hence 

±EI&  =  M,     ......    (16) 

which  is  the  differential  equation  of  the  elastic  curve. 

To  find  the  external  moment  M,  consider  the  beam  as  a 
lever,  subject  to  action  of  forces,  only  on  one  side  of  the  free 
section.  If  we  consider  A  as  the  amount  carried  by  any  abut- 
ment, or  the  resistance  acting  at  one  end,  x  the  distance  to  the 
free  section,  W  the  weight  of  any  load  or  loads  between  the 
abutment  and  the  free  section,  and  x'  the  distance  of  the  point 
of  centre  of  gravity  of  these  loads  to  the  free  section,  then  by 
the  principles  of  moments  we  have  the  general  equation 

M=Ax-  Wx'.    .     .'..-...     .     (17) 

In  problems  relating  to  the  elastic  curve  assume  the  general 
differential  equation 


Find  the  numerical  value  of  M  expressed  in  terms  of  one 
dimension  of  the  beam  as  variable.  Thus,  as  above,  M  =  Ax 
—  Wx.  Select  the  origin  of  co-ordinates  in  such  a  position 
that  the  constants  of  integration  can  be  determined.  Then 

integrate.    The  first  integration  will  give  the  value  of  -~  or 

the  tangent  of  the  elastic  curve  ;  the  second  integration  will 
give  j,  the  ordinate  to  the  elastic  curve. 

The  parallel  shear  is  maximum  in  the  neutral  axis,  and  de- 
creases either  way  proportionally  to  the  ordinates  of  a  parabola. 

The  value  of  the  parallel  shear  per  unit  of  section  in  the 
neutral  axis  is 

-.         (  area  above  neu-  |        (  the  distance  of  its  } 

Z0  =  -jT-X  K       tral   axis   (or  V  X  •<      centre  of  gravity  >;  (18) 

•        I       below)  )        I      from  that  axis.     ) 


EXPERIMENTAL   ENGINEERING. 


[§52. 


in  which  /  is  equal  to  the  moment  of  inertia,  J  the  total  trans- 
verse shear,  and  <£0  the  thickness  of  beam  in  the  neutral  axis. 

In  the  ordinary  cases  of  shearing-forces,  such  as  act  on 
rivets  or  pins,  the  intensity  is  uniform  ;  this  case  is  considered 
later. 

The  following  tables  of  moments  of  inertia,  of  transverse 
loads,  and  of  external  moments  will  be  useful  in  working  up 
the  results  of  the  experiments. 

TABLE    NO.    I. 

MOMENTS  OF  INERTIA. 


Ordinary  Moment. 
7. 

Polar  Moment. 
9 

Max.  Fibre 
Dist. 
c 

Rectangle   width  b  depth  h  

rV^8 

J±6A(t*  4-  tf) 

kk 

Hollow  rectangle,  symmetrical.... 
Triangle,  width  =  bt  height  =  h... 
Circle  of  radius  r                          ... 

t"*(Mi»  -  bM) 

w># 

\Ttr* 

Jritr4 

\m 
& 

& 

Ring  of  concentric  circles     ...        . 

±Tt(r^  —  rJ\ 

±Ti(r,  4       rJ\ 

Rhombus  h  —  vertical  diagonal.  .  . 

&# 

^,6* 

&# 

i£4 

M 

ij 

"              "         (£)at4*°.. 

TV* 

±b* 

2" 
1A  4/n 

^v 

-%u  y  & 

TABLE   NO.    II. 

FORMULAS  FOR  TRANSVERSE  LOADS. 


CANTILEVERS. 

BEAMS  WITH  Two 
SUPPORTS. 

With  one  End 
Load  P-. 
Wt.  of  Beam 
neglected. 

With  Uni- 
form Load. 
W=-wl. 

Load  P,  in 
Middle. 
Wt.  of  Beam 
neglected. 

Uniform 
Load. 
W=wl. 

^Deflection  —  d          

\PP  H-  El 
Pie  -s-  / 
R'l  -*-  le 
Ple^-I 

i 

i 
Pfl  -*-  3^7 
P  at  support 

\WP+  El 
Wle  -j-  27 
*R'I  +  te 

Wle  -f-  27 

2 
f 

i 

WP  -s-  Ml 
W  at  support 

A/V»  -s-  El 
Pie  +  47 
4^'7  H-  le 
Pie  -5-  47 
4 
16 
4 
Pfl  +  tfdl 

$P  at  supp't 

3|,^/3  +EI 
Wle  -f-  87 
8/?'7  -f  le 
Wle  +  87 
8 
*ia 

V 

S»V»-*-384^ 
\W  at  supp't 

Maximum  fibre-strain^  

Coefficient  R' 

Relative  strength,  equal  length    .,. 
Relative  stiffness,  equal  load  
"              "         safe  load  

§  52-J    STRENGTH  OF  MATERIALS— GENERAL  FORMULA.     79 


S 

AS* 


I     I 


S 


Jsj 


Hie* 


•*-  b£O 

o  a  «•> 


•HI 


II 

* 


s    s     s     a     ^ 

O  QJ  V  O 

•F      «?       •?        *P        "2 


V 


s    . 

J--& 

.2rt'C 


I  i 


0     * 
V5     -O 


ill  § 


£o 
'i'i 

II 


m 
f 


«1 

.11 
II 

• 

?'  ^l.j 


0   II  0 


i  -1  a  -:*i  - 

l-.%'p!t  i 

i  ia  i  ill  j? 


80  EXPERIMENTAL   ENGINEERING.  [§53- 

53.  Moment  of  Inertia  by  Experiment. — If  the  body  can 
be  suspended  on  a  knife-edge  so  that  it  can  be  oscillated  back- 
ward and  forward  like  a  pendulum,  its  moment  of  inertia  can  be 
found  as  follows :  First,  balance  the  body  on  a  knife-edge,  and 
find  experimentally  the  position  of  its  centre  of  gravity;  denote 
the  distance  of  the  centre  of  gravity  from  the  centre  of  suspen- 
sion by  5.  Weigh  the  body,  and  compute  its  mass  M\  denote 
its  weight  by  W.  Suspend  the  body  on  the  knife-edge,  and  set 
it  swinging  through  a  very  small  arc ;  find  the  time  of  a  single 
vibration,  by  allowing  it  to  swing  for  a  long  time  and  divid- 
ing by  the  number  of  vibrations.  Let  t  equal  the  time  in 
seconds  of  a  single  vibration  or  beat ;  let  K  equal  radius  of 
gyration,  so  that  MK*  equals  moment  of  inertia. 

Then,  by  mechanics, 


or,  by  reduction, 

/a<rc 

(19) 


In  this  equation  K  is  reckoned  from  the  point  of  suspension, 
and  the  moment  of  inertia  is  the  moment  around  the  point  of 
suspension. 

The  moment  of  inertia  about  a  parallel  axis  through  the 
centre  of  gravity,  may  be  denoted  by  MK*>  and  we  shall  have 


*See  Weisbach,  Vol.  I.,  page  662. 


§  55-]  STRENGTH  OF  MATERIALS—  GENERAL  FORMULA.     8  1 

from  which 

K?  =  K*-  Sa, 

and 

MK;  = 


54.  Shearing-strain.  —  This  strain  acts  in  a  transverse 
direction,  without  an  arm,  and  thus  tends  to  produce  a  square 
break  ;  it  acts  uniformly  over  the  whole  section,  so  that 

P=SF;   S  =  P+F.     .     .     .     .     .     (20) 

The  strain  produces  on  the  molecules  of  the  material  an 
angular  distortion,  which  is  usually  expressed  in  n  measure,  or 
the  linear  length  of  the  degree  of  distortion  to  a  radius  unity, 
and  is  denoted  by  tf. 

Let  /,  be  the  stress  per  square  inch. 


(21) 


Es  is  termed  the  modulus  of  rigidity. 

The  coefficient  of  shearing-strength  S  can  be  obtained  by 
direct  experiments,  by  using  the  specimen  in  the  form  of  pins 
or  rivets  holding  links  together,  the  links  being  fitted  to  go  in 
the  machine  like  tensile  specimens,  and  tensile  force  applied  ; 
if  the  specimen  is  a  plate,  its  resistance  to  shearing-strain  can 
be  found  by  forcing  a  punch  through,  as  in  compression- 
strains.  The  angular  distortion  cannot  be  measured  directly, 
but  may  be  determined  by  tests  in  torsion,  as  described. 

55.  Torsion.  —  The  strain  produced  by  torsion  is  essentially 
a  shearing-strain  on  the  elements  of  the  specimen.  The  effect 
of  torsion  is  to  arrange  the  outer  fibres  of  the  specimen  into 
the  form  of  helices,  as  can  readily  be  seen  by  examining  a  test- 
piece  broken  by  torsion  stress  ;  each  one  of  these  fibres  makes 
an  angle  with  its  original  position  or  axis  of  the  piece,  equal 
to  its  angular  distortion,  or  tf,  which  is  expressed  in  n  measure. 
This  has  the  effect  also  of  moving  any  particle  in  the  surface  of 


82  EXPERIMENTAL   ENGINEERING.  [§  5$. 

the  specimen,  through  an  angle  lying  in  a  plane  perpendicular 
to  the  axis  and  with  its  vertex  in  the  axis.  This  last  angle  is 
called  a.  Letting  /  equal  the  length  of  the  specimen,  e  equal 
its  radius,  we  have,  neglecting  functions  of  small  angles, 

ea  =  ldt      .........     (22) 

from 

6  =  ea  -f-  L    .    .......  (220) 

But  since  Es—  ps  -f-  <?, 

Es=psl-~eoL-,    .....     .    .  (22b) 

from  which  Es  ,  the  modulus  of  rigidity,  may  be  computed. 
Since  the  external  moment  of  forces  is  equal  to  the  internal 
moment  of  resistance,  if  we  let  P  equal  the  external  load,  a  its 
lever-arm,  and  IP  the  polar  moment  of  inertia,  we  will  have 


-',     ......    (23) 

from  which 

ps  =  Pze  +  Ip  .......     (24) 

For  a  circular  rod  of  radius  r^  , 


IP  =  — —,  also  e  =  r. 


Let  the  external  moment  Pa  =  Mt .     Then 


§  57.J  STRENGTH  OF  MATERIALS—  GENERAL  FORMULAE.     83 

The  torsional  resilience,  or  work  done,  will  equal  the  aver- 
age load  multiplied  by  the  space,  or 


(25) 


56.  Modulus  of  Rigidity  of  a  Wire  by  swinging  under 
Torsion.  —  The  transverse  modulus  of  elasticity,  or  the  modu- 
lus of  rigidity,  can  be  determined  by  hanging  a  heavy  weight 
on  the  wire,  and  swinging  it  around  a  vertical  axis  passing 
through  its  point  of  suspension.  Let  /equal  its  length  in  feet,. 
r  its  radius  in  feet,  IP  the  polar  moment  of  inertia  of  the  swing- 
ing weight,  /  the  time  in  seconds  of  an  oscillation.  Let  £f 
be  the  modulus  of  rigidity.  Then 


E  -  (26\ 

'  '  •  '  ( 


57-  Relation  of  Es  and  Et . — Let  the  distortion  in  direc- 
tion of  the  stress  equal  e,  the  angular  lateral  distortion  =  tf,  the 
lineal  lateral  distortion  =  m  ;  then 

tan  (45°  --  -)  =  l-f~  =i-m-e,  nearly. 
But  since  d  is  small, 


tan  Us0 J  =  i  —  tf,  nearly. 


Hence,  by  substituting, 

6  =  m  +  e. 


Now 


,  =       and    £,  =       ; 

6  O 


84  EXPERIMENTAL  ENGINEERING.  [§  58- 

Hence 

Es_  e  e 

Et~~  2$  ~~  2(m-\-  e) 

In  cast-iron,  by  experiment,  Prof.  Bauschinger  found  for 
cast-iron  m  —  .236;  hence  for  this  case  Es  =  0.407^. 

58.  Combination  of  Two  Stresses.  Intensity  of  combined 
Shearing*  and  normal  Stress. — Let  q  be  the  intensity  of  the 
shearing-stress,  which  acts  on  the  transverse  section  and  on  a 
parallel  section,  and  let/  be  the  intensity  of  the  normal  stress 
on  the  transverse  section  ;  it  is  required  to  find  a  third  plane 
such  that  the  stress  on  it  is  wholly  normal,  and  to  find  r  the 
intensity  of  that  stress ;  let  this  plane  make  an  angle  6  with 
the  transverse  section.  Then,  from  equilibrium  of  forces, 

(r  —  p)  cos  6  =  q  sin  6,     and     r  sin  6  =  q  cos  6. 
Hence  (f  =  r(r  —  p\ 

tan  26=  2q-+p (27) 

r  =  %p±  Vf  +  lp\  ....     (28) 

58a.  Twisting  combined  with  Longitudinal  Stress.— In 
a  circular  rod  of  radius  r^  ,  a  total  longitudinal  force  P  in  the 
direction  of  the  axis  gives  a  longitudinal  normal  stress 

/,  =  P  -r-  area  —  /  -r-  nr?. 

A  twisting-couple  M  applied  to  the  same  rod  gives  a  shearing- 
stress  whose  greatest  intensity 


*  Encyc.  Britannica,  art.    "  Strength  of  Materials. 


§  59-]  STRENGTH  OF  MATERIALS— GENERAL  FORMULA.     85 

The  two  together  give  rise  to  a  pair  of  principal  stresses,  as 
above, 


r  =  ~  +  A  /\=^-\  4--^-.    .  (2g\ 

\     ;*/ 


59.  Twisting  combined  with  Bending. — This  important 
practical  case  is  realized  in  a  crank-shaft. 

Let  P  be  the  force  applied  to  the  crank-shaft ;  let  R  be  the 
radius  of  the  crank-shaft ;  let  B  equal  the  outboard  bearing, 
or  the  distance  between  the  plane  of  revolution  of  the  centre 
of  the  crank-pin  and  the  bearing. 

If  we  neglect  the  shearing-force,  there  are  two  forces  acting: 
a  twisting-force  Mt  =  PR,  and  bending-moment  M9  =  PB. 
The  stresses  per  unit  of  area  on  the  outer  fibre  would  be/>,  = 
4M9  -r-  itr*  (in  which  rl  is  the  radius  of  the  crank-shaft)  from 
formulae  for  transverse  strength,  and  /,  =  2Ml  -5-  nr*  from  for- 
mula for  torsion. 

Combining  these  as  in  equation  (27),  we  find  for  the  prin- 
cipal stress 


r  =  2(M,  ±  VM?  +  M?)  +  *rf. 
By  substituting  values  of  Ml  and  M9  , 

r  =  2P(B  ±  VB*  +  R>)  +n  r?.    ....    (30) 
The  greatest  shearing-stress  equals 


The  axes  of  principal  stresses  are  inclined  so  that 

te*26  =  M,  +  Mt  =  R  +  B.     ......     (32) 


86  EXPERIMENTAL   ENGINEERING.  [g  60. 

60.  Thermodynamic  Relations.*  —  Thermodynamic  theory 
shows  that  heat  is  absorbed  when  a  solid  is  strained  by 
opposing  and  is  given  out  when  it  is  strained  by  yield- 
ing to  any  elastic  force  of  its  own,  the  strength  of  which 
would  diminish  if  the  temperature  were  raised.  As,  for 
example,  a  spiral  spring  suddenly  drawn  out  will  become 
lower  in  temperature,  but  when  suddenly  allowed  to  draw 
m  will  rise  in  temperature.  With  an  india-rubber  band  the 
reverse  condition  is  true,  which  indicates  that  the  effect  of 
heat  is  to  contract  instead  of  to  expand  the  rubber.  From 
this  theory  the  rise  in  temperature  can  be  calculated  for  a 
given  strain.  Thus  let  /  equal  the  absolute  temperature  of  the 
body;  0  the  elevation  of  temperature  produced  by  sudden 
specific  stress/  ;  let  e  equal  the  corresponding  strain  ;  J  Joule's 
equivalent  ;  k  the  specific  heat  of  the  body  under  constant 
stress  ;  6  its  density.  Then 


in  which  both  *and/  are  infinitesimal,  or  very  small  quantities., 
Rubber  differs  from  other  material  in  the  relation  of  strain 
to  stress  and  consequently  in  the  direction  of  curvature  of 
the  strain  diagram.  While  most  materials  show  a  great  in- 
crease in  strain  after  passing  the  elastic  limit,  rubber  on  the 
contrary  shows  a  decrease. 

*See  paper  by  Win.  Thomson  in  Philosophical  Magazine  1877,  also  vol.. 
m,  page  814,  ninth  edition  Encyc.  Britannica. 


CHAPTER   IV. 


STRENGTH  OF   MATERIALS-TESTING  MACHINES. 

61.  Testing-machines  and  Methods  of  Testing.— The 

testing-machines  consist  essentially  of,  fin,t,  a  device  for  weigh- 
ing  or  registering  the  power  applied  to  rupture  material ; 
second,  head  and  clamps  for  holding  the  specimen  ;  third,  suit- 
able machinery  for  applying  the  power  to  strain  the  specimen  ; 
and  fourth,  a  frame  to  hold  the  various  parts  together,  which 
must  be  of  sufficient  strength  to  resist  the  stress  caused  by 
rupture  of  the  specimen.  Machines  are  built  for  applying 


FIG.  29.— OLD  FORM. 


FlG.  30.—  f  HURSTON,  POLMEYER. 


tensile,  compressive,  transverse,  and  torsional  stresses ;  they 
vary  greatly  in  character  and  form ;  some  are  adapted  for 
applying  more  thau  one  kind  of  stress,  while  others  are  limited 
to  a  single  specific  purpose. 

lr.  ^11  machines  the  weighing  device  should  be  accurate  and 
sufficiently  sensitive  to  detect  any  essential  variation  in  the 
stress,  and  every  laboratory  should  be  provided  with  means  for 
calibrating  testing-machines  from  time  to  time ;  the  weighing 
system  is  usually  independent  of  the  system  for  applying 
power,  although  in  certain  early  machines  a  single  lever 
mounted  on  a  fulcrum  was  used,  as  shown  in  Figs.  29  and  30, 
and  in  which  the  power  system  and  weighing  system  were  com' 
bined,  the  power  applied  being  measured  by  multiplying  the 
weight  by  the  ratio  of  the  lever-arms  b/a. 


§  6l.]  STRENGTH  OF  MA  TERIALS— TESTING-MACHINES.       89 

The  power  system,  when  independent  of  the  weighing  sys- 
tem, usually  consists  of  a  hydraulic  press,  as  shown  in  Fig.  31,  or 
a  train  of  gears,  as  shown  in  Fig.  32.  The  principal  advantage 
of  having  the  power  system  independent  from  the  weighing 
system  is  due  to  the  fact  that  under  such  conditions  the 
stretching  of  the  specimen,  which  almost  invariably  takes  place, 
does  not  affect  the  accuracy  of  weighing. 

The  shackles  or  clamps  for  holding  the  specimen  vary  with 
the  strain  to  be  applied.  The  clamps  for  tension-tests  usually 
consist  of  truncated  wedges  which  are  inserted  in  rectangular 


FIG.  31.— HYDRAULIC  PRESS. 


FIG.  32.— FORM  OF  GEARING. 


openings  in  the  heads  of  the  testing-machines,  and  between 
which  the  specimen  is  placed.  The  interior  face  of  the  wedges 
is  for  flat  specimens,  plane  or  slightly  convex  and  serrated,  but 
for  round  or  square  specimens  is  provided  with  a  triangle  or 
V-shaped  groove  into  which  the  head  of  the  specimen  is  placed. 
When  the  strain  is  applied  to  the  specimen  the  wedges  are 
drawn  close  together,  exerting  a  pressure  on  the  specimen 
somewhat  in  proportion  to  the  strain  and  often  injurious  to  its 
strength.  In  many  instances  shackles  with  internal  cut  threads 
are  used,  into  which  specimens  provided  with  a  corresponding 
external  thread  are  screwed  ;  this  latter  construction  is  much 
preferable  to  the  former,  though  adding  much  to  the  expense 
of  preparing  the  specimen.  It  is  very  important  that  the 
shackles  should  hold  the  specimens  firmly  and  accurately  in 


90  EXPERIMENTAL   ENGINEERING.  |_8  Ol* 

the  axis  of  the  machine  and  should  not  exert  a  crushing  strain 
which  is  injurious  to  the  material. 

General  Character  of  Testing-machines. 

Testing-machines  are  classified  as  vertical  or  horizontal, 
depending  upon  the  position  of  the  specimen  ;  this,  however^ 
is  not  an  important  structural  difference,  although  certain 
classes  of  machines  are  better  adapted  for  the  one  method  of 
testing  than  the  other.  Machines  may  also  be  classified  as 
tensive,  compressive,  or  transverse  machines,  depending  upon 
whether  they  are  better  suited  to  apply  one  class  of  stresses  than 
the  other,  but  as  the  method  of  testing  is  generally  dependent 
simply  upon  the  method  of  supporting  the  specimen,  this 
classification  is  of  little  importance  structurally.  Machines  can 


B' 


FIG.  33.— WICKSTEED,  MARTENS,  MICHAELIS,  BUCKTON. 

perhaps  be  best  classified  by  the  form  and  character  of  weigh- 
ing mechanism,  it  being  generally  understood  that  power  may 
be  applied  through  the  medium  of  gears  or  by  a  hydraulic 
press,  as  desired,  and  with  any  class  of  machine. 

Under  this  classification  we  have : 

First,  the  simple  lever  machines,  forms  of  which  have  been 
shown  in  Figs.  29  and  30,  in  which  the  power  for  breaking 
was  obtained  from  the  weighing  mechanism.  Fig.  33  shows 
a  single-lever  machine  much  used  at  the  present  time  in  Eng- 
land, in  which  the  power  is  applied  to  the  specimen  at  B,  and 
the  amount  of  stress  is  determined  by  the  position  of  the  jockey 
^weight  w,  and  the  amount  pf  weight  on  the  poise  R. 


§  6 1 .]  S TRENG  TH  OF  MA  TERIA  LS—  TES  TING-MA  CHINES.     9 1 


D(o> 


A  single-lever  machine  in  which  the  lever  is  of  the  second 
order  is  shown  in  Fig.  34.      The  specimen  is  placed  between 
the  fulcrum  and  the  weigh- 
ing mechanism.    The  latter 
consists  of  a  hydraulic  cy- 
linder with  diaphragm  and 
attached  gauge,  and  is  in- 
teresting as  being  the  proto- 
type of  the  Emery  testing-  FIG.  S^- 
machine. 

Second,  differential- lever  machines,  one  kind  of  which  is 
shown  in  Fig.  35.  This  consists  of  a  single  lever  with  poise,  to 
which  the  draw-head  is  connected  by  links  placed  at  unequal 


FIG.  35.— RIEHLE. 

distances   from    the  fulcrum.     A  machine   of    this  form  was 
manufactured  at  one  time  by  Riehle  Brothers.* 

Third,  compound-lever  machines.  These  have  been  much 
used  in  America  for  the  last  twenty  years,  and  are  manufactured 
by  Riehl£  Brothers,  Olsen,  and  Fairbanks.  In  these  machines 
power  is  usually  applied  by  gearing;  at  least,  such  a  construc- 
tion is  generally  preferred  in  this  country.  The  diagram, 

*  The  forces  acting  in  this  machine  can  be  represented  by  the  following 
equation: 


Rd  -f  we  = 


(af-bg). 


92 


EXPERIMENTAL  ENGINEERING. 


[§6i. 


Fig.  36,  shows  the  arrangement  of  levers  adopted  in  the  Fair- 
banks machine.  Power  is  applied  at  F,  specimen  is  placed  at  s9 
and  the  stress  is  transmitted  by  the  various  levers  P,  E,  and  c 


FIG.  36. — FAIRBANKS  MACHINE. 

to  the  weighing-scale.     The  various  fulcrums  marked  r  rest 
on  a  fixed  support. 

Fig.     37     shows   arrangement    of    levers  adopted  in   the 
Olsen  and  Riehle  machines,  power  being  applied  to  the  lower 

draw-head    B,    and     the    stress       ^A 

transmitted  through  the  speci- 
men by  means  of  the  various 
levers  to  the  weighing-scale  w. 
In  this  diagram  P  denotes  the 
position  of  fixed  fulcrums.  By 
placing  the  specimen  between 
the  lower  draw-head  B  and  the 
platform  EE,  it  may  be  broken  FIG.  37.— OLSKN  AND  RIEHLS. 

by  compression.      By  providing  suitable  support   resting  on 
the  platform  EE  a  transverse  stress  can  be  applied. 

Fourth,  direct-acting  hydraulic  machines.  Fig.  38  shows 
a  simple  form  of  a  hydraulic  machine,  in  which  power  is 
applied  by  liquid  pressure  to  move  the  piston  R,  the  speci- 
men being  located  at  s  for  tension  and  at  a'b'  for  compression. 
Machines  of  this  kind  have  been  built  of  the  very  largest 
capacity,  as  for  instance  that  designed  by  Kellogg  at  Athens, 
Pa.,  has  a  capacity  of  1^250,000  pounds,  and  at  the  Phoenix 


F 

*      %         v 

Q                H 

*  y   [ 

ill  ,  A     ii  ap        zjjp 

§  6 1 .  ]  s  TRENG  TH  OF  MA  TERIA  LS—  TES  TING-MA  CHINES.     93 

Iron  Works  has  a  capacity  of  2,000,000  pounds,  while  one 
built  by  Professor  Johnson  at  St.  Louis  has  a  capacity  of 
about  750,000  pounds.  In  all  these  machines  the  stress  is 
measured  by  multiplying  the  readings  of  the  gauge  by  a  con- 
stant depending  upon  the  area  of  the  cylinder,  the  effect  of 


FIG.  38. — KELLOGG,  JOHNSON. 


friction  being  eliminated  by  keeping  the  piston  rotating,  or  in 
other  cases  neglecting  it  or  determining  its  amount  and  cor- 
recting the  results  accordingly.  Such  machines  are  not- 
adapted  for  accurate  testing,  but  are  suited  for  testing  of  a 
character  which  permits  considerable  variation  from  the 
correct  results. 

A  modified  form  of  the  simple  hydraulic  machine  was 
made  by  Werder  in  1852,  having  a  capacity  of  100  tons,  the 
principle  of  its  construction  being  shown  in  Fig.  39.  In  this 
machine  the  line  of  action  of  the  stress  is  in  RF,  while  that 


FIG.  39. — THE  WERDER,  1852. 

of  the  resistance  is  in  the  line  Ad  which  is  to  one  side  of  RF. 
These  forces  are  balanced  by  adjusting  the  weights  on  the 
scale-beam,  thus  providing  means  of  weighing  the  force 
applied  to  the  specimen. 

Fig.  40  is  a  sketch  of  the  working  parts  of  the  Maillard 
machine,  in  which  the  weighing  apparatus  consists  of  a  fluid 
which  is  put  under  pressure  by  means  of  a  diaphragm  against 


94 


EXPERIMEN  TA  L   ENG I  NEE  RING. 


L§  61. 


which  the  stress  applied  to  the  specimen  reacts.  This  force 
is  measured  on  a  hydraulic  gauge  similar  in  many  respects 
to  the  weighing  apparatus  of  the  Emery  testing-machine. 


q_F= 

D 


FIG.  40.  —  MAILLARD. 


Fifth,  the  Emery  machine.  The  general  principle  of  the 
Emery  testing-machine  is  shown  in  Fig.  41.  Power  is 
applied  by  means  of  the  double-acting  hydraulic  press  R  so  as 
to  break  the  specimen  either  in  tension  or  compression,  as 
desired.  The  specimen  is  placed  at  s,  and  the  stress  trans- 
mitted is  received,  if  in  tension,  first  by  the  draw-head  BB, 
thence  transmitted  to  the  draw-head  B'B't  thence  in  turn  to 


B\ 


FIG.  41.— EMERY. 

the  fluid  in  the  hydraulic  support  v  through  a  frictionless  dia- 
phragm, from  which  the  fluid  pressure  is  transmitted  to  the 
vessel  with  the  smaller  diaphragm  d,  the  pressure  of  which  is 
balanced  and  weighed  on  the  weighing-scale  w.  If  the 
specimen  is.  in  compression  the  force  is  transmitted  by  the 
draw-head  BE  to  the  bottom  of  the  hydraulic  support  z>,  thus 
crowding  the  hydraulic  support  and  its  contents  against  the 
diaphragm,  which  in  turn  causes  a  liquid  pressure  which  is 
measured  on  the  weighing-scale  as  before.  The  springs  which 


§  6l.]  STRENGTH  OF  MA  TERIALS-TESTING-MACHINES.      9$ 

receive  the  pressure  of  the  liquid  are  adjusted  by  screws  rr9 
connected  to  the  frame,  and  of  sufficient  strength  to  resist  the 
greatest  stress  applied  in  compression. 

In  order  that  the  levers  of  a  testing-machine  may  transmit 
the  force  to  the  weighing  poise  with  as  little  loss  as  possible, 
and  in  such  a  manner  that  a  large  force  can  be  balanced  by  a 
small  weight,  a  knife-edge  bearing  is  in  nearly  every  case  pro- 
vided for  each  lever.  The  knife-edge  as  usually  constructed 
is  a  piece  of  hardened  steel  with  a  sharp  edge  which  is  inserted 
rigidly  in  the  weighing-lever  and  rests  upon  a  hardened  steel 
plate  fastened  to  the  fulcrum,  although  in  some  cases  the 
positions  of  knife-edge  and  plate  are  reversed.  The  knife-edge 
should  be  as  sharp  as  it  can  be  made  without  crumbling  or  cut- 
ting the  contact-plate,  and  it  should  be  kept  clean  and  free 
from  dirt  or  rust  in  order  to  keep  the  friction  at  the  lowest 
possible  point.  In  practice  the  knife-edge  is  made  from  30 
to  110  degrees,  depending  upon  the  load.  Machines  of  the 
type  shown  in  Fig.  37  have  been  constructed  in  which  the 
friction  and  other  losses  as  shown  by  trial  did  not  exceed  100 
pounds  in  100,000. 

The  fulcrums  for  supporting  the  levers  in  the  Emery  test- 
ing-machine are  thin  plates  of  steel  rigidly  connected  to  both 
the  lever  and  its  support,  as  shown  in  Figs.  41,  51,  and  52. 
A  flexure  of  the  fulcrum-plates  is  produced  by  an  angular 
motion  of  the  levers;  but  as  this  motion  in  practice  is  small, 
and  as  the  fulcrums  are  very  thin,  the  loss  of  force  is  inappre- 
ciable and  all  friction  is  eliminated.  The  plate  fulcrums  also 
possess  the  advantage  of  holding  the  levers  so  that  end  motion 
is  impossible,  and  thus  preventing  any  error  in  weighing  due 
to  change  of  lever-arm.  The  peculiar  form  of  the  plate  kil- 
crums  is  such  as  to  be  unaffected  by  dirt  ;  furthermore  in 
practice  a  higher  degree  of  accuracy  in  weighing  has  been  ob- 
tained than  is  possible  with  knife-edge  levers.  The  principal 
characteristics  of  the  Emery  machine  are,  first,  the  hydraulic 
supports,  which  are  vessels  filled  with  a  liquid  and  having  a 
flexible  side  or  diaphragm,  which  transmits  the  pressure  to  a 
similar  support  in  contact  with  the  weighing  apparatus.  The 


96 


EXPERIMENTAL   ENGINEERING. 


[§62. 


detailed  construction  of  an  hydraulic  support  as  used  in  a  ver- 
tical machine  is  shown  in  Fig.  50,  its  method  of  operation  in 
Fig.  41.  Second,  the  peculiar  steel-plate  fulcrums,  which 
have  been  described.  These  together  with  excellent  work- 
manship throughout  have  served  to  make  the  Emery  testing- 
machine  an  instrument  of  precision  with  a  greater  range  of 
capacity  and  an  accuracy  far  superior  to  that  of  any  other 
machine. 

Fig.  42  gives   a  perspective  view  of  the  Emery  machine 
with  the  working  parts  marked  the  same  as  in  the  diagram. 


FIG.  42.— EMERY  HORIZONTAL  MACHINE. 

In  this  figure  M  is  the  pump  for  operating  the  hydraulic 
press,  hh'  the  connecting  piping,  TT  screws  forming  a  part 
of  the  frame  and  used  for  adjusting  the  position  of  the  press 
for  different  lengths  of  specimens,  and  of  sufficient  strength  to 
withstand  the  shock  due  to  breaking;  Pis  the  weighing-case, 
which  contains  ;>.  very  elaborate  system  of  weights  which  can 
be  npplied  without  handling,  as  described  in  detail  later. 

62.  Weighing  System.— The  weighing  system  in  the  pres- 
ent English  machines,  and  in  former  ones  built  in  this  country, 
consists  of  a  single  lever  or  scale-beam,  along  which  can  be 


§  63 .]    STRENG  TH  OF  MA  TERIALS—  TESTING-MA  CHINES.       97 

moved  a  poise,  and  which  can  be  connected  by  one  or  more 
levers  to  the  test  specimen.  Such  machines  are  objectionable 
principally  from  the  space  occupied. 

The  weighing  device  in  nearly  all  recent  machines  consists 
of  a  series  of  levers,  arranged  very  much  as  in  platform-scales, 
finally  ending  in  a  graduated  scale-beam  over  which  a  poise  is 
made  to  move.  The  machines  are  usually  so  constructed  that 
the  effect  of  the  strain  on  the  specimen  is  transmitted  into 
a  downward  force  acting  on  the  platform,  and  the  effect  of 
a  given  stress  is  just  the  same  as  a  given  load  on  the  plat* 
form. 

The  weighing-levers  usually  consist  of  cast-iron  beams  car- 
rying  hardened  steel  knife-edges,  which  in  turn  rest  on  har- 
dened-steel bearing  plates.  This  is  the  system  adopted  by  most 
scale-makers  for  their  best  scales. 

In  the  Emery  testing-machines,  which  are  especially  noted 
for  their  accuracy  and  sensitiveness,  the  knife-edges  and  bear- 
ing plates  are  replaced  by  thin  plates  of  steel,  the  flexibility  of 
which  permits  the  necessary  motion  of  the  levers. 

The  weighing  device  should  be  accurate,  and  sufficiently  sen- 
sitive to  detect  any  essential  variation  in  the  stress.  The 
amount  of  sensitiveness  required  must  depend  largely  on  the 
purposes  of  the  test.  An  amount  less  than  one  tenth  of  one 
per  cent  will  rarely  make  any  appreciable  difference  in  the  re- 
sult, and  probably  may  be  taken  as  the  minimum  sensitiveness 
needed  for  ordinary  testing.  Means  should  be  provided  for 
calibrating  the  weighing  device.  This  can  be  done,  in  the  class 
of  machines  under  consideration,  by  loading  the  lower  platform 
with  standard  weights  and  noting  the  corresponding  readings 
of  the  scale-beams.  Testing-machines  may  be  calibrated  with  a 
limited  number  of  standard  weights,  by  the  use  of  a  test- 
specimen,  which  is  not  to  be  strained  beyond  the  elastic  limit. 
The  weights  are  successively  added  and  removed,  and  strain  is 
maintained  on  the  test-piece,  equal  to  the  reading  on  the  cali- 
brated portion  of  the  scale-beam. 

63.  The  Frame. — The  frame  of  the  machine  must  be 
sufficiently  heavy  and  strong  to  withstand  the  shock  produced 


98  EXPERIMENTAL  ENGINEERING.  [§  65. 

by  a  weight  equal  to  the  capacity  of  the  machine  suddenly  ap. 

plied. 

The  weighing  levers  must  sustain  all  the  stress  or  force  act- 
ing on  the  specimen,  without  sufficient  deflection  to  affect 
accuracy  of  the  weighing,  and  the  frame  must  be  able  to  sus- 
tain the  shock  consequent  upon  the  sudden  removal  of  the 
load,  due  to  breaking,  without  permanent  set  or  deflection. 

64.  Power  System. — The  power  to  strain  or  rupture  the 
specimen  is  usually  applied  through  the  medium  of  a  train  of 
gears  or  by  a  hydraulic  press,  operated  by  power  or  hand. 
The  hydraulic  machine  is  very  convenient  when  the  stress  is 
less  than   50,000  pounds ;  but  if  there  is  any  leakage  in  the 
valves,  the  stress  will  be  partially  relieved  the  instant  the  pump 
ceases  to  operate,  and  difficulty  may  be  experienced  in  ascer- 
taining the  stretch  for  a  given  load. 

65.  Shackles. — The  shackles  or  clamps  for  holding  the 
specimen  vary  with  the  strain  to  b^  applied.     These  clamps  for 
tension  tests  usually  consist  of  truncated  wedges  which  are  in- 
serted in  rectangular  openings  in  the  heads  of  the  testing-ma- 
chines, and  between  which  the  specimen  is  placed.     The  inte- 
rior face  of  the  wedges  is  for  flat  specimens  plane  and  serrated, 
but  for  round  or  square  specimens  it  is  provided  with  a  trian- 
gular or  V-shaped  groove,  into  which  the  head  of  the  specimen 
is  placed     When  the  strain  is  applied  to  the  specimen  these 
wedges  are  drawn  closer  together,  exerting  a  pressure  on  the 
specimen  somewhat  in  proportion  to  the  strain  and  often  in- 
jurious to  its  strength.     In  tensile  testing  it  is  essential  to  the 
correct  determination  of  the  strength  of  the  specimen  that  the 
force  shall  be  applied  axially  to  the  material ;  in  other  words,  it 
shall  have  no  oblique  or  transverse  component.     This  requires 
that  the  wedge  clamps  shall  be  parallel  to  the  specimen,  and 
that  the  heads  which  contain  the  clamp  shall  separate  in  a 
right  line  and  parallel  to  the  specimen. 

This  construction  is  well  shown  in  the  following  description 
of  the  clamps  used  in  the  Olsen  and  Riehle  testing-machines. 

A  plan  and  section  of  the  draw-heads  used  with  the  Olsen 
machine  is  shown  in  Fig.  43.  The  small  numbers  refer  to 


§  65.]   STRENGTH  OF  MA  TERIALS— TESTING-MACHINES.       99 

the  same  part  in  each  view,  and  also  in  Figs.  56  to  60,  so  that 
any  part  can  be  easily  identified  ;  60,  59  is  a  counterbalanced 
lever  used  to  prevent  the  wedges  falling  out  when  the  strain 
is  relieved ;  63,  63,  is  a  screw  connected  to  a  plunger  for  ad- 
justing  the  space  into  which  the  wedge-clamps  are  drawn.  A 
lateral  motion  of  the  specimen  is  obtained  by  unscrewing  on 
one  side  and  screwing  up  simultaneously  on  the  other  side : 


FIG.  43. — DRAW-HEAD  TO  OLSEN'S  TESTING-MACHINE. 

this  adjustment  is  of  advantage  in  some  instances  in  centring 
the  specimen.  For  use  of  the  other  parts  shown  in  Fig.  43, 
see  Art.  64. 

The  clamps  used  by  Riehl£  Brothers  for  holding  flat  speci- 
mens are  shown  in  Fig.  44  and  Fig.  46,  as  follows : 


100 


EXPERIMENTAL   ENGINEERING. 


[§&>. 


Fig.  45  is  a  plan  of  wedge-clamp,  with  specimen  in  posi- 
tion;  CC,  curve-faced  wedges;  D,  specimen;  A,  draw-head; 
and  BB  tension-rods. 


FIG.  44- 


FIG.  45. 


FIG.  46. 


Fig.  46  is  a  sectional  view  of  same.  Fig.  44  ;s  a  view  of 
the  wedge-faced  clamp.  The  inclination  of  the  surfaces  of  the 
wedges  are  exaggerated  in  the  drawings,so  as  to  distinctly  set 
forth  their  features. 

Wedges  have  been  made  with  spherical  backs,  and  a  por- 
tion of  the  draw-heads  mounted  on  ball  surfaces  in  order  to 
insure  axial  strains.  Special  holders  into  which  screw-threads 
have  been  cut  have  been  used  with  success,  and  in  many 
instances  the  specimens  have  been  fastened  to  the  draw-heads 
by  right  and  left  threaded  screws. 

66.  Specifications  for  Government  Testing-machine. — 
The  large  machine  in  use  by  the  United  States  Government  at 
the  Watertown  Arsenal  was  built  by  Albert  H.  Emery.  The 
machine  is  not  only  of  large  capacity,  but  is  extremely  dnlicate 
and  very  accurate.  A  perspective  view  of  the  machine  is 
shown  in  Fig.  28. 

The  requirements  of  the  United  States  Government  as  ex- 
pressed  in  the  specifications,  which  were  all  successfully  met, 
were  as  follows : 


66.]    STRENGTH  OF  MA  TERIALS— TESTING-MACHINES. 


101 


102  EXPERIMENTAL   ENGINEERING.  [§  6/, 

ist.  A  machine  with  a  capacity  in  tension  or  compression 
of  800,000  pounds,  with  a  delicacy  sufficient  to  accurately  reg- 
ister the  stress  required  to  break  a  single  horse-hair. 

2d.  The  machine  should  have  the  capacity  of  seizing  and 
giving  the  necessary  strains,  from  the  minutest  to  the  greatest, 
without  a  large  number  of  special  appliances,  and  without 
special  adjustments  for  the  different  sizes. 

3d.  The  machine  should  be  able  to  give  the  stresses  and 
receive  the  shocks  of  recoil  produced  by  rupture  of  the  speci- 
men without  injury.  The  recoil  from  the  breaking  of  a  speci- 
men which  strains  the  machine  to  full  capacity  may  amount 
to  800,000  pounds,  instantly  applied.  The  machine  must  bear 
this  load  in  such  a  manner  as  to  be  sensitive  to  a  load  of  a 
single  pound  placed  upon  it,  without  readjustment,  the  next 
moment. 

4th.  The  parts  of  the  machine  to  be  at  all  times  accessible. 

5th.  The  machine  to  be  operated  without  excessive  cost. 

67.  Description  of  Emery  Testing-machine. — These  ma- 
chines are  now  constructed  by  Wm.  Sellers  &  Co.  of  Phila- 
delphia, under  a  license  from  the  Yale  &  Towne  Mfg.  Co.  of 
Stamford,  Conn. 

The  following  description  will  serve  to  explain  the  principle 
on  which  the  machine  acts : 

The  machine  consists  of  the  usual  parts:  I.  Apparatus 
to  apply  the  power.  2.  Clamps  for  holding  the  specimen. 
3.  The  weighing  device  or  scale. 

1.  The  apparatus  for  applying  power  consists  of  a  large  hy- 
draulic press,  which  is  mounted  on  wheels  as  shown  in  the  en* 
gravings,   Fig.  28  and  Fig.  47,  and  can  be  moved  a  greater  or 
less  distance  from  the  fixed  head  of  the  machine.     Two  large 
screws  serve  to  fix  or  hold  this  hydraulic  press  in  any  position 
desired,  according  to  the  length  of  the  specimen  :  and  when 
rupture  is  produced  the  shock  is  received  at  each  end  of  these 
screws,  which  tend  to  alternately  elongate  and  compress,  and 
take  all  the  strain  from  the  foundation. 

2.  Clamps  for  holding  the  specimen.     These  are  peculiar  to 
the  Emery  machine,  and  ar-e  shown  in  Fig.  47  in  section.     This 


§67.]     STRENGTH  OF  MATERIALS— TESTING-MACHINES.     103 

figure  also  shows  a  section  of  the  fixed  head  of  the  machine, 
and  a  portion  of  the  straining-press,  with  elevation  of  the 
holder  for  the  other  end  of  the  specimen. 

The  clamps,  numbered  1484  in  Fig.  47,  ire  inserted  between 
two  movable  jaws  (14/7),    which  are    pressed  together   by  a 


Ftr,.  <8. —  ELEVATION  OF  THE  VERTICAL  MACHINE. 


FIG.  49. — SCALE-BEAM  AND  CASE. 


hydraulic  press  (1480),  resting  on  the  fixed  support  (1476).  By 
this  heavy  lateral  pressure  force  equal  to  1,000,000  pounds  can 
be  applied  to  hold  the  specimen.  The  amount  of  this  force  is 
shown  by  gauges  connected  to  the  press  cylinder,  and  can  be 
regulated  as  required. 


104  EXPERIMENTAL   ENGINEERING.  [§     ?6. 

For  the  vertical  machines  these  shackles  or  holders  are  ar- 


FIG.  50.— THE  BASE-FRAME  AND  ABUTMENTS. 

ranged   so   as  to  have  sufficient  lateral  motion  to  keep  in  the 
line  of  the  test-piece. 

3.   The  weighing  device.    This  is  the  especial  peculiarity  of 


6/.]    STRENGTH  OF  MATERIALS— TESTING-MACHINES. 


I05 


the  Emery  machine  :  instead  of  knife-edges,  thin  plates  of 
steel  are  used,  which  are  flexed  sufficiently  to  allow  the  neces- 
sary motion  of  the  levers.  The  steel  used  varies  from  0.004  to 


FIG.  51.— BEAM  FOR  PLATFORM-SCALE. 


0.05  inch  thick,  and  the   blades  are   so  wide  that  the  stress 
does  not  exceed  40,000  to  60,000  pounds  per  square  inch. 

Fig.  52  shows  the  form  of  fulcrums  used  for  light  forces 
when  the  steel  fulcrums  are  in  tension. 


FIG.  52.— CLAMPING  SUSPENSION  FULCRUMS. 


The  method  of  measuring  the  load  is  practically  that  of 
the  hydraulic  press  reversed,  but  instead  of  pistons,  diaphragms 
having  very  little  motion  are  used.  Below  the  diaphragm  is 
a  very  shallow  chamber  connected  by  a  tube  to  a  seconr 


106  EXPERIMENTAL   ENGINEERING.  [§67. 

chamber  covered  with  a  similar  diaphragm,  but  of  a  different 
diameter.  Any  downward  pressure  on  the  first  diaphragm  is 
transmitted  to  the  second,  giving  a  motion  inversely  as  the 
squares  of  the  diameters.  This  latter  motion  may  be  farther 
increased  in  the  same  manner,  with  a  corresponding  reduction 
in  pressure,  or  it  may  at  once  be  received  by  the  system  of 
weighing  levers.  The  total  range  of  motion  given  the  first 
diaphragm  in  the  5O-ton  testing-machine  is  ^-jnsWff  Part  °f  an 
inch,  but  the  indicating  arm  of  the  scales  has  a  motion  of  T^ 
of  an  inch  fur  each  pound.  This  increase  of  motion  and  cor- 
responding reduction  of  pressure  is  accomplished  practically 
without  friction.  These  parts  will  be  well  understood  by  Figs. 
50,  51,  and  52.  The  diaphram  with  connecting  pipe,/",  is 
shown  between  the  abutments  EE  in  Fig.  50. 

Fig.  48  shows  the  elevation  of  the  vertical  machine  arranged 
for  transverse  tests.  Fig.  49  shows  the  scale-beam  and  case,  and 
Fig.  50  is  a  section  of  the  base-frame  and  hydraulic  supports. 
In  this  last  figure  the  diaphragm,  filled  with  liquid,  is  placed 
between  the  frames  EE.  These  frames  are  allowed  the  neces 
sary  but  slight  vertical  motion  by  the  thin  fulcrum-strips  b  and 
c,  but  at  the  same  time  are  held  from  lateral  motion.  The 
frame  EE  and  diaphragms  are  supported  by  springs  d,  so  as 
to  have  an  initial  tension  acting  on  the  test-piece.  The  dia- 
phragm and  its  enclosing  rings  fill  the  whole  space  between 
the  frame  to  within  0.005  inch,  which  is  the  maximum  amount 
of  motion  permitted. 

The  pressure  on  the  diaphragm  between  the  frames  EE  is 
communicated  by  the  tube  f  to  a  similar  diaphragm  in  com- 
munication with  the  weighing-levers.  Fig.  5 1  represents  the 
weighing-levers  for  platform-scales.  In  case  a  diaphragm  is  used 
it  rs  placed  beneath  the  column  A  ;  the  motion  of  the  column 
A  is  communicated  to  the  scale-beams  by  a  system  of  levers 
as  shown. 

The  scale-beam  of  the  testing-machine  is  shown  in  Fig.  49, 
and  is  so  arranged  that  by  operating  the  handles  on  the  out- 
side of  the  case  the  weights  required  to  balance  the  load  can 
be  added  or  removed  at  pleasure.  The  device  for  adding  the 


§68.]    STRENGTH  OF  MATERIALS— TESTING-MACHINES.     IO/ 


weights  is  shown  in  Fig.  53.  a,  b,  c,  d,  e,  and  /  are  the  weights, 
which  are  usually  gold-plated  to  prevent  rusting.  These  when 
not  in  use  are  carried  on  the  supports  A  and  B  by  means  of 
pins.  When  needed,  these  supports  can  be  lowered  by  the  out- 
side  levers,  and  as  many  weights  as  are 
needed  are  added  to  the  weighing-poise 
CD. 

68.  Riehle  Brothers'  Hydraulic 
Testing-machines. — The  testing-ma- 
chines built  by  Riehle  Brothers  of  Phil- 
adelphia vary  greatly  in  principles  and 
methods  of  construction.  In  the  ma- 
chines built  by  this  firm,  power  is  ap- 
plied either  by  hydraulic  pressure  or  by 
gearing,  and  the  weighing  device  con- 
sists of  one  or  more  levers  working  over 
steel  knife-edges,  as  in  the  usual  scale 
construction. 

Machines  have  been  built  by  this  firm 
since  1876.  The  form  of  the  first 
machine  constructed  was  essentially 
that  of  a  long  weighing-beam  sus- 
pended in  a  frame  and  connected  by 
differential  levers  to  the  specimen,  the 
power  being  applied  by  a  hydraulic 
press.  The  later  forms  are  more  com- 
pact. The  standard  hydraulic  machine 
as  constructed  by  this  firm  is  shown 
in  Fig.  54.  In  this  machine  the  cylin- 
der of  the  hydraulic  press,  which  is 
situated  directly  beneath  the  specimen, 
is  movable,  and  the  piston  is  fixed. 

This  motion  is  transmitted  through  the  specimen,  and  is 
resisted  by  the  weighing  levers  at  the  top  of  the  machine, 
which  are  connected  by  rods  and  levers  to  the  scale-frame. 
Two  platforms  connected  by  a  frame  are  carried  by  the  weigh- 
ing levers:  the  upper  one  is  slotted  to  receive  the  wedges  for 


108  EXPERIMENTAL  ENGINEERING.  [§  69. 

holding  the  specimen  :  the  lower  one  forms  a  plane  table.  The 
intermediate  platform,  or  draw-head,  can  be  adjusted  in  dif- 
ferent positions  by  turning  the  nuts  on  the  screws  shown  in 
the  cut.  For  tension-strains  the  specimen  is  placed  between 
the  upper  and  intermediate  head ;  for  compression  it  is  placed 
between  the  intermediate  and  lower  heads.  An  attachment  is 
often  added  to  the  lower  platform,  so  that  transverse  strains 
can  be  applied. 

The  cylinder  is   connected   by  two  screwed  rods   to  the 
intermediate  platform  or  draw-head,  and  when  it. is  forced 


FIG.  54. — HYDRAULIC  TESTING-MACHINE. 

downward  by  the  operation  of  the  pump   this  draw-head  [9 
moved  in  the  same  direction  and  at  the  same  rate. 

69.  Riehle  Power  Machines. — The  machines  in  which 
power  is  applied  by  gearing  are  now  more  generally  used  than 
hydraulic  machines.  Fig,  55  shows  the  design  of  geared  ma- 
chine now  built  by  Riehle  Bros.,  in  sizes  of  50,000,  100,000,  and 
200,000  pounds  capacity.  In  this  machine  both  the  gearing 
for  applying  the  power  and  the  levers  connected  with  the 
weighing  apparatus  are  near  the  floor  and  below  the  specimen, 
thus  giving  the  machine  great  stability.  The  heads  for  hold- 
ing the  specimen  are  arranged  as  in  the  hydraulic  machine,  and 
power  is  applied  to  move  the  intermediate  platform  up  or  down 


§69.]    STRENGTH  OF  MATERIALS— TESTING-MACHINES. 


as  required.  The  upper  head  and  lower  platform  form  a  part 
of  the  weighing  system.  The  intermediate  or  draw-head  may 
be  moved  either  by  friction-wheels  or  spur-gears  at  various 


speeds,  which  are  regulated  by  two  levers  convenient  to  the 
operator  standing  near  the  scale-beam. 

The  poise  can  be  moved  backward  or  forward  on  the  scale- 


no 


EXPERIMEN  TAL   ENGINEERING. 


[§70- 


beam,  without  disturbing  the  balance,  by  means  of  a  hand- 
wheel,  opposite  the  fulcrum  on  which  the  scale-beam  rests. 

The  scale-beam  can  be  read  to  minute  divisions  by  a 
""ernier  on  the  poise. 

70.  Olsen    Testing-machine.  — General  Form. — The  ma- 


FIG.  56- THE  OLSEN  TESTING  MACHINE.  FRONT  VIEW. 

chines  of  Tinius  Olsen  &  Co.  of  Philadelphia  are  all  operated 
by  gearing,  driven  by  hand  in  the  machines  of  small  capacity, 
and  by  power  in  those  of  larger  capacity. 

The  general  form  of  the  machine  is  shown  in  Figs.  56  and 
57,  from  which  it  is  seen  that  the  principles  of  construction 
iuv,  the  same  as  in  the  machine  last  described. 


^  7  I . J    S  TK /  NG TH  OF  MA  TERIA L S—  TESTING-MA  CHINES.     I  I  I 

The  intermediate  platform  or  draw-head  is  operated  by- 
four  screws  instead  of  by  two,  and  there  is  a  marked  difference 
in  the  arrangement  of  the  weighing-levers  and  in  the  gearing. 

The  machine  can  be  operated  at  various  rates  of  speed  in 
either  direction,  and  is  readily  controlled  by  convenient  levers. 


FJG.  57  —THE  OLSEN  TESTING-MACHINE,  REAR  VIEW. 

71.  The  Olsen  Autographic  Apparatus. — This  apparatus 
for  drawing  strain-diagrams  is  entirely  automatic,  and  is 
Operated  substantially  as  follows : 

The  diagram  is  drawn  on  a  drum  (103),  parallel  to  the  scale- 
beam,  by  a  pencil  actuated  by  a  screw-thread  cut  to  a  fine  piu_. 


112 


EXFER1MEN TAL   E NGINEERING. 


on  the  end  of  the  rod  which  actuates  the  poise  (106),  so  that 
the  pencil  will  move  in  a  definite  ratio  to  that  of  the  poise. 
The  drum  is  actuated  by  the  stretch  of  the  specimen.  This 
is  brought  about  by  four  fingers  shown  in  Fig.  56,  and  on  a 
larger  scale  in  Fig.  58  by  numbers  82  and  83.  These  fingers, 
shown  in  plan  in  Fig.  59'  tend  to  separate  and  follow  any 
motion  of  the  collars  (65)  placed  on  the  test-piece,  as  shown  in 
Fig.  56;  the  motion  of  these  fingers  is  multiplied  five  times, 


FlG.6o. 


FIG.  58. 

and  connected  by  steel  bands  to  the  drum,  102,  in  such  a  man* 
ner  that  the  resultant  force  only  is  effective  to  rotate  the  drum. 
The  poise  is  moved  by  a  friction  device  attached  to  the 
main  power  system,  which  is  thrown  into  or  out  of  gear  auto- 
matically by  an  electric  current,  as  required  to  keep  the  beam 
floating  ;  the  current  passes  through  the  scale-beam  in  opposite 
directions,  according  as  the  place  of  contact  is  above  or  below 


?2.]    STRENGTH  OF  MA  TERIALS— TESTING-MA  CHINES.      1 1  3 


the  beam.  Finally,  an  alarm-bell  is  rung  whenever  the  scale- 
poise  moves  beyond  its  normal  distance,  thus  calling  the  at- 
tention of  the  operator. 

Gauge-marking  Device. — A  special  and  very  ingenious  ar- 
rangement, shown  in  Fig.  60,  is  used  to  hold  the  test-piece  and 
mark  the  extreme  gauge-marks  in  any  position  desired. 

72.  Parts  of  Olsen  Machine. — The  following  reference 
numbers  to  the  parts  of  the  Olsen  machine  will  serve  to  show 
the  construction  : 


1.  Entablature.  61 

2.  Columns.  62 

3.  Platform  supporting  columns.  63 

4.  Pivots.  64 

5.  Lower  moving  head. 

22.  Sleeve  on  driving-shaft.  72. 

24.  Rock-shaft  operating  lever  shifting     73. 

22.  74. 

25.  Hand-lever  operating  24.  75. 

26.  27.   Pulleys  rotating  driving-shaft.      78. 
28,  29.   Friction-clutches   engaging  26     82, 

with  driving-shaft.  85. 

30.  Sleeve  operating  clutches.  86. 

31.  Forked  lever  controlling  sleeve  30.     95. 

33.  Hand-lever  opeiating  30.  96. 

34.  Grooved  wheel  on  driving-shaft.         97. 

40.  Tilting  bearing.  98. 

41.  Band-wheel.  99. 

42.  Endless  band.  100. 
44.    Helical  spring.  loi. 
46.   Fulcrum  of  lever  117.  102. 

48.  Specimen  under  test.  103. 

49.  Gripping  jaws.  104. 

50.  Projecting  flanges  on  jaws  49.  105. 

51.  Block-slide.  106. 

52.  Grooves  in  51.  m. 

53.  Slotted  slide  supporting  49.  117. 

54.  Opening  in  53.  118. 

55.  Eye  in  53.  118'. 

56.  Bolt  connecting  53  and  57.  119. 

57.  Lever  to  open  and  shut  jaws.  144. 

58.  Fulcrum  of  57.  145. 

59.  Counterweight.  146. 

60.  Handle  of  lever  57. 


Plungers  for  slides  51. 

Screws  for  61. 

Screw-bolt. 
.  Collars  or  clamps  for  caliper  bear- 

ing. 
.  Guiding-block. 

Cam. 

Lever  moving  87. 
,  Sliding-blocks. 

Polygonal  prism  in  75. 

83.  Calipers. 

Arm  of  caliper. 

Clamps. 

Cord  operating  recording-cylinder. 

Pulley. 

Lever. 

Fulcrum  to  97. 

Pulley  or  sheave. 

Drum  or  winding-barrel  of  IO2, 

Link. 

Recording-cylinder. 

Pencil. 
Screw. 

Screws  shifting  106. 

Poise  or  weight. 

Balancing  pivot  of  beam. 
Force  multiplying  lever. 
Weighing-beam. 

Slide  to  small  poise  on  118. 
Link. 

Endless  band  for  moving  poise. 
Guiding-pulleys. 
Grooved  wheel. 


114  EXPERIMENTAL  ENGINEERING.  |_§  73- 

73.  Thurston's  Torsion  Testing-machine. — Both  the 
breaking-strength  and  the  modulus  of  rigidity  can  be  obtained 
from  the  autographic  testing-machine  invented  by  Professor 
Thurston  in  1872. 


FIG.  61. — THURSTON'S  AUTOGRAPHIC  TORSION  TESTING-MACHINE. 

In  this  machine  the  power  is  applied  by  a  crank  at  one 
side,  tending  to  rotate  the  specimen,  the  specimen  being  con- 
nected at  the  opposite  end  to  a  pendulum  with  a  heavy 
weight 

The  resistance  offered  by  the  pendulum  is  the  measure  of 


g  73.]    STRENGTH  OF  MA  TERIALS— TESTING-MACHINES.     I  I  5 

the  force  applied,  since  it  is  equal  to  the  length  of  the  lever- 
arm  into  the  sine  of  the  angle  of  inclination,  multiplied  by  the 
constant  weight  P.  A  pencil  is  carried  in  the  axis  of  the 
pendulum  produced,  and  at  the  same  time  is  moved  parallel  to 
the  axis  of  the  test-piece  by  a  guide  curved  in  proportion  to 
the  sine  of  the  angle  of  deviation  of  the  pendulum,  so  that  the 
pencil  moves  in  the  direction  of  the  axis  of  the  specimen  an 
amount  proportional  to  the  sine  of  this  angle.  A  drum  carry- 
ing a  sheet  of  paper  is  moved  at  the  same  rate  as  the  end  of 
the  specimen  to  which  the  power  is  applied.  Now  if  the  pencil 
be  made  to  trace  a  line,  it  will  move  a  distance  around  the 
drum  which  is  equal  to  the  angle  of  torsion  (a)  expressed  in 
degrees  or  n  measure,  and  it  will  move  a  distance  parallel  to 
the  axis  of  the  test-piece  proportional  to  the  moment  of  ex- 
ternal forces,  Pa. 

The  diagram  Fig.  62,  from  Church's  "  Mechanics  of  En- 
gineering," shows  the  working  portions  of  the  machine  very 
clearly.  In  the  figure  P  is  the  pendulum,  the  upper  end  of 


FIG.  62. 


which  moves  past  the  guide  WR,  and  is  connected  by  the  link 
FA  with  the  pencil  A  T.  The  diagram  is  drawn  on  a  sheet  of 
paper  on  the  drum,  which  is  rotated  by  the  lever  b.  The 


II  6  EXPERIMENTAL   ENGINEERING,  [§73- 

drum  moves  through  the  angle  a,  relatively  to  the  pendulum 
which  moves  through  the  angle  ft.  The  test-piece  is  inserted 
between  the  pendulum  and  drum. 

The  value  of  a  in  degrees  can  be  found  by  dividing  the 
distance  on  the  diagram  by  the  length  of  one  degree  on  the 
surface  of  the  paper  on  the  drum,  which  may  be  found  by 
measurement  and  calculation. 

Application  of  the  Equations  to  the  Strain-diagram.—  For 
the  breaking-load  apply  equation  (23)  of  Chapter  III., 


(23) 


The  external  moment  Pa  equals  Pr  sin  ft,  in  which  P  is 
the  fixed  weight,  r  the  length  of  the  pendulum,  ft  the  angle 
made  with  the  vertical.  Hence 

Pr  sin  ft  =  f,ff  +  e. 


In  this  equation  P  and  r  are  constant,  and  depend  upon  the 
machine  ;  Ip  and  e  are  constant,  and  depend  upon  the  test- 
piece. 

sin  ft  is  the  ordinate  in  inches  to  the  autographic  strain- 
diagram,  and  can  be  measured  ;  knowing  the  constant,  /,  may 
be  computed. 


For  the  modulus  of  rigidity,  apply  equation  (220),  Chapter 
III.,  page  72. 

Es  —psl  -~-  ea  =  Plr  sin  ft  -£•  IPOL. 

In  this  equation  sin  ft  is  the  ordinate  to  the  strain-diagram,  and 
a  the  corresponding  abscissa,  the  other  quantities  are  constant, 
and  depend  on  the  machine  or  on  the  test-piece. 

The  Resilience  (see  equation  (25),  page  83)  is  the  area  of  the 
diagram  within  the  elastic  limit,  expressed  in  absolute  units. 

U  =  \Paa  =  \Pr  sin  fta. 


§  75-]    STRENGTH  OF  MATERIALS— TESTING-MACHINES.     I  i; 

The  Helix  Angle  (see  equation  (22),  page  82)  6  =  ea  -r-  /,  in 
which  /  is  the  length  of  the  specimen  in  inches.  The  elongation 
of  the  outer  fibre  can  be  computed  by  multiplying  /  by  secant  d. 
The  per  cent  of  elongation  is  equal  to  secant  tf.  (Sec  d  is 
equal  to  the  square  root  of  I  -f-  tan2  6.) 

74.  Machine  Constants. —  To  obtain  the  Constants  of  the 
Machine. — First,  the  external  moment  Pa.  This  is  obtained  on 
the  principle  that  it  is  equal  to  any  other  external  moment 
which  holds  it  in  equilibrium.  Swing  the  pendulum  until  its 
centre-line  is  horizontal ;  support  it  in  this  position  by  a  strut 
resting  on  a  pair  of  scales;  the  product  of  the  corrected  reading 
of  the  scales  into  the  distance  to  the  axis  on  the  arm  will  give 
Pa.  Check  this  result  by  trials  with  the  strut  at  different  points. 
Correct  for  friction  of  journal.  Second,  the  value  of  the  scale  of 
ordinates  can  be  obtained  by  measuring  the  ordinate  for  ft  =  90° 
and  for  {3  —  30°,  since  sine  90°  =  I  and  sine  30°  —  J.  Third,  the 
value  of  the  scale  of  abscissae  can  be  obtained  by  dividing  the 
abscissa  on  the  diagram  by  the  radius  of  the  drum  including 
the  paper.  This  may  be  expressed  in  degrees  by  dividing  by 
the  length  of  one  degree. 

Constants  of  the  Material  are  obtained  by  measuring  the 
dimensions  of  the  specimen.  The  values  of  /and  e  are  given 
on  page  78. 

Conditions  of  Accuracy. — In  obtaining  these  values,  the  fol 
lowing  conditions  are  assumed  :  Firstly,  the  test-piece  is  exactly 
in  the  centre  of  motion  of  the  pendulum  and  of  the  drum ;  sec- 
ondly, the  pencil  is  in  line  of  the  pendulum  produced  ;  thirdly, 
the  curve  of  the  guides  is  that  of  the  sine  of  the  angle  of  devia- 
tion ;  and,  fourthly,  the  specimen  is  held  firmly  from  rotation 
by  the  shackles  or  wedges,  and  yet  allowed  longitudinal  motion. 
These  constitute  the  adjustments  of  the  machine,  and  must 
be  carefully  examined  before  each  test.  Any  eccentricity  of 
the  axis  of  the  specimen  will  lead  to  serious  error. 

63.  Power  Torsion-machine. — This  machine  is  shown  in 
Fig.  630.  Power  is  applied  at  various  rates  of  speed  by  means 
of  the  gearing  shown.  The  specimen  is  held  by  means  of  two 
chucks:  the  one  on  the  left  is  rotated  an  amount  shown  by  the 


Il8  EXPERIMENTAL   ENGINEERING.  [§75- 

graduated  scale  in  degrees ;  the  one  on  the  right  is  prevented 
from  rotating  by  a  lever,  so  connected  to  the  scale-beam  that 
when  it  is  balanced  the  reading  is  proportional  to  the  torsional 
force  or  external  moment-  transmitted  through  the  specimen, 
expressed  in  foot-pounds,  inch-pounds,  or  any  other  units 
desired.  The  weighing  head  is  suspended  so  as  to  permit  free 
elongation  of  the  specimen.  The  chucks  used  have  self-cen- 
tering jaws  which  will  hold  the  specimen  rigidly  and  central 
during  application  of  the  stress. 

Machines  of  the  general  class  shown  in  the  figure  are  made 
in   Philadelphia   both  by  Riehl£  Brothers  and  Tinius  Olsen, 


FIG.  63.— THE   RIEHLE   TORSION  MACHINE. 

which  are  adapted  to  testing  of  specimens  of  varying  diameters 
and  lengths.  In  the  Riehle  machine  shown,  the  adjustment 
for  specimens  of  various  lengths  is  made  by  moving  the  power 
head  ;  in  the  Olsen  machine  the  adjustment  is  made  by  mov- 
ing the  weighing  head  and  scale-beam,  which  are  arranged  in 
a  plane  at  right  angles  to  the  specimen. 

The  graduated  scale  attached  to  the  machine  for  angle  of 
torsion  should  seldom  be  used  for  that  purpose,  as  the  specimen 
.is  quite  certain  to  slip  to  greater  or  less  extent  in  the  machine 
arid  considerable  error  will  result. 


§75-]  STRENGTH  OF  MATERIALS-TESTING-MACHINES.  1 1  Sa 

In  the  Olsen  machine  the  angle  of  torsion  may  be  measured 
by  clamping  dogs  on  the  specimen  at  each  end  so  as  to  engage 
the  projections,  shown  at  b,  Fig.  630,  of  the  index-rings,  which 
are  free  to  move  over  the  graduated  scales  of  the  chucks.  The 
angle  of  torsion  of  the-  specimen,  for  a  length  represented  by  the 
distance  between  the  centres  of  the  dogs,  is  the  angle  turned 
through  by  the  movable  chuck  less  the  sum  of  the  angles  through 


FIG.  630.  —  OLSEN   TORSION   MACHINE. 


which  the  index-rings  are  pushed  by  the  dogs.  Let  a\=  angle 
through  which  movable  chuck  is  rotated,  0:2  =  angle  through 
which  index-  ring  on  the  movable  chuck  is  pushed  by  the  dog, 
«3  =  angle  through  which  index-ring  on  fixed  chuck  is  pushed  by 
the  dog,  and  a  =  angle  of  torsion.  Then 


This  angle  is  measured  through  short  ranges  by  means  of  two 
index-arms  clamped  to  the  specimen,  as  shown  at  c.  One  arm 
carries  a  pointer  which  plays  over  an  arc  (d),  graduated  in  inches, 
whose  centre  of  curvature  is  the  centre  of  the  specimen.  The 
distance  traversed  by  the  pointer  divided  by  the  radius  of  the  arc 
gives  the  angle  of  torsion  in  circular  measure. 

The  constant  of  the  machine,  or  the  value  of  the  graduations 


EXPERIMENTAL   ENGINEERING. 


on  the  scale-beam,  may  be  found  as  follows  (see  Fig.  636)  :  The 
fixed  chuck  is  rigidly  connected  to  link  K  as  shown.  The  tor- 
sion moment  (Pa)  on  the  specimen  tends  to  rotate  the  chuck  and 

link  as  indicated  by  the  arrow.  The 
only  additional  forces  acting  on  K  are 
the  vertical  forces  of  strut  PI  and  of 
the  frame  through  the  knife-edges  at 
R.  The  right  end  of  link  K  is  pre- 
vented from  dropping  down,  when  no 
load  is  on  the  specimen,  by  a  strut  act- 
ing upward  at  R  (not  shown  in  fig- 
FlG-  63&-  ure).  R  may  therefore  act  either 

upward  or  downward,  depending  upon  the  intensity  of  Pa. 
The  weight  of  K  may,  howerer,  be  entirely  neglected  since  the 
counterpoise  of  the  machine  may  be  so  set  that  the  system  is  in 
equilibrium  with  no  stress  on  the  specimen. 

With  the  dimensions  shown,  weight  of  poise  =40  pounds, 
length  between  divisions  on  scale-beam  =  f  inch,  consider  K 
as  a  free  body.  Then  2(Pa)=o  and  2Y=o.  From  which 

Pa  =  i2Pi+SR    and    Pi=R, 
or  Pa  =  2oPi  ........     (i) 

PI  acts  at  a  lever-arm  of  2  inches  in  the  lower  lever  G,  and  P2 
acts  at  a  lever-arm  of  30  inches.  Then 

2Pi=3oP2     and    Pi  =  isP2.     ....     (2) 
P  acts  on  scale-beam  at  a  lever-  arm  of  2  inches,  and  this  moment 
must  be  balanced  by  moving  the  poise  W  along  the  distance  x. 
From  which 

tPt-Wx.      .......    (3) 

From  (i),  (2),  and  (3)  we  have 


Make  x  =  i  scale  division  =  §  inch. 

Pa  =4000  inch-pounds. 

Since  the  value  of  each  division  as  marked  on  scale-beam  is 
200,  the  constant  of  the  machine  is  20. 


§  77-1  STRENGTH  OF  MATERIALS—  TESTING-MACHINES. 

For  an  accurate  determination  of  the  angle  "of  torsion,  it 
is  important  that  the  specimen  be  kept  straight  during  the 
application  of  stress,  and  that  the  angle  of  torsion  be  measured 
from  arcs  or  scales  having  the  same  centre  as  the  specimen. 
The  method  of  measuring  the  angle  of  torsion,  as  described 
for  a  specimen  in  the  Olsen  machine,  is  accurate  and  generally 
applicable. 

76.  Impact-testing  Machine.  —  The  Drop  Test  —  Testing  by 
Impact.  —  This  test,  see  Art.  105,  is  recommended  for  material 
used  in  machinery,  railroad  construction,  and  generally  when- 
ever the  material  is  likely  to  receive  shocks  or  blows  in  use. 

This  test  is  usually  performed  by  letting  a  heavy  weight 
fall  on  to  the  material  to  be  tested.  The  Committee  on  Stand- 
ard Tests  of  the  American  Society  of  Mechanical  Engineers 
recommend  that  the  standard  machine  for  this  purpose  consist 
of  a  gallows  or  framework  operating  a  drop  of  twenty  feet,  the 
weight  to  be  2000  pounds,  the  machine  to  be  arranged  sub- 
stantially like  a  pile-driver.  The  impact  machine  designed  by 
Mr.  Heisler  consists  of  a  pendulum  with  a  heavy  bob,  which 
delivers  a  blow  on  the  centre  of  a  bar  securely  held  on  two 
knife-edge  supports  affixed  to  a  heavy  mass  of  metal.  This 
machine  is  especially  designed  for  comparative  tests  of  cast- 
iron  ;  it  is  furnished  with  an  arc  graduated  to  read  the  vertical 
fall  of  the  bob  in  feet,  and  a  trip  device  "for  dropping  the  ram 
from  any  point  in  the  arc.  A  paper  drum  can  be  arranged 
for  automatically  recording  the  deflection  of  the  test-pieces. 

Let  W  =  the  weight  of  the  bob  ; 

h  =  the  distance  fallen  through; 
P=  centre  load; 
K  =  deflection. 
Then 

Wh  = 
Hence 


77.  Machines  for  Testing  Cement.  —  Cement  mortar  can 

be  formed  into  cubes,  and  after  hardening  can  be  tested  in  the 


120 


EXPEKIMEN  TA  L   ENGINEERING. 


usual  testing-machines  for  compression ;  but  tensile  tests  are 
usually  required,  and  for  this  purpose  a  delicate  machine  with 
special  shackles  is  needed.  In  order  that  the  tests  may  give 
correct  results,  it  is  necessary  that  the  power  be  applied  uni- 


FIG.  64. — FAIRBANKS'  CEMENT-TESTING  MACHINE. 

formly,  and  absolutely  in  the  line  of  the  axis  of  the  specimen; 
and  to  make  different  tests  comparable,  the  specimen,  or  as  it 
js  called,  the  briquette,  must  be  always  of  the  same  shape  and 
size,  and  made  in  exactly  the  same  manner.  The  engraving 
(Fig.  64)  shows  Fairbanks  Automatic  Cement  Tester,  in  which  the 
power  is  applied  by  the  dropping  of  shot  into  the  pail  F.  The 
specimen  is  held  between  clamps,  which  are  regulated  at  the 


§77-]    STRENGTH  OF  MATERIALS— TESTING-MACHINES.     121 

proper  distance  apart  by  the  screw  P.  At  the  instant  of  rup. 
ture  the  scale-beam  D  falls,  closes  a  valve,  and  stops  the  flow  of 
shot.  In  Fig.  64  M  is  a  closed  mould  for  forming  a  briquette, 
5  the  mould  opened  for  removing  the  briquette,  T  a  briquette 
which  has  hardened,  and  U  one  which  has  been  broken. 

Directions. — Hang  the  cup  F  on  the  end  of  the  beam  D,  as 
shown  in  the  illustration,  See  that  the  poise  R  is  at  the  zero- 
mark,  and  balance  the  beam  by  turning  the  ball  L. 

Place  the  shot  in  the  hopper  B,  place  the  specimen  in  the 
damps  NNt  and  adjust  the  hand- wheel  P  so  that  the  gradu- 


FIG.  65. — OLSEN'S  CEMENT-TESTING  MACHINE. 

ated  beam  D  will  rise  nearly  to  the  stop  K.  Open  the  automatic 
valve  /  so  as  to  allow  the  shot  to  run  slowly.  Stand  back  and 
leave  the  machine  to  make  the  test. 

When  the  specimen  breaks,  the  beam  D  drops  and  closes 
the  valve  /.  Remove  the  cup  with  the  shot  in  it,  and  hang 
the  counterpoise-weight  G  in  its  place.  Hang  the  cup  F  on 
the  hook  under  the  large  balance-ball  £,  and  proceed  to  weigh 
the  shot  in  the  ordinary  way,  using  the  poise  R  on  the  graduated 
beam  D  and  the  weights  H  on  the  counterpoise-weight  G. 
The  result  will  show  the  number  of  pounds  required  to  break 
the  specimen. 

An  automatic  machine  designed  by  Prof.  A.  E.  Fuertes  has 
been  in  use  a  long  time  in  the  cement-testing  laboratory  at 


122 


EXPERIMENTAL   ENGINEERING. 


[§  77- 


Cornell  University.  In  this  machine  water  is  supplied  flowing 
from  a  constant  head  through  a  small  glass  orifice.  The  fall 
of  the  beam  consequent  on  the  breaking  of  the  specimen  in- 
stantly stops  the  flow  of  water ;  the  weight  of  this  water,  mul- 
tiplied by  a  known  constant,  gives  the  breaking-load  on  the 
briquette. 

The  Olsen  Cement-tester  is  shown  in  Fig.  65.     The  power  is 
applied  by  the  hand- wheel  and  screw,  so  that  it  strains  the 


FIG.  66.— R.IEHL6  BROS.'  CEMKNT-TESTING  MACHINE. 


briquette  very  slowly.  The  poise  on  the  scale-beam  is  moved 
by  turning  a  crank  so  that  the  beam  can  readily  be  kept  float- 
ing. The  peculiar  method  of  mounting  the  shackles  or  hold- 
ers to  insure  an  axial  pull  is  well  shown  in  the  engraving. 

The  Riehle"  cement-tester  is  shown  in  Fig.  66.  The  briquette 
to  be  tested  is  placed  between  two  shackles  mounted  on  pivots 
so  as  to  be  free  to  turn  in  every  direction. 

Power  is  applied  to  the  specimen  by  the  hand-wheel  below 
the  machine,  and  is  measured  by  the  reading  on  the  scale-beam 
at  the  position  of  the  poise.  Special  crushing  tools,  consisting 


I  77.]    STRENGTH  OF  MATERIALS—  TESTING-MACHINES.     123 

of  a  set  of  double  platforms,  which  may  be  drawn  together  by 
application  of  the  force,  is  furnished  with  this  machine.  The 
specimen  to  be  crushed  is  placed  between  these  platforms,  and 
the  power  applied  as  for  tension. 

Besides  the  machines  described,  various  machines  for  special 
testing  are  manufactured  ;  these  machines  have  a  limited  use, 
and  do  not  merit  special  description  in  a  work  of  this  character. 


TESTING-MACHINE  ACCESSORIES. 

78.  General  Requirements  of  Instruments  for  Measur- 
ing Strains. — In  the  test  of  materials  it  is  necessary  to  meas- 
ure the  amount  of  strain  or  distortion  of  the  body  in  order  to 
compute  the  ductility  and  the  modulus  of  elasticity.  The 
ductility  or  percentage  of  ultimate  deformation  can  often  be 
obtained  by  measurement  with  ordinary  scales  and  calipers, 
since  the  latter  is  usually  a  large  quantity.  Thus  in  the 
tension-test  of  a  steel  bar  8  inches  long,  it  will  increase  in 
length  before  rupture  nearly  or  quite  2  inches  ;  if  in  the  meas- 
ure of  this  quantity  an  error  equal  to  one  fiftieth  of  an  inch 
be  made,  the  resulting  error  in  ductility  is  only  one  half  of 
one  per  cent.  In  the  measure  of  deformation  or  strain  oc- 


FIG.  67.— THE  WEDGE  SCALE. 

curring  within  the  elastic  limit  the  case  is  very  different,  as 
the  deformation  is  very  small,  and  consequently  a  very  small 
error  is  sufficient  to  make  a  great  percentage  difference  in  the 
result. 

The  instruments  that  have  been  used  for  this  purpose  are 
called  extensometers,  and  vary  greatly  in  form  and  in 'principle 
of  construction..  The  instrument  is  generally  attached  to  the 
test-piece,  either  on  one  or  on  both  sides,  and  the  strain  is  ob- 
tained by  direct  measurement  with  one  or  two  micrometer- 
screws,  or  by  the  use  of  levers  which  multiply  the  deformation 
so  that  the  results  can  be  read  on  an  ordinary  scale.  As  a 

124 


TES  TING-MA  CHINE  A  CCESSORIES. 


125 


rule,  instruments  which  attach  to  one  side  of  the  test-piece 
will  give  errpneous  readings  if  the  test-piece  either  be  initially 
curved,  or  strained  so  as  to  draw  its  axis  out  of  a  right  line, 
and  this  error  may  be  large  or  small,  as  the  conditions  vary. 

The  extensometers  in  use  generally  consist  of  some  form 
of  a  multiplying-lever  the  free  end  of  which  moves  over  a 
scale  which  may  or  may  not  be  provided  with  a  vernier,  a 
micrometer-screw  which  is  used  to  measure  the  distance 
between  fixed  points  attached  to  the  specimen  or  the  roller 
and  mirror  and  also  various  forms  of  cathetometers. 

The  Paine  Extensometer,  which  is  described  later,  is  a  very 
simple  and  admirable  form  of  the  lever  micrometer. 

The  B ausc /linger  s  Roller  and  Mirror  Extensometer. — To 
Professor  Bauschinger  belongs  the  credit  of  first  systematically 
taking  double  measurements  on  opposite  sides  of  a  test-bar. 


FIG.  68. — BAUSCHINGER'S  MIRROR  APPARATUS. 

The  general  principle  of  his  apparatus  is  shown  in  the  annexed 
figure.  It  is  seen  to  consist  of  two  knife-edged  clips,  b,  b, 
which  are  connected  to  the  specimen  and  carry  two  hard 
ebonite  rollers,  d,  d,  which  turn  on  accurately  centred 
spindles.  The  spindles  are  prolonged,  and  support  mirrors, 
g,  g,  which  rotate  in  the  plane  of  the  figure  as  the  spindles 
rotate.  A  clip,  aa,  is  fastened  to  each  side  of  the  test-piece 
at  the  opposite  extremity,  and  is  connected  by  spring-pieces, 


126 


EXPERIMENTAL   ENGINEERING. 


[§73. 


with  the  rollers.  The  spring-pieces  are  slightly  roughened  by 
file,  and  turn  the  rollers  by  frictional  contact,  so^that  the  least 
extension  of  the  test-piece  causes  a  rotation  of  the  mirror 
through  an  angle.  If  a  scale  be  placed  at  s,  s,  and  telescopes 
at  e,  e,  the  reflection  of  the  scale  will  be  seen  in  the  mirror  in 
looking  through  the  telescope,  and  any  extension  of  the  test- 
piece  will  cause  a  variation  in  the  reading  of  the  scale  as  seen 
in  the  mirror.  The  apparatus  is  equivalent  to  a  lever 
apparatus  having  for  a  small  arm  the  radius  of  the  roller  g, 
and  for  a  long  arm  the  double  distance  of  the  scale  from  the 
mirror.  With  this  instrument  it  is  evidently  possible  to  obtain 
very  accurate  measurements,  but  on  the  other  hand  the  instru- 
ment is  very  cumbrous  and  difficult  to  use.  The  mean  of  the 
two  readings  with  the  Bauschinger  instrument  is  the  true 
extension  of  the  piece. 

Professor  Unwin  obviates  the  use  of  two  mirrors  and  two 
telescopes  -by  attaching  clips  to  the 
centre  of  the  specimen  and  having  the 
single  mirror  revolve  in  a  plane  at 
right  angles  with  the  plane  passing 
through  the  clips  and  the  axis  of  the 
specimen. 

Strohmeyers  Roller  Extensometer 
was  designed  in  1886.  and  is  a  double- 
roller  extensometer  similar  in  principle 
to  Buzby's  and  Johnson's.  The  appa- 
ratus consists  of  a  roller  carrying  a 
needle  which  is  centred  with  respect 
to  a  graduated  scale.  The  roller 
moves  between  side-bars  extending  to 
clips  which  are  fastened  to  each  end  of  the  specimen.  The 
tension  between  these  side-bars  can  be  regulated  by  a  spring 
with  a  screw  adjustment.  The  objections  to  this  form  of 
extensometer  are  due,  first,  to  slipping  of  side-bars  on  the 
roller,  and  second,  to  the  difficulty  in  making  the  roller  per- 
fectly round. 

Regarding  the  various  forms  of  extensometers,  the  writer 


FIG.  69. — THE   STROHMEYER 
EXTENSOMETER. 


§8i.] 


TESTING-MACHINE  ACCESSORIES. 


127 


would  say  that  his  experience  has  covered  the  use  of  nearly 
every  form  mentioned,  and  none  have  proved  to  be  superior 
in  accuracy  to  that  with  the  double  micrometer-screw,  and  few 
can  be  applied  so  readily. 

79.  Wedge-scale. — The  wedge-shaped  scale,  Fig.  67,  which 
could  be  crowded  between  two  fixed  points 

on  the  test-piece,  was  one  of  the  earliest 
devices  to  be  used.  In  using  the  scale  two 
projecting  points  were  attached  to  the  speci- 
men, and  as  these  points  separated,  the  scale 
could  be  inserted  farther,  and  the  distance 
measured. 

80.  The  Paine   Extensometer. —  This 
instrument,  shown  in  Fig.  70,   operates  on 
the  principle  of  the  bell-crank  lever,  the  long 
arm  moving  a  vernier  over  a  scale  at  right 
angles  to  the  axis  of  the  specimen.     It  reads 
by  the  scale  to  thousandths  of  an  inch,  and 
by  means  of  the  vernier  to  one  ten-thou- 
sandth  of   an  inch.     Points    on   the  instru- 
ment are  fitted  to  indentations  in  one  side 
of  the  test-piece,  and  the  instrument  is  held 
in  place  by  spring  clips.     It  is  of  historical 
importance,   having  been   invented   by  Col- 
onel W.  H.  Paine,  and  used  in  the  tests  of 
material  for  the  Brooklyn  Bridge,  and  also 
on  the  cables  of   the    Niagara   Suspension 
Bridge  when,  a  few  years  since,  the  question 
of  its  strength  was  under  investigation. 

81.  Buzby  Hair-line  Extensometer.— 
This  is  an  extensometer  in  which  the  strain 
is  utilized  to    rotate   a   small   friction-roller 
connected  with  a  graduated  disk  as  shown  in 
Fig.  71.       A  projecting  pin  placed  in    the 
axis  of  the  graduated  disk  is  held  between 

two  parallel  bars,  each  of  which  is  connected  FlG'  TO. 

to  the  specimen.     The  strain  is  magnified  an  amount  proper- 


128  EXPERIMENTAL   ENGINEERING.  [§  8l. 

tional  to  the  ratio  of  diameters  of  the  disk  and  pin.  The 
amount  of  strain  is  read  by  noting  the  number  of  subdivisions 
of  the  disk  passing  the  hair-line.  To  prevent  error  of  parallax 
in  reading,  a  small  mirror  is  placed  back  of  the  graduations, 
and  readings  are  to  be  taken  when  the  graduations,  the  cross- 
hair, and  its  reflection  are  in  line.  In  the  late  styles  of  this 


FIG.  71.— BUZBY  HAIR-LINE  EXTENSOMKTER.          FIG.  72.— THE  RiEHLfi  EXTENSOMETRR. 

instrument  the  disk  is  made  of  aluminium,  with  open  spokes, 
to  reduce  its  weight. 

To  operate  this  instrument  it  is  only  necessary  to  clamp 
it  to  the  specimen,  to  adjust  the  mirror  and  cross-hair,  and 
then  to  revolve  the  disk  by  hand  until  the  zero-line  corre- 
sponds with  the  cross-hair  and  its  reflection.  Stress  is  then 
applied  to  the  specimen,  and  readings  taken  as  desired  in  the 
manner  described. 

The  Riehtt  Extensometer. — The  Riehle  extensometer  is 
a  combination  of  compound  levers  which  are  attached  to  both 
sides  of  the  specimen,  and  arranged  so  that  one  side  carries  a 
scale  and  the  other  a  vernier.  It  is  only  mechanical  in  opera- 
tion, and  can  be  used  on  specimens  varying  in  length  from  6 
to  8  inches.  It  is  adjusted  to  the  specimen  by  the  clamp 
screws  in  the  usual  manner,  and  the  ends  of  the  graduations 
are  then  brought  together  at  zero  at  both  sides  at  the  same 
time.  Pressure  is  then  applied  to  the  specimen  and  the 


§82.] 


TES  TING -MA  CHINE  A  CCESSORIES. 


129 


readings  taken  in  the  same  manner  as  any  scale  and  vernier, 
the  scale  being  graduated  to  thousandths  and  the  vernier  to 
ten  thousandths. 

Johnson  s  Extensometer. — Johnson's  extensometer,  shown 
in  Fig.  73,  is  a  modification  of  the 
Strohmeyer,  the  elongation  being  de- 
noted by  the  motion  of  a  needle  over  a 
graduated  scale.  The  elongation  for  each 
side  is  shown  separately,  and  the  alge- 
braic sum  of  the  two  readings  gives  the 
total  elongation. 

82.  Thurston's    Extensometer 

This  extensometer  was  designed  by  Prof. 
R.    H.   Thurston  and   Mr.   Wm.   Kent, 
and  was  the  first  to  employ  two  microm- 
eter-screws, at   equal   distances  from  the 
axis  of  the  specimen.     These  were  con- 
nected to  a  battery  and  an  electric  bell 
in    such    a    manner  that  the   contact  of 
the  micrometer-screws  was  indicated  by 
sound  of  the  bell.     The  method  of  using 
this  instrument   is   essentially  the    same 

as  that  of  the  Henning  and  Marshall  instrument,  to  be 
described  later. 

With  instruments  of  this  nature  a  slight  bending  in  the 
specimen  will  be  corrected  by  taking  the  average  of  the  two 
readings. 

The  accuracy  of  such  extensometers  depends  on — 

1.  The  accuracy  of  the  micrometer-screws. 

2.  The  screws  to  be  compensating  must  be  two  in  number, 
in  the  same  plane,  and  at  equal  distances  from  the  axis  of  the 
specimen. 

3.  The  framework  and  clamping  device  must  hold  the  mi- 
crometers rigidly  in  place,  and  yet  not  interfere  with  the  ap- 
plication of  stress. 

83.  The  Henning  Extensometer. — This  instrument,  which 
was  designed  by  G.  C.  Henning  and  C.  A.  Marshall,  is  shown  in 
Fig.  74-    It  is  constructed  on  the  same  general  principles  as  the 


FIG.  73.— JOHNSON'S  EXTHN- 

SOMETER. 


1 3o 


EXPERIMENTAL  ENGINEERINGS 


[§83. 


Thurston  Extensometer,  but  the  clamps  which  are  attached  to 
the  specimen  are  heavier,  and  are  made  so  that  they  are  held 
firmly  in  position  by  springs  up  to  the  instant  of  rupture. 
This  extensometer  is  furnished  with  links  connecting  the  two 
parts  together.  The  links  are  used  to  hold  the  heads  exactly 
eight  inches  apart,  and  are  unhooked  from  the  upper  head 


FIG.  74.— THE  HENNING  MICROMETER. 

before  stress  is  applied  to  the  specimen.  The  micrometer  is 
connected  to  an  electric  bell  in  the  same  manner  as  the 
Thurston  extensometer. 

Henning's  Mirror  Extensometer.* — In  1896  Gus.  C.  Henning 
designed  a  mirror  extensometer  differing  in  several  particulars 
from  that  of  Bauschinger.  The  instrument  is  intended  for 
accurate  measurements  of  the  extension  or  compression  on 
both  sides  of  the  test-piece  within  the  elastic  limit,  and  is  said 
to  fulfil  the  following  conditions :  (a)  It  is  applicable  for 
measures  of  extension  or  compression,  (b)  Readings  in  either 
direction,  negative  or  positive,  can  be  taken  without  interrup- 
tion or  adjustment,  (c)  The  instrument  is  free  from  changes 
of  shape  during  the  test,  (d)  There  is  neither  slip  nor  play  of 
the  working  parts. 

*  See  Transactions  American  Society  Mechanical  Engineers,  vol.  xvm. 


§84-] 


TESTING  MA  CHINE  A  CCESSORIES. 


The  instrument  consists  of  two  parts;  the  first  is  a  telescope 
provided  with  levelling-screws,  mounted  on  a  horizontal  and 
vertical  axis  and  furnished  with  supports  tor  two  linear  scales, 
which  may  be  arranged  so  that  the  reflection  will  show  in 
mirrors  attached  to  the  specimen.  The  second  part  consists  of 
a  frame  which  can  be  fastened  to  the  test-specimen  near  one 
end  by  opposite-pointed  screws,  and  which  is  connected  to 
spindles  carrying  the  mirrors  by  spring  side-bars.  A  portion 
of  each  mirror-spindle  is  double  knife-edged,  and  when  adjusted 


FIG.  75. — THE  MARSHALL  EXTENSOMETER 


FIG.  76. —  IENNING'S  EXTENSOMETER. 


is  brought  in  contact  on  one  side  with  the  test-piece,  and  on 
the  other  with  the  spring  side-bar.  The  elongation  of  the 
test-piece  causes  an  angular  motion  of  the  mirror,  which  in 
turn  causes  a  multiplied  motion  of  the  reflection  of  the  scale 
as  seen  from  the  telescope.  The  mirrors  are  so  arranged  that 
the  reflections  from  both  scales  can  be  seen  continually  and 
without  adjustment  of  the  telescope,  and  the  apparatus  as  a 
whole  has  fewer  parts  and  is  more  readily  adjusted  than  the 
Bauschinger.  It  is  limited  to  a  total  elongation  of  about  0.04 
inch  and  hence  is  accurate  only  for  measurements  within  the 
elastic  limit. 

84.  The  Marshall  Extensometer. — This  extensometer, 
shown  in  Fig.  75,  is  the  latest  design  of  the  late  Mr.  C.  A. 
Marshall.  Its  principal  difference  from  the  Thurston  exten- 


132 


EXPERIMENTAL  ENGINEERING. 


[§85- 


someter  is  in  the  convenient  form  of  clamps,  which  are  well 
shown  in  the  cut,  and  in  the  spring  apparatus  for  steadying 
the  lower  part. 

The  micrometer-screw   used   with   this   instrument   has   a 
motion    of   only   one   inch.     When    the.  motion  exceeds  the 
range  of  the  micrometer-screws,  the  movable  bars  BP,  B'Pf 
are  changed  in  position,  and  a  new  series 
of   readings    taken  with   the   micrometer- 
screw.     To  facilitate  the   change  of  posi- 
tion of  these  bars,  and  allow  the  microme- 
ter-screw to  return  to  zero  at  each  change, 
the    arrangement    shown    in    Fig.   77    is 
adopted,  which  consists  of  a  nut  to  which 
FIG.  77.  is  attached  a  slotted  taper-screw,  on  which 

screws  a  second  nut,  which  serves  to  clamp  the  lower  nut  to 
the  bar ;  by  turning  the  lower  nut  when  clamped,  the  desired 
adjustment  can  be  made. 

The  following  are  the  directions  for  use : 
Run  wire  (Fig.  76)  from  one  terminal  of  battery  to  lower 
clamp  at  A,  from  B  and  B'  to  binding-post  C  on  the  electric 
bell,  from  the  other  binding-post  marked  D  to  switch  E,  and 
from  there  back  to  the  other  terminal  of  battery. 

To  measure  strain,  screw  up  micrometer-screws  at  P and  Pr 
until  each  of  them  makes  connection  and  bell  rings;  then  take 
the  readings  on  both  sides. 

85.  Boston  Micrometer  Extensometer. — This  instru- 
ment consists,  as  shown  in  Fig.  78,  of  the  graduated  microm- 
eter-screw, reading  in  thousandths  up  to  one  inch,  and  haying 
pointed  extension-pieces  attached,  for  gauging  the  distance 
between  the  small  projections  on  the  collars  fastened  to  the 
specimen  at  the  proper  distance.  These  collars  are  made  partly 
self-adjusting  by  the  springs  which  help  to  centralize  them. 
They  are  then  clamped  in  place  by  means  of  the  pointed 
set-screws  on  the  sides,  and  measurements  are  made  between 
the  projections  on  opposite  sides  of  the  specimen  and  com- 
pared, to  denote  any  changes  in  shape  or  variations  in  the 
two  sides. 


§86.] 


TESTING-AIA  CHINE   A  CCESSORIES. 


133 


The  Brown  and  Sharpe  micrometer  can  readily  be  used  with 
similar  collars, thus  forming  an  exten- 
someter ;  the  accuracy  of  this  form  is 
considerably  less  than  those  in  which 
the  micrometers  are  fixed,  but  it 
will,  however,  be  found  with  careful 
handling  to  give  good  results. 

Of  the  various  extensometers  de- 
scribed, the  Paine,  Buzby,  Marshall, 
and  Riehle  are  manufactured  by 
Riehle  Bros.,  Philadelphia;  the 
Thurston,  by  Olsen  of  Philadelphia ; 
the  others,  by  the  respective  de- 
signers. 

86.  Combined  Extensometer 
and  Autographic  Apparatus. — An 
extensometer  designed  by  the 
author,  and  quite  extensively  used 
in  the  tests  of  materials  in  Sibley 
College,  is  shown  in  Fig.  80  in  ele- 
vation and  in  Fig.  81  in  plan.  In 
this  extensometer  micrometers  of 
the  kind  shown  in  Fig.  22,  Article  42, 
p.  60,  with  the  addition  of  an  exten- 
sion-rod for  holding,  are  used^  This 
rod  sets  into  a  socket  A,  which  holds 
the  micrometer  in  position.  Read- 
ings are  taken  on  the  thimble  B,  as 
explained  on  p.  52.  Connections  are  made  with  bell  and 
battery  at  ;;/,  n,  and  m' ,  ri ',  so  that  contact  of  the  micrometer- 
screws  is  indicated  by  sound.  The  construction  of  the  clamp- 
ing device  is  fully  shown  in  the  plan  view,  Fig.  8t. 

The  principal  peculiarity  of  this  extensometer  consists  in  the 
addition  of  four  pulleys,  Clt  C^,  C3  and  C4 ,  which  are  arranged 
so  that  a  cord  ab  can  be  fastened  at  Ct  and  passed  down  and 
around  the  pulley  Clt  thence  over  the  guide-pulley  W,  Fig.  81, 
to  pulley  C9 ,  thence  over  the  pulley  Ct ,  and  thence  to  a  paper 


FIG.  78. 


134 


EXPERIMENTAL  ENGINEERING. 


[§86. 


drum.  It  is  at  once  evident  that  any  extension  of  the  speci- 
men SS'  will  draw  in  the  free  end  of  the  cord  at  twice  the 
rate  of  the  extension ;  moreover,  any  slight  swinging  or  rock- 
ing of  the  extensometer  head  will  produce  compensating 
effects  on  the  length  of  the  cord.  By  connecting  the  free  end 
of  the  cord  to  a  drum,  the  drum  will  be  revolved  by  the  stretch 


FIG.  80. 


FIG.  81. 


of  the  specimen.  As  this  work  may  be  done  against  a  fixed 
pull,  there  may  be  a  uniform  tension  on  the  cord  so  that  the 
motion  of  the  drum  would  be  uniform  and  proportional  to  the 
stretch.  A  pencil  is  moved  along  the  axis  of  the  drum  pro- 
portional to  the  motion  of  the  poise. 

An  autographic  device  constructed  in  this  way  has  given 
excellent  diagrams,  and  in  addition  has  served  as  an  extensom- 
eter for  accurate  measurements  of  strain  within  the  elastic 
limits.  Wire  has  been  used  to  connect  extensometer  to  drum 
in  place  of  the  cord  with  success.  A  suggested  improvement  is 


§87-]  TESTING-MACHINE  ACCESSORIES.  135 

to  rotate  the  drum  by  the  motion  of  the  poise,  and  to  move 
the  pencil  by  the  stretch  of  the  material,  using  two  pencils, 
one  of  which  is  to  move  at  a  rate  equal  to  fifty  times  the 
strain,  the  other  at  a  rate  equal  to  five  times  the  strain ;  thus 
producing  two  diagrams — one  on  a  large  scale,  for  use  in  deter- 
mining the  strains  during  the  elastic  limit;  the  other  on  a 
small  scale,  for  the  complete  test. 

87.  Deflectometer  for  Transverse  Testing. — Instru- 
ments for  measuring  the  deflection  of  a  specimen  subjected  to 
transverse  stress  are  termed  deflectometers. 

The  deflectometer  usually  used  by  the  author  consists  of  a 
light  metal-frame  of  the  same  length  as  the  test-piece,  and 
arched  or  raised  sufficiently  in  the  centre  to  hold  a  micrometer 
of  the  form  used  in  the  extensometer  described  in  Article  86, 
above  the  point  to  which  measurements  are  to  be  taken.  In 
using  the  deflectometer  it  is  supported  on  the  same  bearings 
as  the  test-piece,  and  measurements  made  to  a  point  on  the 
specimen  or  to  a  point  on  the  testing-machine  which  moves 
downward  as  the  specimen  is  deflected.  This  instrument 
eliminates  any  error  of  settlement  in  the  supports.  A  steel 
wire  is  sometimes  stretched  by  the  side  of  the  specimen,  and 
marks  made  on  the  specimen  showing  its  original  position  with 
reference  to  the  wire.  The  deflection  at  any  point  would  be 
the  distance  from  the  mark  on  the  specimen  to  the  corre- 
sponding point  on  the  wire.  The  cathetometer,  see  Article  43, 
page  63,  is  very  useful  in  determining  the  deflection  in  long 
specimens.  The  deflection  is  often  measured  from  a  fixed 
point  to  the  bottom  of  the  specimen,  thus  neglecting  any  error 
due  to  the  settlement  of  the  supports.  One  of  the  most  use- 
ful instruments  of  this  kind  is  made  by  Riehl£  Bros.,  and  is 
shown,  together  with  the  method  of  attachment,  in  Fig.  82. 


FIG.  82. 


CHAPTER  V. 
METHODS  OF  TESTING  MATERIALS  OF  CONSTRUCTION. 

Standard  Methods. — The  importance  of  standard 
methods  of  testing  material  can  hardly  be  overestimated  if  it 
is  desired  to  produce  results  directly  comparable  with  those 
obtained  by  other  experimenters,  since  it  is  found  that  the  re- 
sults obtained  in  testing  the  strength  of  materials  are  affected 
by  methods  of  testing  and  by  the  size  and  shape  of  the  test- 
specimen.  To  secure  uniform  practice,  standard  methods  for 
testing  various  materials  have  been  adopted  by  several  of  the 
engineering  societies  of  Germany  and  of  the  United  States,  as 
well  as  by  associations  of  the  different  manufacturers.  The 
general  and  special  standard  methods  adopted  by  these  asso- 
ciations form  the  basis  of  methods  described  in  this  chapter. 

88.  Form  of  Test-pieces. — The  form  of  test-pieces  is 
found  to  have  an  important  bearing  on  the  strength,  and  for 
this  reason  engineers  have  adopted  certain  standard  forms  to 
be  used.  The  form  recommended  by  the  Committee  on 
Standard  Tests  and  Methods  of  Testing,  of  the  American 
Society  of  Mechanical  Engineers  is  as  follows:* 

"  Specimens  for  scientific  or  standard  tests  are  to  be  pre- 
pared with  the  greatest  care  and  accuracy,  and  turned  accord- 
ing to  the  following  dimensions  as  nearly  as  possible.  The 
tension  test-pieces  are  to  have  different  diameters  according  to 
the  original  thickness  of  the  material,  and  to  be,  when  ex- 
pressed in  English  measures,  exactly  0.4,  0.6,  0.8,  and  i.o  inch 
in  diameter;  but  for  all  these  different  diameters  the  angle,  but 

*  See  Vol.  XI.  of  Transactions. 

136 


§88.]         TESTING  MATERIALS  OF  CONSTRUCTION.  137 

not  the  length,  of  the  neck  is  to  remain  constant.  This  neck 
is  a  cone,  not  a  fillet  connecting  the  shoulders  and  body.  The 
length  of  the  gauged  or  measured  part  to  be  8  inches,  of  th~ 
cylindrical  part  8.8  inches.  The  length  of  the  coned  neck  to 
be  2^  times  the  diameter,  increasing  in  diameter  from  the 
cylindrical  part  to  I J  times  the  cylindrical  part.  The  shoul- 
ders to  have  a  length  equal  to  the  diameter,  and  to  be  con- 
nected with  a  round  fillet  to  a  head,  which  has  a  diameter 
equal  to  twice  that  of  the  cylinder,  and  a  length  at  least  ij 
the  diameter. 

Fig.  83   shows   the  form  of  the  test-piece   recommended 
for  tension  ;  the  numbers  above  the  figure  give  dimensions  in 


f-25--* 

<-20-4<  50—  -ty  220  millimetres-—  ~- 

—  4,1  50  * 

,20^ 

*-25-» 

•f 

^    i          i 

1 

* 

S3 

TT      _J     £                       J 

2           —  i- 

«o 

i 

T       —  t"    ?"      "     "     "           1 

?           3 

| 

1 

8.8-inches J< 2 »|«M»|»-  -l-*f 

FIG.  83.— STANDARD  TEST-PIECE  IN  TENSION. 


millimeters,  those   below  in  inches.     For  flat  test-pieces  the 
shape  as  shown  in  Fig.  84  is  recommended :  such  specimens 


& 

£  __-as»  -*f-12-r 

[_     I^X 

1 

, 

• 

X            T  # 

i                                                                      Jr 

1 

f 

< 

"R.                               r\ 

; 

FIG.  84.— TEST-PIECE  FOR  FLAT  SPECIMENS. 

are  to  be  cut  from  larger  pieces  ;  the  fillets  are  to  be  accurately 
milled,  and  the  shoulders  made  ample  to  receive  and  hold  the 
full  grip  of  the  shackles  or  wedges. 

The  length  for  rough  bars  is  to  remain  the  same  as  for  fin 
ished  test-pieces,  but  the  length  of  specimen  from  the  gauge- 
mark  to  the  nearest  holder  is  to  be  not  less  than  the  diameter 


138 


EXPERIMENTAL  ENGINEERING. 


[§89- 


of  the  test-piece  if  round,  or  one  and  a  half  times  the  greatest 
side  if  flat. 

For  commercial  testing  the  standard  form  cannot  always 
be  adhered  to,  and  no  form  is  recommended.* 

It  is  recommended  in  all  cases  that  the  specimens  be  held 
by  true  bearing  on  the  end  shoulders,  as  gripping  or  holding 
devices  in  common  use  produce  undesirable  effects  on  the 
cylindrical  portion  of  the  specimen. 

The  forms  of  test-specimens  which  have  been  heretofore 
used  are  somewhat  different  from  the  standards  recommended. 
These  forms  are  shown  in  Fig.  85,  No.  I  to  No.  5,  and  are  as 
follows : 


No.  5. 


No.  t.  Square    or    flat    bar, 
rolled. 


No.  a.  Round  bar,  as  roJled. 

No.  3.  Standard  shape  for  flats  of 
squares.  Edges  must 
be  smooth  and  true.  Fil- 
lets, one  half  inch  radius. 
Specimens  not  over  three 
inches  wide. 


No.  4.  Standard  shape  for  rounds. 


No:  5.  Government  shape  for 
marine-boiler  plates  only. 
Not  in  general  use,  as  it 
gives  too  high  a  test. 

FIG.  85.—  ^ORMS  OF  SPECIMEN  FOR  TENSILE  STRAINS  FORMERLY  USED. 


89.  Test-pieces  of  Special  Materials.—  Wood. — Wood  is 
a  difficult  material  to  test  in  tension,  as  the  specimen  is  likely 
to  be  crushed  by  the  shackles  or  holders.  The  author  has  had 
fairly  good  success  with  specimens,  made  with  a  very  large 
bearing-surface  in  the  shackles,  of  the  form  shown  in  Fig.  84, 


*  A  discussion  of  the  effect  of  varying  proportion  of  test-pieces  is  given  in 
Tburston's  "  Text-book  of  Materials,"  pages  356-7. 


§»9-] 


TESTING  MATERIALS   OF  CONSTRUCTION. 


139 


page  137  for  flat  specimens,  but  with  the  breadth  of  the  shoul 
ders  or  bearing-surfaces  increased  an  amount  equal  to  one  half 
the  diameter  of  the  specimen  over  that  shown  in  Fig.  84. 

Cast-iron. — Cast-iron  specimens  of  the  usual  or  standard 
forms  are  very  likely  to  be  broken  by  oblique  strains  in  tension 
tests  much  before  the  true  breaking-point  has  been  reached. 
To  insure  perfectly  axial  strains  Riehl£  Bros,  propose  a  form 
of  specimen  shown  in  Fig.  86,  A,  B,  and  C,  cast  with  an  enlarged 


FIG.  86.— PROPOSED  FORM  FOR  CAST-IRON  SPECIMENS. 

head,  the  projecting  portion  of  which,  as  shown  in  C,  has 
a  knife-edge  shape.  The  specimen  is  carried  in  holders  o*- 
shackles,  A  and  B,  which  rest  on  knife-edges  extending 
at  right  angles  to  those  of  the  specimen.  This  permits 
free  play  of  the  specimen  in  either  direction,  and  renders 
oblique  strains  nearly  impossible. 

Chain. — In  the  case  of  chain,  large  links  are  welded  at  the 
ends,  as  shown  in  Fig.  87  ;  these  are  passed  through  the  heads 
of  the  testing-machine  and  held  by  pins. 


FIG.   87.— CHAIN  TEST-PIECE. 


140 


EXPERIMENTAL  ENGINEERING. 


l§8o, 


Hemp  Rope. — A  similar  method  is  used  in  testing  hemp 
rope,   the   specimen   being    prepared   as  shown   in   Fig.   88. 


FIG.  88.— :lo?E  TEST-PIECE. 


Special  hollow  conical  shackles  have  also  been  used  for  hold- 
ing the  rope  with  success. 

Wire  Rope. — Wire-rope   specimens   may   be   prepared   as 
shown  in  Fig.  89,  or  they  may  be  prepared  by  pouring  a  mass 


FIG.  89.— WIRE-ROPE  TEST-PIECE. 

of  melted  Babbitt  metal  around  each  end  and  moulding  into  a 
conical  form,  taking  care  that  the  rope  is  in  the  exact  centre 
of  the  metal. 

Cement. — Cement  test-pieces  for  tension  are  made  in  moulds 
and  permitted  to  harden  for  some  time  before  being  tested.  It 
is  found  that  the  strength  is  affected  by  the  form  of  the  sped- 


FIG.  90. — OLD  C.  E.  STANDARD  SPECIMEN  FOR  CEMENT. 

men,  by  the  amount  of  water  used,  and  by  the  method  of  mix- 
ing  the  cement.  To  get  results  which  may  safely  be  compared, 
it  is  necessary  to  have  the  test-specimens  or  briquettes  of 
exactly  the  same  form,  and  pulled  apart  in  shackles  or  holders 


§«9-] 


TESTING    MATERIALS   OF   CONSTRUCTION. 


141 


which  exert  no  side  strain  whatever,  and  the  strain  applied  uni- 
formly and  without  any  jerky  motion.  Various  standard  forms 
of  briquettes  have  been  employed ;  the  one  most  used  in  America 
prior  to  1904  is  shown  full  size  in  Fig.  90.  That  recently  adopted 
is  shown  half  size  in  Fig.  94. 


FIG.  91. — CEMENT  MOULDS  AND  BRIQUETTES. 

The  form  of   the  mould  for  making  the  briquettes,  and   the 
holders  or  shackles  generally  used,  are  shown  in  Figs.  91  to  93. 


DETAILS  FOR  GANC.  MOULD 
FIG.  93. 


FORM  OF  CLIP  DETAILS  FOR  BRIQUETTE 

FIG.  93.  FIG.  94. 

STANDARD  CLIP  AND  BRIQUETTE  ADOPTED  BY  THE  AMERICAN  SOCIETY  FOR  TESTING 
MATERIALS,  1904. 

The  gang-mould,  as  shown  in  Fig.  92,  consisting  of  several  moulds 
united  in  one  construction,  is  preferred  when  numerous  briquettes 
are  to  be  made. 


142  EXPERIMENTAL   ENGINEERING.  [§  9°. 

Standard  revised  specifications  for  testing  cement  were  adopted 
by  the  American  Society  of  Civil  Engineers  and  approved  by  the 
American  Society  of  Testing  Materials,  1904.  The  form  of 
briquette  adopted  is  shown  in  Fig.  94,  which  differs  from  the 
earlier  form  principally  in  the  use  of  rounded  instead  of  sharp 
corners,  as  noted  by  comparing  Figs.  90  and  94. 

90.  Compression-test    Specimens— Test-pieces. — Test- 
pieces  are  in  all  cases  to  be  prepared  with  the  greatest  care,  to 
make  sure  that  the  end  surfaces  are  true  parallel  planes  normal 
to  the  axis  of  the  specimen. 

1.  Short  Specimens. — The  standard  test  specimens  are  to  be 
cylinders  two  inches  in  length  and  one  inch  in  diameter,  when 
ultimate  resistance  alone  is  to  be  determined. 

2.  Long  Specimens. — For  all  other  purposes,  especially  when 
the  elastic  resistances  are  to  be  ascertained,  specimens  one  inch 
in  diameter  and  ten  or  twenty  inches  long  (see  No.  2,  Fig.  85) 
are  to  be  used.     Standard  length  on  which  strain  is  to  be  meas- 
ured is  to  be  eight  inches,  as  in  the  tension-tests.     Greatest  care 
must  be  taken  in  all  cases   to   insure  square  ends  and  that  the 
force  be  applied  axially. 

The  specimens  are  to  be  marked  and  the  compression  meas- 
ured as  explained  for  tension- test  pieces,  page  126. 

91.  Transverse-test    Specimens.  —  For    standard    trans- 
verse tests,  bars  one  inch  square  and  forty  inches  long  are  to  be 
used,   the  bearing  blocks   or  supports   to   be  exactly  thirty-six 
inches  apart,  centre  to  centre.     For  standard  or  scientific  tests 
of  cast-iron,  such  bars  are  to  be  cut  out  of  a  casting  at  least  two 
inches  square  or  two  and  a  quarter  inches  in  diameter,  so  as  to 
remove  all  chilling  effect.     For  routine  tests,  bars  cast  one  inch 
square  may  be  used,  but  all  possible  precautions  must  be  taken 
to  prevent  surf  ace- chilling  and  porosity. 

Test-bars  of  wood  are  to  be  forty  inches  in  length,  and  three 
inches  square  in  section. 

92.  Torsion-test   Specimens. — For  standard  tests,  cylin- 
drical specimens  with  cylindrical  concentric  shoulders  are  to  be 
used;    the  two  are  connected  by  large  fillets.      The  specimen 


§93-1         TESTING  MATERIALS   OF  CONSTRUCTION.  143 

is  to  be  held  in  the  chuck  or  heads  of  the  machine  by  three 
keys,  inserted  in  key-ways  \  inch  deep,  cut  in  the  shoulder. 

93.  Elongation — Fracture. — The  character  of  the  fracture 
often  affords  important  information  regarding  the  material. 
The  structure  of  the  fractured  surface  should  be  described  as 
coarse  or  fine,  either  fibrous,  granular,  or  crystalline.  Its  form, 
whether  plane,  convex,  or  concave,  cup-shaped  above  or  below, 
should  in  each  case  be  stated.  Its  location  should  be  accu- 


15  14  13  12  11   10    9    8    7     6    5     4     3    2   1      0    1    2     3 


19  18  17   16  15   14  13  12  11  10    9     8     765    |4     3    2 


FIG    95- 

*ately  given,  from  marks  on  the  specimen  one  half  inch  or  less 
apart.  The  reduction  of  diameter  which  accompanies  fracture 
should  be  accurately  measured.  Accompanying  the  report 
should  be  a  sketch  of  the  fractured  specimen. 

Fracture  occurs  usually  as  the  result  of  a  gradual  yielding 
of  the  particles  of  the  specimen.  The  strain,  so  long  as  the 
.stress  is  less  than  the  maximum  load,  is  distributed  nearly  uni- 
jformly  over  the  specimen,  but  after  that  point  is  passed  the  dis- 
tortion becomes  nearly  local ;  a  rapid  elongation  with  a  corre- 
sponding reduction  in  section  is  manifest  as  affecting  a  small 
portion  of  the  specimen  only.  This  action  in  materials  with 
sensible  ductility  takes  place  some  little  time  before  rupture; 
in  very  rigid  materials  it  cannot  be  perceived  at  all.  This 
peculiar  change  in  form  is  spoken  of  as  "  necking.'* 

The  drawing  Fig.  95  shows  the  appearance  of  a  test  speci- 
men in  which  the  "  necking "  is  well  developed.  Rupture 
occurs  at  b— b,  a  point  in  the  neck  which  may  be  near  one 
end  of  the  specimen. 

In  order  to  measure  the  elongation  of  the  specimen  fairly,  a 
correction  should  be  applied,  so  that  the  reduced  elongation 
shall  be  the  same  as  though  the  stretch  either  side  of  the  point 


144  EXPERIMENTAL  ENGINEERING.  [§  94. 

of  rupture  were  equal.  This  can  only  be  done  by  dividing  up 
the  original  specimen  into  equal  spaces,  each  of  which  is  marked 
so  that  it  can  be  identified  after  rupture. 

Supposing  that  twenty  spaces  represent  the  full  length  be- 
tween gauge-marks :  then  if  the  rupture  be  nearest  the  mark 
O,  Fig.  95,  three  spaces  from  the  nearest  gauge-mark,  the 
total  length  to  compare  with  the  original  length  is  o  to  3  on 
the  right,  plus  o  to  10  on  the  left,  plus  the  distance  3  to  10 
on  the  left.  These  spaces  are  to  be  measured,  and  the  sum 
taken  as  the  total  length  after  rupture.  The  stretch  is  the 
difference  between  this  and  the  original  length ;  the  per  cent 
of  stretch,  or  elongation,  is  the  stretch  divided  by  the  original 
length.  This  method  is  stated  in  a  general  form  as  follows : 

Divide  the  standard  length  into  m  equal  parts,  and  repre- 
sent the  number  of  these  parts  in  the  short  portion  after  rupture 
by  s.  Note  two  points  in  the  long  portion,  A  and  B,  at  s  and 
-£m  divisions  respectively  from  the  break.  Lay  the  parts  to- 
gether, and  measure  from  the  gauge-mark  in  the  short  por- 
tion to  point  A.  This  distance  increased  by  double  the 
measured  distance  from  A  to  B  gives  the  total  length  after 
rupture.  Subtract  the  original  length  to  obtain  the  total  elon- 
gation: thus  the  elongation  of  the  standard  m  parts  will  be 
obtained  as  though  the  fracture  were  located  at  the  middle 
division. 

94.  Strain-diagrams. — The  results  of  measurements  of 
the  strain  should  be  represented  graphically  by  a  curve 
termed  a  strain-diagram. 

Strain-diagrams  are  drawn  (see  Art.  46,  page  70)  by  taking 
the  loads  per  square  inch  (/>)  as  ordinates,  and  the  relative 
stretch  or  strain  (e)  to  a  suitable  scale  as  abscissae.  The  curve 
so  formed  will  be  a  straight  line  from  the  origin  to  the  elastic 
limit,  and  the  tangent  of  the  angle  that  it  makes  with  the  axis 
of  X  (p  -r-  €  =  E)  will  be  proportional  to  the  modulus  of  elas- 
ticity. The  area  included  between  the  axis  of  X  and  that  por- 
tion of  the  curve  preceding  the  elastic  limit  will  represent  the 
Elastic  Resilience  or  work  done  by  the  resistance  of  the 
material  to  that  point. 


§  95-]  TESTING  MATERIALS  OF  CONSTRUCTION.  145 

Autographic  Strain-diagrams  are  drawn  automatically 
on  a  revolving  drum.  In  most  machines  the  drum  is  revolved 
by  the  stretch  of  the  material  and  a  pencil  is  moved  parallel 
to  its  main  axis  and  proportional  to  the  motion  of  the  weigh- 
ing  poise,  although  in  some  devices  for  drawing  autographic 
diagrams  the  drum  is  actuated  by  the  poise  motion,  the  pencil 
by  the  stretch.  The  Olsen  autographic  apparatus  is  described 
in  Article  71,  Figs.  56  to  60,  page  1 1 1.  This  apparatus  is  very 
perfect  in  all  its  details,  and  produces  a  diagram  similar  to 
that  shown  in  Fig.  96. 

The  ordinates  on  this  diagram  are  proportional  to  the 
load,  the  abscissae  to  the  strain.  The  lines  are  straight  and 
nearly  vertical  until  the  yield-point ;  then  for  a  time  the  strain 
rapidly  increases,  with  little  increase  of  stress  as  shown  by  the 
line  of  stress  ;  this  is  followed  by  an  increase  of  both  stress  and 
strain,  until  the  point  of  maximum  loading  is  reached.  After 
passing  the  elastic  limit  the  strain  increases  very  rapidly,  the 
stress  but  little. 

The  autographic  attachment  is  a  valuable  addition  to  a 
testing-machine,  especially  if  its  use  does  not  interfere  with 
the  measurement  by  micrometers ;  but  if  the  scale  of  the  dia- 
gram does  not  exceed  five  or  ten  times  that  of  the  actual 
strain,  it  is  of  value  only  in  showing  the  general  character  of 
the  strain,  and  is  not  to  be  considered  of  value  in  obtaining 
coefficients  or  moduli  within  the  elastic  limit. 


TENSION  TESTS. 

95.  Objects  of  Tension  Tests. — Tension  tests  are  con- 
sidered  valuable  as  affording  information  of  the  qualities  of 
material,  and  a  certain  tensile  strength  is  required  of  nearly 
all  materials  used,  even  though  in  practice  they  may  be  sub- 
jected to  different  kinds  of  strain.  The  breaking-strength  is 
frequently  specified  within  limits,  and  is  to  be  accompanied  with 
a  certain  amount  of  ductility. 

Directions  for  Tension  Tests. — Examine  the  test-piece  care- 


§95-]         TESTING  MATERIALS  OF  CONSTRUCTION.  147 

fully  for  any  flaw,  defect,  irregularity,  or  abnormal  appearance, 
and  see  that  it  is  of  correct  form  and  carefully  prepared.  In. 
dentations  from  a  hammer  often  seriously  affect  the  results. 
In  wood  specimens,  abrasions,  slight  nicks  at  the  corners,  or 
bruises  on  the  surface  will  invariably  be  the  cause  of  failure. 

Next,  carefully  measure  the  dimensions,  record  total  length, 
gauge-length  (or  length  on  which  measurements  of  strains  are 
made),  also  form  and  dimensions  of  shoulders.  Divide  the 
specimen  between  the  gauge-marks  into  inches  and  half  inches, 
which  may  be  marked  with  a  special  tool,  or  by  rubbing  chalk 
on  the  specimens  and  marking  each  division  with  a  steel  scratch. 


FIG.  97. —  LAYING-OFF  GAUGE. 

A  special  gauge  as  shown  in  Fig.  97  is  convenient  for  this  pur 
pose.  These  marks  serve  as  reference  points  in  measuring  the 
elongation  after  rupture,  and  this  elongation  should  be  meas- 
ured, not  from  the  centre  of  the  specimen,  but  from  the  point 
of  rupture  either  way,  as  explained  in  Art.  93,  page  143. 

See  that  the  testing-machine  is  level  and  balanced  before 
each  test ;  insert  the  specimen  in  a  truly  axial  position  in  the 
machine  by  measuring  carefully  its  position  in  two  directions, 
and  by  applying  a  level.  Calculate  from  the  known  coefficients 
of  the  material  the  probable  load  at  elastic  limit.  Take  one 
tenth  of  this  as  the  increment  of  load.  The  Committee  on 
Standard  Tests,  American  Society  of  Mechanical  Engineers, 
recommend  that  the  increment  be  one  half  or  one  third  that  of 
the  probable  load  at  the  elastic  limit,  thus  giving  larger  strains 
but  fewer  observations.  Apply  one  increment  of  load  to  the 
specimen  before  measurements  of  elongation  are  made,  since  by 
loading  specimens  up  to  1000  or  2000  pounds  per  square  inch 
the  effect  of  initial  errors,  such  as  occur  generally  at  the  com- 
mencement of  each  test,  are  lessened.  The  auxiliary  apparatus 


148  EXPERIMENTAL  ENGINEERING.  [§  96. 

adjusts  itself  somewhat  during  this  period  of  loading,  and  the 
specimen  assumes  a  true  position  should  any  slight  irregularity 
exist. 

96.  Attachment  of  Extensometer. — Attach  the  auxiliary 
apparatus  for  measuring  stretch,  or  obtaining  autographic  dia- 
grams. The  method  of  attaching  extensometers  will  depend 
on  the  special  form  used  (see  Articles  80  to  86),  but  this  act 
should  always  be  carefully  performed,  and  the  specimen  exactly 
centred  in  the  extensometer,  and  the  gauge-points  arranged 
8  inches  apart.  The  following  directions  for  applying  and  using 
the  Henning  extensometer  will  serve  to  show  the  method  to  be 
used  in  all  cases. 

The  Henning  extensometer  (see  Article  83,  Fig.  74,  page 
130)  is  attached  and  used  as  follows:  Before  attaching  the  in- 
strument, adjust  the  knife-edges  in  the  clamps  by  means  of  the 
two  milled  nuts  so  that  they  are  equally  distant  from  the 
frame  and  not  so  far  apart  as  the  diameter  of  the  test-piece. 
Then,  since  the  springs  acting  on  the  knife-edges  are  of  equal 
strength,  the  instrument  will  adjust  itself  in  the  plane  of  the 
screws  symmetrically  with  respect  to  the  test-piece.  Advance 
or  withdraw  the  set-screws  until  their  points  are  equally 
distant  from  the  frame  and  far  enough  apart  to  admit  the  test- 
piece. 

Separate  the  upper  portion  of  the  instrument,  put  it  around 
the  test-piece  (already  inserted  in  the  machine)  near  the  upper 
shoulder,  with  the  smaller  part  to  the  right,  force  together  and 
fasten  securely.  Advance  the  set-screws  simultaneously  until 
their  points  indent  the  test-piece.  Separate  the  lower  portion, 
put  it  around  the  test-piece  with  the  vertical  scales  to  the  front, 
force  together  and  secure.  Hang  the  links  on  the  proper  bear- 
ings on  both  portions  of  the  instrument.  Then  advance  the 
set-screws  as  above.  Throw  the  links  out,  take  readings  of  the 
micrometers,  apply  the  first  increment  of  load,  and  proceed 
with  the  test  as  directed.  To  read  the  micrometers  make  the 
electrical  connections ;  advance  one  micrometer  until  the  bell 
rings  announcing  contact,  back  off  barely  enough  to  stop  ring, 
ing,  and  advance  the  other  until  the  bell  rings.  Back  off  as 


§  98-]          TESTING  MATERIALS   OF   CONSTRUCTION.  149 

before,  and  read  both  micrometers.  The  vertical  scale  and  the 
micrometer  head  are  graduated  so  that  readings  to  T^-Q-Q-  inch 
can  be  obtained  directly. 

97.  Tension   Test. — The  test   is  made  by  applying  the 
stress  continuously  and  uniformly  without  intermission  until 
the  instant  of  rupture,  only  stopping  at  intervals  long  enough 
to  make  the  desired   observations    of   stretch  and  change  of 
shape.     The  stress   should   at   no   time  be  decreased  and  re- 
applied  in  a  standard  test,  but  should  be  maintained  continu- 
ously.    The  auxiliary  apparatus  for  measuring  strain  must  be 
removed  before  rupture  takes  place,  except  it  is  of  a  character 
not  likely  to  be  injured.     It  should  usually  be  taken  off  very 
soon   after   the  elastic   limit   is   passed  ;   although   for  ductile 
material  it  may  be  left  in  place  for  a  longer  time  after  the 
elastic  limit  has  been  passed  than  for  hard  and  brittle  materials. 
The  material  is  then  to  be  loaded  until  fracture  takes  place, 
keeping  the  beam  floating,  after  which  the  distortion  for  each 
part  is  to  be  measured  by  comparison  with  the  reference  divi- 
sions on  the  test-piece,  measured  from  the  point  of  rupture  as 
previously  explained.     It  is  to  be  noted  that  measurements 
within  the  elastic  limit  are  of  especial  importance,  since  materials 
in  use  are  not  to  be*  strained  beyond  that  point. 

98.  Report. — Remove  the  fractured  piece  from  the  machine ; 
make  measurements  of  shape,  external  and  fractured  surface ; 
give  time  required  in  making  the  test.*    When  fracture  is  cup- 
shaped,  state  the  position  of  cup — whether  in  upper  or  lower 
piece. 

In  recording  the  results  of  tests,  loads  at  elastic  limit,  at 
yield-point,  maximum,  and  instant  of  rupture  are  all  to  be  noted. 

The  load  at  elastic  limit  is  to  be  that  stress  which  produces 
a  change  in  the  rate  of  stretch. 

The  load  at  yield-point  is  to  be  that  stress  under  which  the 
rate  of  stretch  Jbddenly  increases  rapidly. 


*See  Report  of  Committee  on  Standard  Tests,  Vol.  XL,  Am.  Society  Mech. 
Engrs. 


150  EXPERIMENTAL   ENGINEERING.  [§  98. 

The  maximum  load  is  to  be  the  highest  load  carried  by  the 
test-piece. 

The  load  at  instant  of  rupture  is  not  the  maximum  load 
carried,  but  a  lesser  load  carried  by  the  specimen  at  the  instant 
of  rupture. 

In  giving  results  of  tests  it  is  not  necessary  to  give  the  load 
per  unit  section  of  reduced  area,  as  such  figure  is  of  no  value; 
(i)  because  it  is  not  always  possible  to  obtain  the  load  at  in- 
stant of  rupture  ;  (2)  because  it  is  generally  impossible  to  obtain 
a  correct  measurement  of  the  area  of  section  after  rupture; 
(3)  lastly,  because  the  amount  of  reduction  of  area  is  principally 
dependent  upon  local  and  accidental  conditions  at  the  point  of 
rupture.  The  modulus  or  coefficient  of  elasticity  is  to  be 
deduced  from  measurements  of  strain  observed  between  fixed 
increments  of  load  per  unit  section  ;  between  2000  pounds  per 
square  inch  and  12,000  pounds  per  square  inch;  or  between 
IOOO  pounds  per  square  men  and  11,000  pounds  per  square 
inch.  With  this  precaution  several  sources  of  error  are 
avoided,  and  it  becomes  possible  to  compare  results  on  the 
same  basis. 

In  the  report  describe  the  testing-machine  and  method  of 
testing,  form  and  dimensions  of  specimen,1  character  and  posi- 
tion of  rupture.  Calculate  coefficients  of  elasticity,  maximum 
strength,  breaking-strength,  strength  at  elastic  limit,  and  resili- 
ence, and  submit  a  complete  log  of  test.  Also,  draw  a  strain 
diagram  on  cross-section  paper;  make  a  sketch  of  surface  of 
rupture.  The  curve  of  stress  and  strain  is  to  be  drawn  as 
follows:  Plot  a  curve  of  stress  and  strain  up  to  a  point  beyond 
the  elastic  limit,  using  for  ordinates  values  of  /,  on  the  scale 
I  div.  =  2000  Ibs.  per  sq.  in.,  and  for  abscissae  values  of  e,  on 
the  scale  I  div.  =  o.oooi";  compute  E  and  p.  Then  plot  the 
complete  curve  of  stress  and  strain  to  the  point  of  rupture, 
using  scales  of  I  div.  =  10,000  Ibs.  per  sq.  in.,  and  i  div.  =  o.oi 
inch  for  ordinates  and  abscissae,  respectively. 

A  blank  form  for  the  log  is  shown  below,  which  is  to  be 
filled  out  and  filed.  On  this  log  is  to  be  entered,  value  of  the 


§98.] 


TESTING  MATERIALS  OF  CONSTRUCTION. 


modulus  of  elasticity,  load  at  elastic  limit,  character  of  rupture, 
area  of  least  section,  and  measurements  between  each  mark 
made  on  the  specimen. 

The  following  form  is  used  by  the  author  for  both  tension 
and  compression  tests : 

Test  of by ,.„ 

Kind  of  Test 

Material  from 

Machine  used Date 189 

Time  of  Testing min.  Tempt degrees  F. 


No. 

Load. 

Micrometer- 
readings. 

Extension. 

Modulus 
Elasticity. 
E     ' 

Actual. 
P 

Per  sq.  in. 
/ 

I 

II 

Mean. 

Actual. 
A 

Difference. 
AA 

Per  in. 

e 

Original  length in.    Diameter in.    Area sq.  in. 

Final  "     in.    Diameter in.    Area " 

Form  of  section Fracture:  position ;  character 

Moduli:  resilience ;  breaking-strength 

Load  per  sq.  inch:  elastic  limit max breaking 

Equivalent  elongation  for  8  inches inches per  cent. 

Elongation Reduction  area per  cent.     Local  elongation  each 

half-inch,  from  top,  ist ;  2d ;  3d ;  4th ;    5th ; 

6th ;  7th ;  8th ;  gth ;  loth ;  nth ;  I2th  ...; 

i3th ;  I4th ;  isth ;  i6th 


The  following  form,  from  Vol.  XL  Trans.  American  Society 
Mech.  Engineers,  is  excellent  for  reporting  the  principal 
results  of  a  series  of  tests.  Attention  is  called  to  the  full 
descriptions  accompanying  the  report. 


152 


EXPERIMENTAL  ENGINEERING. 


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TESTING  MATERIALS   OF  CONSTRUCTION. 


Prof.  G.  Lanza  of  the  Massachusetts  Institute  of  Tech- 
nology uses  the  following  forms  for  log  and  report  of  tension- 
tests  : 


TENSION-TEST. 
Date . . 


No 

Specimen 

Length  between  clamps. Tested  by. 

Original  section 


Loads. 


Actual.     Per  sq.  in. 


Micrometer-readings. 


Mean. 


Differences. 


Actual.     Per  inch. 


Remarks. 


Fractured  section Breaking-stress  per  sq.  in.  fractured  section. , 

Reduction  of  area  of  cross-section Modulus  of  elasticity 

Ultimate  extension Modulus  of  elastic  resilience 

Cross-section  at  maximum  load Modulus  of  ultimate  resilience, 

Tensile  limit  per  sq.  in , 

REPORT. 

No Date , 

Specimen , 

Length  between  clamps,      , 

Original  section, , 

Elastic  limit, , 

Breaking-load, , 

Fractured  section, , 

Reduction  of  area  of  cross-section, 

Ultimate  extension, 

Breaking-stress  per  square  inch  fractured  section, 

Modulus  of  elasticity,     . 

Signed , 


154  EXPERIMENTAL  ENGINEERING.  L§  99> 


COMPRESSION-TESTS. 

99.  Methods  of  Testing  by  Compression,  i.  Short 
Pieces:  Method  of  Testing. — In  case  of  short  pieces,  measure- 
ments of  strain  cannot  be  made  on  the  test-piece  itself,  but 
must  be  made  between  points  on  the  heads  of  the  testing- 
machine.  It  is  necessary  to  ascertain  and  make  a  correction 
for  the  error  due  to  the  yielding  of  the  parts  of  the  testing- 
machine.  This  is  done  as  follows :  Lower  the  moving-head 
until  the  steel  compression-plate  presses  on  the  steel  block  in 
the  lower  platform  with  a  force  of  about  500  pounds.  Attach 
the  micrometers  to  the  special  frame,  which  is  supported  by 
the  upper  platform,  and  read  to  a  point  on  the  movable  head. 
With  load  at  500  pounds,  read  both  micrometers.  Apply  loads 
by  increments  of  1000  pounds  up  to  three  fourths  the  limit  of 
the  machine,  taking  corresponding  readings.  Plot  a  curve  of 
loads  and  deflections  with  ordinates  I  long  division  =  1000 
pounds,  and  abscissae  I  long  division  =  o.ooi  inch.  From 
this  curve  obtain  corrections  for  the  deflections  caused  by  the 
loads  used  in  the  compression-test.  In  making  the  test  calcu- 
late the  increment  of  load  as  explained  for  tensile  strain,  Arti- 
cle 98.  Conduct  the  experiment  in  the  same  manner  as  for 
tension,  except  that  the  stress  is  applied  to  compress  instead 
of  to  stretch  the  specimen.  If  the  material  tested  is  hard  or 
brittle,  as  in  cast-iron,  care  should  be  taken  to  protect  the 
person  from  the  pieces  which  sometimes  fly  at  rupture. 

Report  and  draw  curve  as  for  tension-tests,  and  in  addition 
show  why  brittle  material  breaks  in  planes,  making  angles  of 
about  45°  with  the  axis  of  the  piece ;  compare  the  results 
obtained  for  wrought-iron  in  compression  with  those  obtained 
in  tension. 

2.  Long  Pieces:  Method  of  Testing. — In  this  case  the  exten- 
someters  used  for' tension-tests  can  be  connected  directly  to 
the  specimen,  and  the  measurements  taken  in  substantially  the 
same  way,  except, that  the  heads  of  the  extensometer  will 
approach  instead  of  recede  from  each  other ;  this  makes  it 


§  100.]        TESTING  MATERIALS  OF  CONSTRUCTION.  I$$ 

necessary  to  run  the  screws  back  each  time  after  taking  a  meas- 
urement a  distance  greater  than  the  compression  caused  by 
the  increment  of  load.  In  case  large  specimens  are  tested 
horizontally,  initial  flexion  is  to  be  avoided  by  counterweight- 
ing  the  mass  of  the  test-piece. 

Calculate  the  increment  of  load  as  one  tenth  the  breaking- 
load  given  by  Rankine's  formula,  Article  51,  page  74.  Apply 
the  first  increment  and  take  initial  reading  of  micrometers; 
continue  this  until  after  the  elastic  limit  has  been  passed,  after 
which  remove  the  extensometer,  and  apply  load  until  rupture 
takes  place.  Protect  yourself  from  injury  by  flying  pieces. 
Compute  the  breaking  coefficient  C  by  Rankine's  formula,  and 
compare  with  the  usual  results. 

Compute  the  modulus  of  elasticity  by  Ruler's  formula: 

(1)  />"  =EIn*+-r*  (Church,"  Mechanics  of  Materials,"  p.  366). 

(2)  E  =  /"V>0"  4-  **/.    /"  =  /  -  A".    (3)  £  =  (/-  IdJP'  -r-  *•/. 

Also  by  the  method  used  in  testing  short  specimens. 

In  the  above  approximate  formula  the  notation  is  the  same 
as  in  Article  48,  page  72. 

Note  in  the  report,  load  at  elastic  limit,  yield-point,  and 
ultimate  resistance,  as  well  as  increase  of  section  at  various 
points,  and  total  compression  calculated  as  explained  for 
tension. 

Submit  a  strain-diagram,  and  follow  the  same  general  direc- 
tions as  prescribed  in  the  report  for  tensile  strain,  Article  98. 

TRANSVERSE  TESTS. 

100.  Object. — This  test  is  especially  valuable  for  full-sized 
pieces  tested  with  the  load  they  will  be  required  to  carry  in 
actual  practice. 

The  deflections  of  such  pieces,  with  loads  at  centre  or  in 
various  other  positions,  afford  means  of  computing  the  coeffi- 
cients of  elasticity  and  the  form  of  the  elastic  curve. 

Method  of  Testing. — Arrange  the  machines  for  such  tests 


156  EXPERIMENTAL  ENGINEERING.  [§  IOO. 

by  putting  in  the  supporting  abutments,  and  by  arranging  the 
head  for  such  tests,  or  else  by  using  the  special  transverse 
testing-machine. 

In  this  experiment  the  test-piece  is  usually  a  prismatic 
beam,  3  feet  long  (see  Article  91,  page  142),  and  it  is  supported 
at  both  ends,  the  stress  being  applied  at  the  centre.  The 
same  data  are  required  to  be  observed  as  in  the  preceding 
experiment,  viz.,  loads  and  deflections,  or  stresses  and  corre- 
sponding strains. 

Sharp  edges  on  all  bearing-pieces  are  to  be  avoided,  and 
the  use  of  rolling  bearings  which  move  accurately  with  the 
angular  deflections  of  the  ends  of  the  bars  are  recommended  ; 
otherwise  the  distance  between  fixed  supports  measured  along 
the  axis  of  the  specimen  is  continually  changing. 

Place  the  test-bar  upon  the  supports,  and  adjust  the  latter 
36  inches  apart  between  centres,  and  so  that  the  load  will  be 
applied  exactly  at  the  middle.  Obtain  the  necessary  dimen- 
sions, and  calculate  the  probable  strength  at  elastic  limit  and 
at  rupture  by  means  of  the  formula/  =  Wle  -=-  4/.  (See  Arti- 
cle 52,  page  78.)  Adjust  the  specimen  in  the  machine  in  a 
horizontal  plane,  and  apply  the  stress  at  the  centre  normal 
to  the  axis  of  the  specimen,  and  in  a  plane  passing  through 
the  three  points  of  resistance. 

Measure  the  deflections  at  the  centre  from  a  fixed  plane 
or  base,  allowing  for  the  settling  of  the  supports,  or  by  the 
special  deflectometer  (see  Article  87,  page  135),  from  which 
compute  the  coefficient  of  resilience  and  the  modulus  of 
elasticity. 

Balance  the  scale-beam  with  the  test-bar  in  position  and 
the  deflectometer  lying  on  the  platform.  Set  the  poise  for  one 
increment  of  load  and  apply  stress  until  the  beam  tips.  Place 
the  poise  at  zero,  and  balance  by  gradually  removing  the  load. 
Place  the  deflectometer  in  position  on  the  supports,  and  with 
the  micrometer  at  zero  make  contact  and  record  zeio-reading 
iind  zero-load. 

Apply  the  load  in  uniform  increments  equal  to  about  one 
fifth  the  calculated  load  for  the  elastic  limit,  stopping  only 


§  101.]       TESTING  MATERIALS  OF  CONSTRUCTION. 


157 


long  enough  to  measure  the  deflections.  Wrought-iron  is  to 
be  strained  only  until  it  has  a  sensible  permanent  set,  but  cast- 
iron  and  wood  are  to  be  tested  to  rupture.  Wood  specimens 
generally  rupture  on  one  side  only :  in  that  case  turn  over  and 
make  complete  test  as  in  the  first  instance. 

101.  Form  of  Report. — In  the  report  describe  the  ma- 
chine, method  of  making  test,  form  of  cross-section,  peculi- 
arities of  the  section,  and  make  a  sketch  showing  position  and 
form  of  rupture.  Submit  a  complete  log  of  the  test,  together 
with  drawing  of  the  elastic  curve,  to  be  filed  for  permanent 
record.  The  following  is  a  form  for  data  and  results  of  a 
transverse  test : 


DATA  OF  TRANSVERSE  TEST  OF. 


Form  of  cross-section .... 

Length  between  supports ins. 

On Testing-machine. 

Time hrs mins. 


Date Observers 


No. 

Load 

W. 

Deflection. 

Remarks. 

Reading. 

Net. 

REPORT  OF  TRANSVERSE  TEST. 

Material I Wt.  per  cu.  ft, 

Form  

Composition Specific  Gravity 

Load  A  pplied 

t  estimj  machine 

Time hrs min. 

Cate ,189         Observers:?" 


Jbs. 


I58 


EXPERIMENTAL  ENGINEERING. 


[§  101. 


Dimensions. 

Symbol 

in. 

7 

D 

b 

in. 

h 

e 

I 

Load. 

Actual. 

Reduced  per  sq.  in. 
in  Outer  Fibre. 

Deflection. 

3 

%                 8 

-3              ? 

fi 

ft    Ibs 

v« 

iL              ° 

Remarks: 

*c             •% 

*         5 

The  following  forms  are  used  by  Prof.  Lanza  in  the  labora- 
tory of  the  Institute  of  Technology  for  log  and  report  of  trans 
verse  test : 

LOG. 

No Date 

Specimen 

Span Wt.  of  beam Wt.  of  yoke,  etc....... 

Position  of  load 


Tested  by. 


Loads. 

Micrometer-readings. 

Mean. 

Differences. 

Remarks. 

i 

a 



2 

Modulus  of  elasticity 

Modulus  of  rupture  (including  weight  of  beam). 
Maximum  intensity  of  longitudinal  shear 


102.]       TESTING  MATERIALS  OF  CONSTRUCTION.  159 


No  

REPORT 
Date  

Span,     

Dimensions, 

Weight  of  beam 

Weight  of  yoke,  etc.,    . 

Deflection,      

Modulus  of  elasticity, 

Modulus  of  rupture  (including  weight  of  beam), 

Maximum  intensity  of  longitudinal  shear ; 

(Signed) 

102.  Elastic  Curve. — The  object  of  this  experiment  is  to 
determine  the  coefficient  and  moduli  of  the  material,  by  loads 
less  than  that  required  at  the  elastic  limit.  The  required 
general  formulae  are  to  be  found  in  Art.  52,  page  77.  A  table 
of  deflections  corresponding  to  various  centre  loads  is  to  be 
found  on  page  79.  The  beam  is  to  be  supported  at  both  ends 
on  rounded  supports  or  on  rollers.  The  loads  consist  of  weights 
of  known  amount  that  can  be  suspended  at  various  points. 

Apparatus  needed. — Cathetometer  or  other  suitable  instru- 
ment for  measuring  deflection. 

Directions. — Obtain  dimensions  of  beam,  compute  moment 
of  inertia  of  cross-section ;  note  material  of  beam,  and  com- 
pute probable  deflection  and  corresponding  load  at  elastic 
limit. 

Carefully  divide  the  length  of  the  beam  into  equal  parts, 
and  mark  these  divisions  on  the  centre-line  of  the  beam.  With 
no  load  on  the  beam,  take  cathetometer-readings  of  each  point, 
then  apply  successive  increment  of  loads,  each  equal  to  one 
fifth  the  f  robable  load  at  the  elastic  limit,  and  take  correspond- 
ing readings  of  the  cathetometer.  From  readings,  obtain 
the  deflections  for  each  point,  and  plot  the  elastic  curve. 
Compute  the  deflections  for  the  corresponding  points  from  the 
formula,  using  tabulated  values  of  E,  and  plot  the  correspond- 
ing theoretical  curve.  Make  deductions  concerning  the  rela- 
tion of  the  two  curves. 


l6o  EXPERIMENTAL  ENGINEERING.  [}  103 

The  above  experiment  is  to  be  performed  with  the  load  at 
center,  and  again  with  the  load  at  a  point  one  fourth  or  one 
third  the  length  of  the  beam. 

Similar  experiments  may  be  performed  on  beams  fixed  at 
one  end,  or  fixed  at  one  end  and  supported  at  the  other. 


TORSION-TEST. 

103.  Object. — The  object  of  this  experiment  is  to  find  the 
strength  of  the  material  to  resist  twisting  forces,  to  find  its 
general  properties,  and  its  moduli  of  rigidity  and  shearing- 
strength. 

Thurston's  Machine. — The  special  directions  apply  only  to 
Thurston's  torsion-machine  (see  Article  73,  Figs.  61  and  62, 
page  114).  In  the  use  of  the  machine  the  constants  are  first  ob- 
tained, the  test-piece  inserted  between  the  jaws  of  the 
machine,  stress  applied,  and  the  autographic  strain-diagram 
obtained.  This  diagram  is  on  a  large  scale,  and  gives  quite 
accurate  measures  of  the  stresses  or  loads.  The  diagram  is, 
however,  drawn  by  attachment  to  the  working  parts  of  the 
frame,  and  consequently  any  yielding  of  the  frame  or  slipping 
of  the  jaws  appears  on  the  diagram  as  a  strain  or  yield  of  the 
specimen.  The  angular  deformation  or,  as  obtained  from  the 
diagram,  is  likely  to  be  too  great,  especially  within  the  elastic 
limit.  This  error  should  be  determined  in  each  test  by  attach- 
ing index  arms  at  each  end  of  the  specimen,  and  corrections 
made  to  the  results  obtained  from  the  diagram. 

The  characteristic  form  of  diagram  given  by  the  torsion- 
machine  is  shown  in  Fig.  98,  in  which  the  results  of  tests  of 
several  materials  is  shown.  In  the  above  diagrams*  the  ordi- 
nates  are  moments  of  torsion  (Pa\  the  abscissae  are  develop- 
ments of  the  angle  of  torsion  (a).  The  value  of  one  inch  of 
ordinate  is  to  be  found  by  measuring  the  ordinate  correspond- 
ing  to  a  known  moment  of  torsion,  and  the  abscissa  corre- 

*  See  "  Mechanics  of  Materials,"  page  240,  by  I.  P.  Church.  Published  by 
Wiley  &  Son,  N.  Y. 


IO4-]       TESTING  MATERIALS   OF  CONSTRUCTION. 


161 


spending  to  one  degree  of  torsion  is  to  be  calculated  from 
the  known  radius  of  the  drum.  Knowing  these  constants, 
numerical  values  can  readily  be  obtained,  and  the  coefficients 
of  the  strength  of  the  material  can  be  computed. 

During  the  test,  relax  the  strain  occasionally  :  if  within  the 
elastic  limit,  the  diagram  will  be  retraced ;  but  if  beyond  that 


FIG.  98. 


limit,  a  new  path  is  taken,  called  an  "  elasticity "  line  by 
Thurston, which  is  in  general  parallel  to  the  first  part  of  the  line, 
and  shows  the  amount  of  angular  recovery  BC,  and  the  per- 
manent angular  set  OB. 

104.  Methods  of  Testing  by  Torsion  with  Thurston's 
Autographic  Testing-machine.     (See  Articles  55  and  73.) 

Method. — Determine  first  the  maximum  moment  of  the, 
pendulum.  This  may  be  done  by  swinging  the  pendulum  so 
that  its  centre-line  is  horizontal,  supporting  it  on  platform- 
scales  and  taking  the  weight  and  the  distance  of  the  point  ot 
support  from  the  centre  of  suspension  of  the  pendulum.  The 
product  of  these  two  quantities  is  the  maximum  moment  of 
the  pendulum.  Make  three  determinations,  using  different 
lever-arms,  and  take  the  mean  for  the  true  moment  of  the 
pendulum.  A  correction  for  the  friction  of  the  journal  of  the 
pendulum  must  be  made.  When  hanging  vertically,  measure 
with  a  spring-balance,  inserted  in  the  eye  near  the  bob,  the 
force  necessary  to  start  the  pendulum.  Add  this  moment  to 
that  obtained  above,  and  the  result  is  the  total  maximum 
moment  of  the  pendulum.  From  this  the  value  of  the  mo 
ment  for  any  angular  position  may  be  calculated. 


1 62 


EXPERIMENTAL  ENGINEERING. 


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§  105-]       TESTING  MATERIALS  OF  CONSTRUCTION.  163 

Note  the  variation  of  the  pencil-point  between  the  vertical 
and  the  horizontal  positions  of  the  pendulum.  This  distance 
laid  down  on  the  F-axis  of  the  record-sheet  corresponds  to 
the  maximum  moment  obtained  above,  whence  calculate  the 
value  of  one  inch  of  ordinate.  Calculate  the  length  corre- 
sponding to  one  degree  on  the  surface  of  the  paper  drum, 
parallel  to  the  X-axis.  This  will  be  the  unit  to  be  used  in 
calculating  the  angle  of  torsion.  Fix  the  paper  on  the  drum 
and  draw  the  datum-line  or  J5f-axis.  Insert  the  test-piece  be- 
tween the  centres  and  screw  in  the  centre  until  the  neck  of  the 
test-piece  is  about  midway  between  the  jaws.  Wedge  the  test- 
piece  between  the  jaws  as  firmly  as  possible  by  hand,  and  then 
tap  the  wedges  slightly  with  a  copper  hammer.  Fasten  an 
index-arm  to  each  end  of  the  specimen  in  such  a  manner  that 
twisting  or  slipping  of  the  specimen  can  be  observed  by  ref- 
erence to  the  centre  of  the  pendulum  on  one  end,  and  to  a 
fixed  point  on  the  drum  on  the  opposite  end.  Throw  the 
worm  into  gear  and  turn  the  handle  slowly  and  steadily  until 
rupture  occurs,  only  relaxing  the  stress  once  or  twice  during 
the  test.  Take  the  record  of  all  the  test-pieces  on  the  same 
sheet  with  the  same  origin  of  co-ordinates. 

Correct  each  diagram  for  amount  of  slipping  of  test-piece 
or  yielding  of  frame  by  reference  to  index-arms  carried  by  the 
test  specimen. 

The  record  of  torsion-tests,  page  162,  is  a  numerical  example, 
obtained  from  diagrams  similar  to  those  shown  in  Fig.  98. 


IMPACT  TESTS. 

105.  Directions  for  Testing  Cast-iron  by  Impact  with 
Heisler's  Impact  Testing-machine.  (See  Article  76,  p.  1 19.) 

Method. — Take  a  transverse  test-bar  of  cast-iron  and  place 
it  in  the  machine,  cope  side  out,  so  that  the  blow  will  be 
struck  in  the  middle  of  its  length.  Arrange  the  autographic 
device  so  that  it  will  register  the  deflection  of  the  bar.  Place 
the  tripping  device  or  "dog"  for  a  fall  of  two  inches 
Catch  the  bob  at  this  point,  and  trip  at  every  notch  above 


1 64  EXPERIMENTAL  ENGINEERING.  [§  IO6. 

successively  until  the  bar  breaks.  Note  the  maximum  height 
of  fall.  Report  on  the  experiment  the  behavior  of  the  test- 
bar  and  character  of  its  fracture,  and  the  number  of  impacts 
and  the  force  in  inch-pounds  of  the  last  blow.  Compute  the 
resilience  of  the  test-piece.  Try  a  similar  bar  at  same  ultimate 
fall,  and  observe  the  number  of  blows  required  to  break  it. 
Draw  conclusions.  Write  complete  report,  and  give  moduli 
and  coefficients. 

106.  Drop-tests. — The  following  method  of  making  drop- 
tests  has  been  recommended  by  the  Committee  on  Standard 
Methods  of  Testing  appointed  by  the  American  Society  of 
Mechanical  Engineers,  and  is  substantially  the  same  as  adopted 
by  the  German  Engineers  at  Munich  in  1888 : 

Drop-tests  are  to  be  made  on  a  standard  drop,  which  is  to 
embody  the  following  essential  points : 

a.  Each  drop-test  apparatus  must  be  standardized. 

b.  The  ball  (falling  mass)  shall  weigh  1000  or  1500  pounds; 
the  smaller  is,  however,  preferable. 

c.  The   ball  may  be  made  of  cast-iron,  cast  or  wrought 
steel ;  the  shape  is  to  be  such  that  its  centre  of  gravity  be  as 
low  as  possible. 

d.  The  striking-block  is  to  be  made  of  forged  steel,  and  is 
to  be  secured  to  the  ball  by  dovetail  and  wedges  in  a  rigid 
manner,  and  so  that  the  striking-face  is  placed  strictly  sym- 
metrical about  and  normal  to  its  vertical  axis  passing  through 
the  centre  of  gravity.     Special  permanent  marks  are  to  indi- 
cate the  correctness  of  the  face  in  these  respects. 

Special  marks  should  be  made  to  indicate  the  centre  of 
the  anvil-block. 

e.  The  length  of  guides  on  the  ball  should  be  more  than 
twice  the  width  between  the  guides,  which  are  to  be  made  of 
metal ;  i.e.,  rails  so  placed  that  the  ball  has  but  a  minimum 
amount  of  play  between  them.     Graphite  is  recommended  as 
lubricant. 

/.  The  detachment  or  shears  must  not  cause  the  ball  to 
oscillate  between  the  guides,  and  must  be  readily  and  freely 
controllable,  with  the  point  of  suspension  truly  above  the 


§  lO?.]       TESTING  MATERIALS   OF  CONSTRUCTION.  165 

centre  of  gravity  of  the  ball ;  and  a  short  movable  link,  chain, 
or  rope  is  to  be  fixed  between  the  ball  and  shears  or  detach- 
ment. 

g.  When  a  constant  height  of  drop  is  used,  an  automatic 
detaching  device  is  recommended. 

h.  The  bearings  for  the  test-piece  are  to  be  rigidly  attached 
to  the  scaffold  or  frame,  and  they  should  be,  wherever  possible, 
in  one  piece  with  it. 

i.  The  weight  of  frame,  bearings,  and  anvil-block  should  be 
at  least  ten  times  that  of  the  ball. 

k.  The  foundation  should  be  inelastic,  and  consist  of 
masonry,  the  magnitude  of  which  is  to  be  determined  by  the 
locality  and  subsoil. 

/.  The  surface  struck  should  always  be  accurately  level; 
therefore  proper  shoes  or  bearing-blocks  are  to  be  provided 
for  testing  rails,  axles,  tires,  springs,  etc.,  etc.,  to  insure  a 
proper  level  upper  surface ;  these  blocks  are  to  be  as  light  as 
possible. 

The  exact  shape  of  these  bearing-blocks  is  to  be  given  on 
each  test  report. 

m.  The  gallows  or  frame  should  be  truly  vertical  and  the 
guides  accurately  parallel. 

n.  The  height  of  fall  of  ball  should  be  20  feet  clear,  be- 
tween striking  and  struck  surfaces. 

0.  Drops  which  by  friction  of  ball  on  guides  absorb  two 
per  cent  of  the  work  due  to  impact  are  to  be  discarded. 

/.  For  large  tests  a  ball  weighing  2000  pounds  is  to  be 
used. 

q.  A  sliding-scale  is  to  be  attached  to  the  frame,  and  in 
such  a  manner  that  the  zero-mark  can  always  be  placed  on  a 
level  with  the  top  of  the  test-piece. 

SPECIAL  TESTS  OF  MATERIALS. 

107.  The  following  comparative  tests  are  often  useful : 

1.  The  Welding-test. — This  is  to  be  done  with  a  hammer 
weighing  eight  to  ten  pounds,  with  a  given  number  of  blows. 


1 66  EXPERIMENTAL   ENGINEERING.  [§  lO/« 

The  weld  is  to  be  a  simple  scarf  weld,  made  in  a  coke  or  gas 
flame  without  fluxes.  Each  bar  to  be  tested  to  be  treated  in 
the  same  way,  using  in  each  case  two  or  three  samples  of 
iron ;  one  sample  to  be  tested  on  the  tension-machine,  the 
other  to  be  nicked  to  the  depth  of  the  weld  and  then  bent  or 
broken,  to  show  the  character  of  the  welded  surfaces. 

2.  The  Bending-test. — This  affords  a  ready  means  of  find- 
ing  the  ductility  of  metals.     The  test-piece  is  to  be  bent  about 
a  stud  having  a  diameter  twice  that  of  the  specimen.     The 
piece  is  to  be  bent  with  a  lever,  and  no  pounding  is  permitted. 
If  the  plate  holding  the  stud  is  graduated,  the  angular  deflec- 
tion at  time  of  permanent  set  may  be  read  at  once.     A  modi- 
fication of  the  bending-test   is  often   used   to  determine  the 
property  of  toughness,  by  bending  the  specimen,  first  hot  and 
then  cold,  until  it  is  doubled  over  on  itself. 

3.  The  Hardening-test  is  used  in  connection  with  the  other 
tests  to  determine  the  qualities  of  the  specimen ;  the  mate- 
rial, one  specimen  of  which,  having  been  previously  welded,  is 
carefully  heated  to  a  red  heat,  and  plunged  in  water  having  a 
temperature  of  32—40  degrees.      This  specimen  is  tested  by 
torsion  and  bending,  the  same  as  the  unhardened  specimen. 

4.  The  Forging-test. — The  material   is   brought  to   a    red 
heat  and  hammered  until  cracks  begin  to  show,  the  relative 
amount  of  flattening  indicating  the  red-shortness  of  the  ma- 
terial.    Useful  principally  with  rivet-rods. 

5.  Punching-tests. — Find  the  least  material  that  will  stand 
between  the  edge  and  the-  hole  punched,  by  measurement. 

6.  Abrasion-tests. — Find  the  amount  of  wear  from  a  given 
amount  of  work. 

7.  Hammer-test. — This  is  made  with  a  light  hammer,  and 
the   character   of   the   material   is  determined    by  the  sound 
emitted.      Is  useful  in  locating  defects  in  finished  products, 
but  of  little  value  on  test  specimens. 

Fatigue  of  Metals,  or  the  effect  of  repeated  stresses,  is  a 
matter  of  great  practical  importance,  and  was  investigated 
very  extensively  by  Wohler.  These  results  are  discussed  in 
full  m  a  work  by  Weyrauch.  It  is  well  established  that  the 


§  108.]        TESTING  MATERIALS   OF  CONSTRUCTION.  1 67 

breaking-point  is  lowered  by  a  large  number  of  applications 
of  stress.  The  proportional  loads  for  wrought-iron,  according 
to  Wohler,  being  as  follows :  Breaking-load  applied  once,  4 ; 
tension  alternating  with  no  stress,  2  ;  tension  alternating  with 
compression,  I. 

Rest  of  materials  or  removal  of  stress  in  some  instances 
seems  to  restore  both  strength  and  elasticity. 

Viscosity  or  the  fluidity  of  metals  under  certain  conditions 
is  also  well  established. 

The  effect  of  temperature  on  the  strength  of  metals  has  now 
been  thoroughly  investigated.  The  investigations  at  the 
Watertown  Arsenal  show  that  steel  and  wrought-iron  bars  in- 
crease slightly  in  tensile  strength  as  the  temperature  increases 
to  600°  F.,  and  then  decrease  in  proportion  to  increase  of 
temperature,  so  that  the  breaking  coefficients  at  1600°  F.  lie 
between  10,000  and  20,000  pounds.  See  U.  S.  Report,  Test 
of  Metals,  1888. 

108.  Tests  required  for  Different  Material.*— In  general 
the  material  is  to  be  tested  in  such  a  manner  as  to  develop 
the  same  strains  that  will  be  called  forth  in  the  peculiar  use  to 
which  it  is  devoted. 

The  table,  page  148,  shows  the  tests  that  are  prescribed  for 
materials  for  various  uses,  by  the  Committee  on  Standard 
Tests  and  Methods  of  Testing  of  the  American  Society  of 
Mechanical  Engineers. 

Pipes  and  Pipe-fittings. — These  should  be  subject  to  an 
internal  hydraulic  pressure. 

Car-wheels. — Car-wheels  are  usually  subjected  to  the  drop- 
test.  The  following  method  is  employed  by  the  Pennsylvania 
Railroad  Company  for  testing  cast-iron  wheels  : 

For  each  fifty  wheels  which  have  been  shipped,  or  are 
ready  to  ship,  one  wheel  is  taken  at  random  by  the  railroad 
company's  inspector,  either  at  the  railroad  company's  shops  or 
at  the  wheel-manufacturer's,  as  the  case  may  be,  and  subjected 
to  the  following  test:  The  wheel  is  placed  flange  downward 
on  an  anvil-block  weighing  1700  pounds,  set  on  rubble  masonry 
two  feet  down,  and  having  three  supports  not  more  than  five 

*  For  detailed  information  see  Proceedings  Am.  Soc.  Testing  Materials. 


168 


EXPERIMENTAL  ENGINEERING. 


§  109. 


TABLE  SHOWING  TESTS  REQUIRED. 
Required  Test  denoted  by  x. 


Material  used  for 

Tension. 

Compression. 

Transverse. 

Torsion. 

ti 

£ 

Welding. 

Bending. 

Hardening. 

Forging, 

Abrasion. 

Punching. 

X 

Shafting 

x 

X 

x 

x 

X 

X 

x 

x 

X 

X 

X 

'  '            high  steel 

x 

x 

X 

X 

X 

X 

X 

X 

X 

x 

X 

X 

X 

"     plates  

Wire    

r* 

rf 

Cast-iron          .      ..    .  ...    . 

X 

X 

X 

Woods  

X 

X 

X 

Stones  

X 

X 

*  Repeat  in  both  directions— also  by  winding.         t  Longitudinal. 

inches  wide  for  the  wheel  to  rest  upon.  This  arrangement 
being  effected,  the  wheel  is  struck  centrally  on  the  hub  by  a 
weight  of  140  pounds,  falling  from  a  height  of  twelve  feet. 
Should  the  wheel  break  in  two  or  more  pieces  before  nine 
blows  or  less,  the  fifty  wheels  represented  by  it  are  rejected. 
If  the  wheel  stands  eight  blows  without  breaking  in  two  or 
more  pieces,  the  fifty  wheels  are  accepted. 

109.  Methods  of  Testing  Bridge-materials.— The  follow- 
ing directions  are  abstracted  from  the  standard  specifications 
adopted  by  bridge-builders.* 

Wrought-iron.  I.  Appearance. — All  wrought-iron  must  be 
tough,  ductile,  fibrous,  and  of  uniform  quality  for  each  class  ; 


See  Handbook  published  by  Carnegie,  Phipps  &  Co.,  Pittsburg. 


109.]       TESTING  MATERIALS  OF  CONSTRUCTION. 


169 


straight,  smooth,  free  from  cinder  pockets  or  injurious  flaws, 
buckles,  blisters,  or  cracks.  When  rolls  are  working  at  maxi- 
mum thickness,  poorer  finish  will  be  accepted. 

2.  Manufacture. — No  special   process   of    manufacture    re- 
quired. 

3.  Standard  Test-piece. — The  tensile  strength,  limit  of  elas- 
ticity and  ductility  shall  be  determined  from  a  standard  test- 
piece,  not  less  than  one  quarter-inch  in  thickness,  cut  from  a 
full-sized  bar,  and  planed  or  turned  parallel ;  if  the  cross-sec- 
tion  is  reduced,   the   tangent   between   shoulders  shall  be  at 
least  twelve  times  its  shortest  dimensions,  and  the  minimum 
area  of  cross-section  shall  not  be  less  than  one  fourth  square 
inch  in  area  and  not  more  than  one  square  inch.     Whenever 
practicable,  two  opposite  sides  of  the  piece  are  to  be  left  as 
they  come  from  the  rolls.     A  full-sized  bar  if  less  than  the  re- 
quired dimensions  may  be  used  as  its  own  test-piece. 

The  ductility,  or  per  cent  of  strain,  is  obtained  by  measuring 
the  elongation  after  breaking  from  the  point  of  rupture  both 
ways,  on  an  original  length,  ten  times  the  least  cross-section, 
or  at  least  five  inches  long. 

In  this  length  must  occur  the  curve  of  reduction  of  area. 

4.  Strength. — The  strength  of  the  specimens  to  be  a  func- 
tion of  the  size,  and  to  be  determined  by  the  formulae  in  the 
following  table : 


STRENGTH  OF  IRON  REQUIRED  FOR  BRIDGE-BUILDING. 


Character  of  the  Iron. 

Formulae  for  Ulti- 
mate Strength. 
Pounds  per  sq.  in. 

Strength  at 
Elastic  Limit. 
Per  cent  of 
Breaking. 

Elongation 
at  Rupture. 
Per  cent. 

Tension-iron,  pins   and   bolts,  and  ) 

"joooA 

plate-iron  less  than  8  inches  wide,  f 
Plate-iron  8  to  24  inches  wide   ....... 

B 
48000 

5° 

C.A     2 

12 

46000 

ei  .  e 

IO 

"        q6  to  d8       "         " 

« 

« 

5' 

Shaped  iron  not  specified  above  : 

7000^ 

"           over  •§•  inch  thick 

B 
« 

5° 
« 

15 
12 

1 70  EXPERIMENTAL  ENGINEERING.  [§  1 09. 

In  above  formulae  A  represents  area  in  square  inches,  B 
circumference  in  inches. 

5.  Hot-bending. — All   plates   and  angles   must   stand   at  a 
working  heat  a  sharp  bend  at  right  angles  without  sign  of 
fracture. 

6.  Rivet-iron. — Rivet-iron   must  be    tough   and   soft,  and 
capable  of  bending  cold  until  the  sides  are  in  close  contact. 

7.  Cold-bending. — All   tension-iron   pins,    bolts,   and    plate 
less  than  8  inches  wide,  must  bend  cold  180°,  to  a  curve  whose 
inner  radius  equals  the  thickness,  without  sign  of  fracture. 

8.  Specimens  of   full   thickness,   from    plate-iron    or  from 
flanges  or  webs  of  shaped  iron,  must  bend  cold  through  90°  to 
a  curve  whose  inner  radius  is  if  times  its  thickness. 

9.  Number  of  Test-pieces. — Four  standard  test-pieces  to  be 
tested  free  of  cost  on  each  contract,  with  one  additional  for 
each  50,000  pounds  of  iron,  and  as  many  more  as  the  con- 
tractor will  pay  for  at  $5  each.     If  any  test-piece  gives  results 
more  than  4  per  cent  below  the  requirements,  the  particular 
bar  from  which  it  was  taken  may  be  rejected,  but  the  results 
shall   be   included  in  the  average.     If  any  test-piecd  have  a 
manifest  flaw,  its  test  shall  not  be  considered.     Two  test-bars 
out  of  ten  falling  more  than  4  per  cent  below  the  requirements 
shall  be  a  cause  for  rejecting  the  whole  lot  from  which  they 
were  taken  as  a  sample. 

A  variation  of  more  than  2-f  per  cent  of  weight  will  also  be 
a  cause  for  rejection. 

Steel. — The  requirements  as  for  manufacture,  finish,  num- 
ber of  test-pieces  and  method  of  testing  as  for  iron. 

1.  Test-pieces. — Round  test-pieces  are  to  be  obtained  from 
three  separate  ingots  of  each  cast,  not  less  than  three  quarters 
of  an  inch  in  diameter  and  of  a  length  not  less  than  eight 
inches  between  the  jaws  of  the  testing-machine.     These  bars 
are  to  be  truly  rounded,  finished  at  a  uniform  heat,  and  ar- 
ranged to  cool  uniformly,  and  from  these  test-pieces  alone  the 
quality  of  the  material  shall  be  determined. 

2.  Strength. — All  the  above-described   bars  are  to  have  a 
tensile  strength,  not  Iess7than  4000  pounds  of  that  specified,  an 


§  I09-J        TESTING  MATERIALS  OF  CONSTRUCTION.  171 

elastic  limit  not  less  than  one  half  the  tensile  strength  of  the 
test-bar,  a  percentage  of  elongation  not  less  than  1,200,000, 
divided  by  the  tensile  strength  in  pounds  per  square  inch  ;  and 
a  percentage  of  reduction  of  area  not  less  than  2,400,000  di- 
vided by  the  tensile  strength  in  pounds  per  square  inch.  The 
elongation  should  be  measured  after  breaking  on  a  specimen, 
with  length  at  least  ten  times  the  least  diameter  of  the  cross- 
section,  in  which  length  must  occur  the  entire  curve  of  reduc- 
tion from  stretch. 

Directions  for  testing  and  rejecting  specimens  same  as  for 
iron. 

3.  Rivet-steel. — The  required  strength  is  60,000  pounds 
tensile  strength,  with  elastic  limit,  elongation,  and  fracture  as 
in  clause  2.  To  be  rejected  if  under  56,000  pounds,  and  to 
stand  the  same  bending-test  as  rivet-iron. 

Cast-iron. — All  castings,  except  where  chilled  iron  is 
specified,  shall  be  tough  gray  iron,  free  from  cold-shuts  or 
blow-holes,  true  to  pattern  and  of  workmanlike  finish.  Sample 
pieces  I  inch  square,  cast  from  the  same  heat  of  metal  in  sand- 
moulds,  shall  sustain  on  a  clear  space  of  4  feet  6  inches  a  cen- 
tral load  of  500  pounds. 

Workmanship. — Workmanship  must  be  first-class  ;  fin- 
ished surfaces  protected  by  white-lead  and  tallow  ;  rivet- 
holes  accurately  spaced,  and  truly  opposite  before  the  rivets 
are  driven. 

Rivets  must  completely  fill  the  holes,  and  be  of  a  height 
not  less  than  0.6  diameter  of  the  rivet. 

Eye-bars  and  Pin-holes. — Pin-holes  must  be  accurately 
bored,  and  within  -^  inch  of  position  shown  on  drawing;  its 
diameter  not  to  exceed  that  of  the  pin  by  0.02  inch  if  under  3^ 
inches,  or  by  0.03  inch  if  over  3^  inches. 

Eye-bars  must  be  straight,  with  holes  in  centre-line  and  in 
centre  of  head,  and  no  welds  in  the  body  of  the  bar.  All 
chord  eye-bars  from  the  same  panel  must  permit  pins  to  be 
easily  inserted  when  placed  in  a  pile. 

Tests    of  Eye-bars. — Tests   are   to   be   made   on    full-size 


EXPERIMENTAL  ENGINEERING.  [§  l  IO- 

specimens,  rolled  at  the  same  time  as  those  required  for  the 
structure. 

The  lot  to  which  the  sample  test-bars  belong  shall  be  ac- 
cepted when — 

a.  Not  more  than  one  third  the  bars  tested,  break  in  the 
eye. 

b.  Or  if   more  than  one  third  break  in  the  eye,  the  ten- 
sile  strength  is  within    5   per  cent  required    by  the  formula, 

T=  52000  —  ~^~D 5°°  (width  of  bar) ;  all  in  inches. 

Steel  bars  must  show  a  strength  within  4000  pounds  of 
that  required  in  clause  13. 

A  variation  in  thickness  of  heads  will  be  allowed,  not  ex- 
ceeding ^  inch  small,  or  T^-  inch  large,  from  the  specifications. 

Annealing. — If  a  steel  piece  is  partially  heated  during  the 
progress  of  the  work,  the  whole  piece  must  be  subsequently 
annealed.  All  bends  in  steel  must  be  made  cold,  or  the  piece 
must  be  subsequently  annealed. 

1 10.  Admiralty  Tests. 

Tests  for  Iron  Plate. 

Hot,  to  bend  without  fracture  from  90°  to  125°. 

Cold,  to  bend  without  fracture  to  the  following  angles : 
l-inch  plate. .  .lengthwise  10°  to  15°,  crosswise     5° 
i-  "         "...         "          20°  to  25°,         "  5°  to  10° 

i-  "         "...         "          30°  to  35°,         "  10°  to  15° 

i-  "         "...         "          55°  to  70°,        "          2o°to3oa 

Tests  for  Plate  Steel.* 

i.  Strength. — Strips  cut  lengthwise  or  crosswise  of  the  plate 
to  have  an  ultimate  tensile  strength  of  not  less  than  26  and 
not  exceeding  30  tons  per  square  inch  of  section,  with  an 
elongation  of  20  per.  cent  in  a  length  of  8  inches. 

*  See  "  Manual  of  the  Steam-engine,"  Vol.  II.,  page  488,  by  R.  H.  Thurston. 


§  III.]       TESTING  MATERIALS  OF  CONSTRUCTION.  173 

2.  Temper. — Strips  cut  lengthwise  of  the  plate   ij-  inches 
wide,  heated   uniformly  to    a  low  cherry-red    and    cooled   in 
water  of  82°  F.,  must  stand  bending  in  a  press  to  a  curve  of 
which  the  inner  radius  is  one  and  a  half  times  the  thickness  of 
the  plates  tested. 

3.  The  strips  are  to  be  cut  in  a  planing-machine,  and* have 
sharp  edges  removed. 

4.  The  ductility  of  every  plate  is  to  be  tested  by  the  appli- 
cation of  the  shearing  or  bending  tests  on  the  contractor's 
premises  and  at  his  expense.     The  plates  are  to  be  bent  cold 
with  the  hammer. 

5.  All   plates   to   be    free  from  lamination   and    injurious 
surface  defects. 

6.  One  plate  out  of  every  fifty  or  fraction   thereof   to  be 
taken  for  testing  by  tensile  and  tempering  test  from  every 
invoice. 

7.  The  pieces  cut  out  for  testing  are  to  be  of  parallel  width 
from  end  to  end,  or  for  at  least  8  inches  in  length.     A  latitude 
or  variation  in  thickness  will  be  permitted  of  10  per  cent  for 
plates  less  than  one  half-inch  thick,  and  of  5  per  cent  for  plates 
over  that  thickness. 

Tests  for  Angle,  Bulb,  or  Bar  Steel. 

1,  2.  Strength  and  Temper. — The  requirements  the  same  as 
for  plate  steel. 

3.  Number  of  Tests. — Cross  ends  to  be  cut  off,  and  one 
piece  for  each  fifty  or  fraction  thereof  to  be  tested  in  each 
invoice. 

in.  Lloyd's  Tests  for  Steel  used  in  Ship-building.* 
I.  Strength. — Strips  cut  lengthwise  or  crosswise  of  the  plate, 
and  also  angle  and  bulb  steel,  to  have  an  ultimate  tensile 
strength  of  not  less  than  27  and  not  exceeding  31  tons  per 
square  inch  of  section,  with  an  elongation  corresponding  to  20 
per  cent  on  a  length  of  8  inches  before  fracture. 

2.  Temper. — Tempering  test  the  same  as  the  Admiralty 

*See  Thurston's  "  Steam-engine,"  Vol.  II. 


174  EXPERIMENTAL   ENGINEERING.  [§  II 3, 

test,   except    that   inner   radius   of   bend  is  three  times   the 
thickness. 

Rivets  to  be  same  size  as  required  for  iron. 

1 1.2.  Standard  Specifications  for  Cast-iron  Water-pipe, 

Adopted  by  the   American  Water-works  Association,   Phila- 
delphia, 1891.     (Abstract  from  Transactions.) 

I.  Length. — Each  pipe  shall  be  of  the  kind  known  as 
"socket  and  spigot,"  and  shall  be  12  feet  long  from  bottom 
of  the  socket  to  the  end  of  the  pipe. 

2-7.  Metal. — The  metal  shall  be  best  quality  neutral  pig- 
iron,  with  no  admixture  of  cinder,  cast  in  dry-sand  moulds, 
placed  vertically,  numbered  and  marked  with  name  of  maker 
and  date  of  making.  The  shell  to  be  smooth  and  round,  with- 
out imperfections,  and  of  uniform  thickness. 

8-10.  Test-bars. — Test-bars  to  be  26  inches  long,  2  inches 
wide,  and  I  inch  thick,  and  to  be  tested  for  transverse  strength. 
These  bars  shall  stand,  when  carried  flatwise  on  supports  24 
inches  apart,  a  centre  load  of  1900  Ibs.,  and  show  a  deflection 
of  not  less  than  0.25  inch  before  breaking.  Test-bars  are  to 
be  cast  when  required  by  the  inspector,  and  to  be  as  nearly  as 
possible  the  specified  dimensions. 

12-16.  All  pipes  to  be  thoroughly  cooled  when  taken  from 
the  pit,  afterward  thoroughly  cleaned  without  the  use  of  acid, 
then  heated  to  300°  F.,  and  plunged  into  coal-pitch  varnish. 
When  removed,  the  coating  to  fume  freely  and  set  hard  within 
an  hour. 

17.  Testing. — The  pipes  to  be  tested  after  the  varnish  hard- 
ens with  hydrostatic  pressure  of  300  Ibs.  per  square  inch  for  all 
sizes  below  12  inches  diameter,  and  250  Ibs.  for  all  above  that 
diameter,  and  simultaneously  to  be  struck  with  a  3-lb.  hammer. 

18-20.  Templates  to  be  furnished  by  the  maker ;  the  weight 
of  pipe  to  vary  not  over  3  per  cent  from  the  standard ;  all  tests 
to  be  made  at  expense  of  maker. 

113.  Tests  of  Stone,  Brick,  Cements. — These  materials 
are  principally  used  in  walls  of  buildings  and  for  foundations. 
For  this  use  they  are  subjected  principally  to  compression 


§  1 1 4-]       TESTING  MATERIALS  OF  CONSTRUCTION.  1/5 

or  crushing  stresses.  The  important  properties  are  strength 
and  durability.  Stone  is  usually  tested  for  compressive  and 
transverse  strength,  brick  for  compressive  strength,  and  cement 
and  mortar  for  tension. 

114.  Testing  Stones. — The  specimens  for  compressive 
strength  are  cubes  of  various  sizes,  depending  principally  on 
the  capacity  of  the  testing-machine.  These  cubes  are  to  be 
nicely  made  with  the  opposite  sides  perfectly  parallel  to  pro- 
vide a  uniform  bearing-surface.  It  is  found  that  the  larger 
the  blocks  the  greater  the  strength  per  unit  of  area.* 

To  test  Stone  for  Compressive  Strength. — Have  the  specimen 
dry  and  dressed,  and  ground  to  a  cube  —  inches  on  each 
edge,  and  with  the  opposite  faces  parallel  planes.  This  is 
important,  as  imperfect  or  wedge-shaped  faces  concentrate  the 
stress  on  a  small  area.  In  testing,  use  a  layer  of  wet  plaster-of- 
Paris  between  the  specimen  and  the  faces  of  the  machine,  to 
distribute  the  stress. 

To  test  Stone  for  Transverse  Strength. — In  this  case  the 
specimen  is  dressed  into  the  form  of  a  prism  8  inches  long 
and  2  by  2  inches  in  section.  It  is  supported  on  bearings  6 
inches  apart,  and  a  centre  load  applied.  The  strength  is 
computed  as  explained  under  head  of  Transverse  Testing, 
page  78. 

Durability  of  stone  is  tested  accurately  only  by  actual  trial. 
Some  idea  can  be  formed  by  noticing  the  effect  of  the  weather 
on  the  exposed  rocks  in  the  quarry  from  which  the  specimen 
came. 

In  the  method  of  standard  tests  adopted  in  Munich  in  1887 
the  following  additional  tests  are  recommended: 

I.  Trial  method  with  (a)  a  jumper  or  drill,  (b)  by  rotary 
boring.  The  amount  of  work  done  by  the  drill  to  be  deter- 
mined by  the  momentum  of  drop,  its  velocity  of  rotation,  arid 
the  shape  or  cutting  angle  of  the  drill  or  cutting  tool.  These 
qualities  are  to  be  determined  by  comparison  with  a  standard 


*  See  Unwin,  "Testing  of  Materials." 


i;6  EXPERIMENTAL  ENGINEERING.  [§  114. 

drill  working  under  definite  conditions.     2.  Examine  the  stone 
for  resistance  to  shearing  as  well  as  to  boring. 

Report  the  results  of  the  boring  test  on  the  following  form : 

STANDARD  REPORT  BLANK  FOR  BORING  TEST. 

1.  Description  of  stone  in  its  geological  and  mineralogical  relations. 

2.  Miner's  classification  (hard,  very  hard,  or  extremely  hard). 

3.  Texture  \i.  e.,  coarse-grained,  fine-grained,  parallel,  normal  to  or  inclined 
to  axis  of  drill-hole). 

4.  Specific  gravity  of  the  stone. 

5.  Diameter  of  hole  drilled. 

6.  Diameter  of  hole  and  core  when  boring. 

7.  Straight  or  curve  edged  drills. 

8.  Angle  of  edge  of  drills. 

9.  Number  of  blows  per  revolution  of  drill. 

10.  Effective  weight  of  drill. 

11.  Mean  effective  drop  of  drill. 

12.  Number  of  blows  required  to  drill  the  depth  of  hole. 

13.  Number  and  form  of  teeth  of  borer. 

14.  Statement  of  pressure  on  and  velocity  of  bore,  while  boring. 

15.  Actual  or  total  depth  of  bore-hole. 

16.  Calculated  or  indicated  work  done  during  boring  stated  in  meter-kilo- 
grams per  c.  m.  of  hole  bored.    (When  using  a  hollow  borer  the  annulus  of 
stone  cut  away  is  alone  to  be  considered.) 

3.  Find  when  possible  the  position  in  the  quarry  originally 
occupied  by  the  specimen  tested. 

4.  Find  out  the  intended  use  of  the  stone,  and  determine 
the  character  of  tests  largely  from  that.     5.  Dry  the  stone 
until  no  further  loss  of  weight  occurs  at  a,  temperature  of  30°  C. 
(86°  F.),  and  test  in  a  dry  condition. 

Make  the  tests  for  strength  as  described,  using  as  large 
specimens  as  possible.  Also,  test  by  compression  rectangular 
blocks.  Test  also  for  tension  and  bending. 

6.  Obtain  the  specific  gravity,  after  drying  at  a  temperature 
of  86°  F. 

7.  Examine  the  specimen  for  resistance  to  frost  by  using 
samples  of  uniform  size,  7  cm.  (2.76  inches)  on  each  edge. 

8.  The  frost-test  consists  of : 

a.  The  determination  of  the  compressive  strength  of  satu- 
rated stones,  and  its  comparison  with  that  of  dried  pieces. 


§  II4-J        TESTING  MATERIALS  OF  CONSTRUCTION.  177 

b.  The  determination  of  compressive  strength  of  the  dried 
stone  after   having   been  frozen   and  thawed  out  twenty-five 
times,  and  its  comparison  with  that  of   dried   pieces   not  so 
treated. 

c.  The  determination  of   the  loss  of  weight  of   the  stone 
after  the  twenty-fifth  frost  and  thaw.     Special  attention  must 
be  had  to  the  loss  of  those  particles  which  are  detached  by  the 
mechanical  action,  and  also  those  lost  by  solution  in  a  definite 
quantity  of  water. 

d.  The  examination  of  the  frozen  stone  by  use  of  a  magni- 
fying-glass,  to  determine  particularly  whether  fissures  or  seal- 
ing  occurred. 

9.  For  the  frost-test  are  to  be  used  : 

Six  pieces  for  compression-tests  in  dry  condition,  three 
normal  and  three  parallel  to  the  bed  of  the  stone,  provided 
these  tests  have  not  already  been  made,  in  which  it  is  permis- 
sible, on  account  of  the  law  of  proportions,  to  use  cubical  test- 
blocks  larger  than  7  cm.  (2.76  inches). 

Six  test-pieces  in  saturated  condition — not  frozen,  how- 
ever ;  three  tested  normal  to  and  three  parallel  to  bed. 

Six  test-pieces  for  tests  when  frozen,  three  of  which  are  to 
be  tested  normal  to  and  three  parallel  to  bed  of  stone. 

10.  When  making  the  freezing-test  the  following  details  are 
to  be  observed : 

a.  During  the  absorption  of  water  the  cubes  are  at  first  to 
be  immersed  but  2  cm.  (0.77  inch)  deep,  and  are  to  be  lowered 
little  by  little  until  finally  submerged. 

b.  For  immersion,  distilled  water  is  to  be  used  at  a  tem- 
perature of  from  15°  C.  (59°  F.)  to  20°  C.  (68°  F.). 

c.  The  saturated  blocks  are  to  be  subjected  to  temperatures 
of  from  —  10°  to  —  15°  C.  (14°  to  5°  F.).     This  can  be  done  in 
a  vessel  surrounded  with  melting  ice  and  salt. 

d.  The  blocks  are  to  be  subjected  to  the  influence  of  such 
cold  for   four   hours,  and  they  are  to  be  thus   treated  when 
completely  saturated. 

e.  The  blocks  are  to  be  thawed  out  in  a  given  quantity  of 
distilled  water  at  from  59°  F.  to  64°  F. 


178  EXPERIMENTAL  ENGINEERING.  [§  11$. 

ii.  An  investigation  of  weathering  qualities — stability  un- 
der influences  of  atmospheric  changes — can  be  neglected  when 
the  frost-test  has  been  made.  However,  the  effects  in  this  re- 
spect, in  nature,  are  to  be  carefully  observed  and  compared  with 
previous  experience  in  the  use  of  similar  material.  Observe — 

a.  The  effect  of  the  sun  in  producing  cracks  and  ruptures 
in  stones. 

b.  The  effect  of  the  air,  and  whether  carbonic-acid  gas  is 
given  off. 

c.  The  effect  of  rain  and  moisture. 

d.  The  effect  of  temperature. 

115.  Bricks  or  Artificial  Building-stone. — Brick  are  tested 
for  strength,  principally  by  compression. 

1.  They  should  be  ground  to  a  form  with  opposite  parallel 
faces,  and  are  tested  between  layers  of  thin  paper;  or,  without 
grinding,  between  thin  layers  of  plaster-of-Paris,  as  explained  for 
stone.    The  variation  in  size  of  specimen,  and  whether  the  brick 
is  tested  on  end,  side-ways,  or  flat-ways,  will  make  a  great  differ- 
ence in  the  results.     The  test,  to  be  of  any  value,  must  state 
the  method  of  testing.     Whole  bricks  are  stronger  per  unit  of 
area  than  portions  of  bricks,  and  should  be  used  when  practi- 
cable. 

2.  It  is  also  recommended  that  brick  be  tested  for  compres- 
sion in  the  shape  of  two  half-bricks  superimposed,  united  by  a 
thin  layer  of  Portland  cement,  and  covered  on  top  and  bottom 
with   a   thin   layer  of   such   paste   to   secure   even   bearing- 
surfaces.* 

3.  The  transverse  test  for  brick  is  believed  to  be  a  valuable 
index  to  its  building  properties.     Support  the  brick  on  knife- 
edges  6  inches  apart,  and  apply  the  load  at  the  centre.     Com- 
pute the  modulus  of  rupture : 


*See  Vol.  XI.  (Standard  Method  of  Testing),  Transactions  of  American 
Society  Mechanical  Engineers,  regarding  Articles  114-118. 


§  1 1 6.]       TESTING  MATERIALS   OF  CONSTRUCTION.  179 

in  which  W  equals  the  centre-load,  /  the  length,  b  the  breadth, 
d  the  depth,  all  in  inches. 

4.  Dry  as  for  stone,  and  determine  the  specific  gravity. 

5.  Test  hard-burned  and  soft-burned  from  the  same  kiln. 

6.  Determine  the  porosity  of  the  brick  as  follows : 
Thoroughly  dry  ten  pieces  on  an  iron  plate ;  weigh  these 

pieces  ;  then  submerge  in  water  to  one  half  the  depth  for 
twenty-four  hours  ;  then  completely  submerge  for  twenty-four 
hours,  dry  superficially,  and  weigh.  Determine  porosity  from 
the  weight  of  water  absorbed,  which  should  be  expressed  as 
per  cent  of  volume.  Express  absorption  as  per  cent  of  weight. 

7.  Determine    resistance   against    frost,   as    previously  ex- 
plained for  stones,  using   five   specimens,  and   repeating   the 
operation  of  freezing  and  thawing  twenty-five  times  for  each 
specimen.     Observe  the  effect  with  a  magnifying-glass.     After 
freezing,  test  for  compression,  and  compare  the  results  with 
that  obtained  with  a  dry  brick. 

8.  To  test  brick  for  soluble  salts,  obtain  samples  from  an 
underburned  brick  and  grind  these  to  dust.     Sift  through  a 
sieve  4900  meshes   per  square  cm.  (31,360  per   square  inch). 
The  dust  sifted  out  is  lixiviated  in  250  c.c.  of  distilled  water, 
boiled  for  about  one  hour,  filtered,  and  washed.     The  amount 
of  soluble  salts  is  then  determined  by  boiling  down  the  solu- 
tion and  bringing  the  residue  to  a  red  heat  for  a  short  time. 
The  amount  is  determined  by  weight  and  expressed  in  per- 
centage ;  its  composition  is  determined  by  a  chemical  analysis. 

9.  Determinations  of   the  presence  of  carbonate  of  lime, 
mica,  or  pyrites  are  to  be  made  by  chemical  analysis. 

116.  Tests  of  Paving  Material,  Stones,  and  Ballast, 
Natural  and  Artificial. — In  this  case  the  following  observa- 
tions and  tests  should  be  made : 

1.  Information    in    regard    to    petrographic   and   geologic 
classification,  the  origin  of  the  samples,  etc.,  etc. ;  also : 

2.  Statement  in  regard  to  utilization  of  same. 

3.  Specific  gravity  of  the  samples  is  to  be  determined. 

4.  All  materials  used  in  the  construction  of  roads,  provided 
they  are  not  to  be  used  under  cover  or  in  localities  without 


180  EXPERIMENTAL   ENGINEERING.  [§  1 1 6. 

frost,  are  to  be  tested  for  their  frost-resisting  qualities  by  similar 
test  to  those  prescribed  for  natural  stone. 

5.  Stones  or  brick  used  for  paving  are  tested  most  satisfac- 
torily in  a  manner  representing  their  mode  of  utilization  by  de- 
termining the  wearing  qualities  by  an  abrasion-test  described 
by  Prof.  I.  O.  Baker  as  follows  :*  The  abrasion-tests  are  made 
by  putting  the  bricks  and  a  number  of  pieces  of  iron  into  a  re- 
volving horizontal  cylinder.     The  cylinder  used  by  Prof.  Baker 
was  a  foundry-rattler  45  inches  long,  26  inches  in  diameter,  and 
revolved  at  rate  of  24  revolutions  per  minute.     The  iron  used 
consisted  of  546  pieces  of  "  foundry-shot,"  weighing  about  J- 
pound  each,  thus  making  a  total  weight  of  83^  pounds. 

In  making  the  test,  the  "  brick  "  is  inserted  in  the  rattler, 
which  is  put  in  motion  and  the  loss  determined  by  weighing 
at  the  end  .of  each  run.  Three  runs  are  made,  each  one  half- 
hour  in  length ;  the  comparisons  are  all  made  from  the  loss 
during  the  third  run,  expressed  in  percentages.  Granite  and 
various  stones  treated  in  the  same  way  afford  a  valuable  basis 
for  comparison. 

The  uniformity  of  wearing  qualities  of  brick  for  parts  more 
or  less  distant  from  the  exterior  surface  is  determined  by  re- 
peating the  trial  on  the  same  piece,  and  not  merely  testing  one, 
but  a  greater  number  of  pieces.  It  is,  moreover,  necessary  to 
test  samples  of  the  best,  the  poorest,  and  the  medium  qualities 
of  bricks  in  any  one  kiln. 

6.  Obtain  the  transverse  strength  as  explained. 

7.  Obtain  the  per  cent  of  water  absorbed  after  the  bricks 
have  been  thoroughly  dried  at  30°  C.  (83°  F.),  as  explained 
Arts.  91-95. 

8.  Test  materials  for  ballast  in  a  similar  manner. 

9.  In  some  cases  it  may  be  desirable  to  test  stones  as  to  the 
capacity  for  receiving  a  polish. 

10.  Examinations   of   asphalts  can   only  be  made  in   an 
exhaustive  manner  by  the  construction  of   trial  roads.     An 


*  See  Clay-worker  /August  and  September  1891. 


§  1 1 7»]       TESTING  MATERIALS   OF   CONSTRUCTION.  l8l 

opinion  coinciding  with  the  results  of  such  trial  may  be  formed 
by- 

(a)  Determination  of  the  quantity  and  quality  of  the  bitu- 
men contained   therein  (whether  the  bitumen  be  artificial  or 
natural). 

(b)  By  physical  and  chemical  determination  of  the  residue,, 

(c)  By  determination  of  the  specific  density  of  test-pieces  of 
the  material  used  by  a  needle  of  a  circular  sectional  area  of  I 
sq.  mm.,  carrying  a  weight  of  300  grams.     (See  Art.  1 18,  p.  163.) 

(d)  By  the  determination  of  the  wear  of  such  test-pieces  by 
abrasion  or  grinding  trials. 

(e)  By  the  determination  of  the  resistance  to  frost  of  these 
test-pieces.     (See  Art.  119,  page  163.) 

117.  Hydraulic  Cements  and  Mortars — Definitions. — 
The  standard  scientific  methods  of  testing  cements  depend  prin- 
cipally upon  researches  conducted  in  the  German  laboratories. 
The  standard  method  as  here  given  is  that  recommended  by 
the  Committee  on  Standard  Methods  of  Testing  at  Munich  in 
1888. 

The  following  definitions  will  serve  to  distinguish  the  dif- 
ferent classes  of  hydraulic  bond  materials : 

1.  Common  limes  are  produced  by  roasting  or  burning  lime- 
stones containing  more  or  less  clay  or  silicic  acid,  and  which 
when  moistened  with  water  become  wholly  or  partly  pulverized 
and  slaked.     According  to  local  circumstances,  these  are  sold 
in  shape  of  lumps  or  in  a  hydrated  condition  in  the  shape  of  a 
fine  flour. 

2.  Water-limes  and  Roman  cements  are  products  obtained  by 
burning  clayey  lime  marls  below  the  temperature  of  decrepita- 
tion, and  which  do  not  disintegrate  upon  being  moistened,  but 
must  be  powdered  by  mechanical  means. 

3.  Portland  cements  are  products  obtained  by  burning  clayey 
marls  or  artificial  mixtures  of  materials  containing  clay  and  lime 
at  decrepitation  temperature,  and  are  then  reduced  to  the  fine- 
ness  of   flour,  and  which    contain  for  one   part  of   hydraulic 
material  at  least  1.7  parts  of  calcareous  earth.     To  regulate 


1 82  EXPERIMENTAL  ENGINEERING.  [§  1 1 8. 

properties  technically  important,  an  admixture  of  2  per  cent 
of  foreign  matter  is  admissible. 

4.  Hydraulic  fluxes  are  natural  or  artificial  materials  which 
in  general  do  not  harden  of  themselves,  but  do  so  in  presence 
of  caustic  lime,  and  then  in  the  same  way  as  a  hydraulic  ma- 
terial ;  i.e.,  puzzuolana,  santorine  earth,  trass  produced  from  a 
proper  kind  of  volcanic  tufa,  blast-furnace  slag,  burnt  clay. 

5.  Puzzuolana  cements  are  products  obtained  by  most  care- 
fully mixing  hydrates  of  lime,  pulverized,  with  hydraulic  fluxes 
in  the  condition  of  dust. 

6.  Mixed  cements  are  products  obtained  by  most  carefully 
mixing  existing  cements  with  proper  fluxes.     Such  bond  ma- 
terials are  to  be  particularly  stated  as  "  Mixed  Cements,"  st 
the  same  time  naming  the  base  and  the  flux  used. 

Mortar  is  made  by  mixing  three  or  four  parts  of  sharp  sand 
with  one  part  of  quick-lime  or  cement,  and  adding  water  until 
of  tne  proper  consistency.  Mortar  made  from  quick-lime  will 
neither  set  nor  stay  hard  underwater;  that  made  from  hydraulic- 
or  water-lime,  if  allowed  to  set  in  the  air,  will  not  be  softened 
by  water;  while  that  made  from  cement  will  harden  under 
water. 

118.  Method  of  Testing  Cements. — The  principal  prop- 
erties which  are  necessary  to  know  are  :  (i)  its  fineness;  (2)  time 
of  setting ;  (3)  its  tensile  strength  ;  (4)  its  soundness  or  freedom 
^rom  cracks  after  setting ;  (5)  its  heaviness  or  specific  gravity ; 
(6)  its  crushing  strength ;  (7)  its  toughness  or  power  to  resist  defi- 
nite blows. 

The  following  standard  method  of  testing  cements  was  adopted 
by  a  committee  ot  the  American  Society  of  Civil  Engineers  and 
of  the  American  Society  of  Testing  Materials  in  1903  and  1904. 

Selection  of  Sample. — The  sample  shall  be  a  fair  average  of 
the  contents  of  the  package;  it  shall  be  passed  through  a  sieve 
having  20  meshes  per  lineal  inch  before  testing  to  remove  lumps. 
In  obtaining  a  sample  from  barrels  or  bags,  an  auger  or  sampling- 
iron  reaching  to  the  centre  should  be  used. 

A  chemical  analysis,  if  required,  should  be  made  in  accord- 


§  1 1 8.]        TESTING   MATERIALS   OF  CONSTRUCTION.  183 

ance  with  the  directions  in  the  Journal  of  the  Society  of  Chemical 
Industry,  published  Jan.  15,  1902. 

Specific  Gravity. — This  is  most  conveniently  made  with  Le 
Chatelier's  apparatus,  which  consists  of  a  flask  (Z)),  Fig.  99,  of 


FIG.  99.— LE  CHATELIER'S   SPECIFIC-GRAVITY  APPARATUS. 

120  cu.  cm.  (7.32  cubic  inches)  capacity,  the  neck  of  which  is  about 
20  cm.  (7.87  inches)  long;  in  the  middle  of  this  neck  is  a  bulb 
(C),  above  and  below  which  are  two  marks  (F  and  E)\  the 
volume  between  these  marks  is  20  cu.  cm.  (1.22  cubic  inches).  The 
neck  has  a  diameter  of  about  9  mm.  (0.35  in.),  and  is  gradu- 
ated into  tenths  of  cubic  centimeters  above  the  mark  F.  Ben- 
zine (62°  Baume  naphtha),  or  kerosene  free  from  water,  should 
be  used  in  making  the  determination. 

The  specific  gravity  can  be  determined  in  two  ways:  (i)  The 
flask  is  filled  with  either  of  these  liquids  to  the  lower  mark  (E), 
and  64  gr.  (2.25  ounces)  of  powder,  previously  dried  at  100°  C. 
(212°  F.)  and  cooled  to  the  temperature  of  the  liquid,  is  grad- 
ually introduced  through  the  funnel  (B)  [the  stem  of  which  ex- 
tends into  the  flask  to  the  top  of  the  bulb  (C)],  until  the  upper 
mark  (F)  is  reached.  The  difference  in  weight  between  the 
cement  remaining  and  the  original  quantity  (64  gr.)  is  the  weight 
which  has  displaced  20  cu.  cm. 


1 84  EXPERIMENTAL   ENGINEERING.  [§   I  1 8. 

(2)  The  whole  quantity  of  the  powder  is  introduced,  and  the 
level  of  the  liquid  rises  to  some  division  of  the  graduated  neck. 
This  reading  plus  20  cu.  cm.  is  the  volume  displaced  by  64  gr.  of 
the  powder.  The  specific  gravity  is  then  obtained  from  the 
formula : 

.       .  Weight  of  cement 

Displaced  volume* 

The  flask  during  the  operation  is  kept  immersed  in  water  in 
a  jar,  A,  in  order  to  avoid  variations  in  the  temperature  of  the 
liquid.  Different  trials  should  agree  within  i  per  cent. 

The  apparatus  is  conveniently  cleaned  by  inverting  the  flask 
over  a  glass  jar,  then  shaking  it  vertically  until  the  liquid  starts 
to  flow  freely.  Repeat  this  operation  several  times. 

Fineness. — The  fineness  is  determined  by  the  use  of  circular 
sieves,  about  20  cm.  (7.87  inches)  in  diameter,  6  cm.  (236  inches) 
high,  and  provided  with  a  pan  5  cm.  (1.97  inches  deep,  and  a 
cover. 

The  wire  cloth  should  be  woven  (not  twilled)  from  brass  wire 
having  the  following  diameters: 

No.  100,  0.0045  inch;  No.  200,  0.0024  inch. 

This  cloth  should  be  mounted  on  the  frames  without  distor- 
tion; the  mesh  should  be  regular  in  spacing  and  be  within  the 
following  limits: 

No.  100,    96  to  100  meshes  to  the  linear  inch; 
No.  200,  188  to  200       "'       "    " 

50  to  ioo  gr.  dried  at  a  temperature  of  212°  F.  prior  to  sieving 
should  be  used  for  the  test,  the  sieves  having  previously  been 
dried. 

The  coarsely  screened  sample  is  weighed  and  placed  on  the 
No.  200  sieve,  which  is  moved  forward  and  backward,  at  the 
same  time  striking  the  side  gently  with  the  palm  of  the  other 
hand,  at  the  rate  of  about  200  strokes  per  minute.  The  opera- 
tion is  continued  until  not  more  than  one  tenth  of  one  per  cent 
passes  through  per  minutev  The  work  is  expedited  by  placing 


§  1 1 8.]        TESTING   MATERIALS   OF  CONSTRUCTION.  185 

in  the  sieve  a  small  quantity  of  large  shot,  or,  better,  some  flat 
pieces  of  brass  or  copper  about  the  size  of  a  cent.  The  residue 
is  weighed,  then  placed  on  a  No.  100  sieve  and  the  operation 
repeated.  The  results  should  be  reported  to  the  nearest  tenth 
of  one  per  cent. 

Normal  Consistency. — The  use  of  a  proper  percentage  of 
water  in  mixing  the  cement  or  mortar  is  exceedingly  important. 
No  method  is  entirely  satisfactory,  but  the  following,  which  con- 
sists in  the  determination  of  the  depth  of  penetration  of  a  wire 
of  a  known  diameter  carrying  a  specified  weight,  is  recommended 
The  apparatus  recommended  is  the  Vicat  needle  shown  in  Fig. 
100,  which  is  also  used  for  determining  the  time  of  setting.  This 
consists  of  a  frame,  K,  bearing  a  movable  rod,  L,  with  a  cap, 
D,  at  one  end,  and  at  the  other  the  cylinder,  G,  i  cm.  (0.39  inches) 
in  diameter,  the  cap,  rod,  and  cylinder  weighing  300  gr.  (10.58 
oz.).  The  rod,  which  can  be  held  in  any  desired  position  by  a 
screw,  Fj  carries  an  indicator,  which  moves  over  a  graduated 
scale  attached  to  the  frame,  K.  The  paste  is  held  by  a  conical 
hard- rubber  ring,  /,  7  cm.  (2.76  inches)  in  diameter  at  the  base, 
4  cm.  (1.57  inches)  high,  resting  on  a  glass  plate,  /,  about  10  cm. 
(3.94  inches)  square. 

In  making  the  determination,  the  same  quantity  of  cement 
as  will  be  subsequently  used  for  each  batch  in  making  the 
briquettes  (but  not  less  than  500  grams)  is  kneaded  into  a  paste 
and  quickly  formed  into  a  ball  with  the  hands,  completing  the 
operation  by  tossing  it  six  times  from  one  hand  to  the  other, 
maintained  6  inches  apart ;  the  ball  is  then  pressed  into  the  rubber 
ring,  through  the  larger  opening,  smoothed  off,  and  placed  (on 
its  large  end)  on  a  glass  plate  and  the  smaller  end  smoothed 
off  with  a  trowel;  the  paste,  confined  in  the  ring,  resting  on  the 
plate,  is  placed  under  the  rod  bearing  the  cylinder,  which  is 
brought  in  contact  with  the  surface  and  quickly  released. 

The  paste  is  of  normal  consistency  when  the  cylinder  pene- 
trates to  a  point  in  the  mass  10  mm.  (0.39  inch)  below  the  top 
of  the  ring.  Great  care  must  be  taken  to  fill  the  ring  exactly 
to  the  top. 


1 86 


EXPERIMENTAL   ENGINEERING. 


[§u8. 


The  trial  pastes  are  made  with  varying  percentages  of  water 
until  the  correct  consistency  is  obtained. 

The  Committee  has  recommended,  as  normal,  a  paste  the 
consistency  of  which  is  rather  wet,  because  it  believes  that  varia- 
tions in  the  amount  of  compression  to  which  the  briquette  is 
subjected  in  moulding  are  likely  to  be  less  with  such  a  paste. 


FIG.  100. — VICAT  NEEDLE. 

Time  of  Setting. — The  object  of  this  test  is  to  determine  the 
time  which  elapses  until  the  paste  ceases  to  be  fluid  and  plastic, 
called  the  initial  set,  and  also  the  time  required  for  it  to  acquire 
a  certain  degree  of  hardness,  called  the  final  set. 

For  this  purpose  the  Vicat  needle,  which  has  already  been 
described,  should  be  used.  In  making  the  test,  a  paste  of  normal 
consistency  is  moulded  and  placed  under  the  rod  (L),  Fig.  100; 
this  rod  when  bearing  the  cap  (D)  weighs  300  gr.  (10.58  oz.). 
The  needle  (H),  at  the  lower  end,  is  i  mm.  (0.039  inch)  in 


§   I  19.]  TESTING   MATERIALS   OF  CONSTRUCTION.         187 

diameter.  Then  the  needle  is  carefully  brought  in  contact  with 
the  surface  of  the  paste  and  quickly  released. 

The  setting  is  said  to  have  commenced  when  the  needle  ceases 
to  pass  a  point  5  mm.  (0.20  inch)  above  the  upper  surface  of  the 
glass  plate,  and  is  said  to  have  terminated  the  moment  the  needle 
does  not  sink  visibly  into  the  mass. 

The  test-pieces  should  be  stored  in  moist  air  during  the  test. 
This  is  accomplished  by  placing  them  in  a  rack  over  water  con- 
tained in  a  pan  and  covered  with  a  damp  cloth,  the  cloth  to  be 
kept  away  from  them  by  means  of  a  wire  screen,  or  preferably 
they  may  be  stored  in  a  moist  box  or  closet. 

The  determination  of  the  time  of  setting  is  only  approxi- 
mate, since  it  is  materially  affected  by  the  temperature  of  the 
mixing  water,  the  percentage  of  the  water  used,  and  the  amount 
of  moulding  the  paste  receives. 

Standard  Sand. — -The  committee  recommend  at  present  the 
use  of  a  natural  sand  from  Ottawa,  111.,  screened  to  pass  a  sieve 
having  20  meshes  per  lineal  inch  and  retained  on  a  sieve  having 
30  meshes  per  lineal  inch;  the  wires  to  have  diameters  of  0.0165 
and  0.0112  inch  respectively.  This  sand  will  be  furnished  by 
the  Sandusky  Portland  Cement  Co.,  Sandusky,  Ohio,  at  a  mod- 
erate price.  This  sand  gives  in  testing  considerably  more  strength 
than  the  crushed  quartz  of  the  same  size  formerly  employed 
for  this  purpose. 

Form  oj  Briquette. — The  form  of  briquette  recommended  is 
shown  in  Fig.  94.  It  is  substantially  like  that  formerly  used 
except  that  the  corners  are  rounded. 

Moulds. — The  moulds  should  be  made  of  brass,  bronze,  or 
some  equally  non-corrodible  material,  and  gang  moulds  of  the 
form  shown  in  Fig.  92  are  recommended.  They  should  be 
wiped  with  an  oily  cloth  before  using. 

lip.  Mixing. — All  proportions  should  be  stated  by  weight; 
the  quantity  of  water  to  be  used  should  be  stated  as  a  percentage 
of  the  dry  material.  The  metric  system  is  recommended  be- 
cause of  the  convenient  relation  of  the  gram  and  the  cubic  centi- 
meter. The  temperature  of  the  room  and  the  mixing  water 


1 88  EXPERIMENTAL   ENGINEERING.  [§  1 1 9. 

should  be  as  near  21°  C.  (70°  F.)  as  it  is  practicable  to  main- 
tain it. 

The  sand  and  cement  should  be  thoroughly  mixed  dry.  The 
mixing  should  be  done  on  some  non- absorbing  surface,  preferably 
plate  glass.  If  the  mixing  must  be  done  on  an  absorbing  surface, 
it  should  be  thoroughly  dampened  prior  to  use.  The  quantity 
of  material  to  be  mixed  at  one  time  depends  on  the  number  of 
test-pieces  to  be  made;  about  1000  gr.  (35.28  oz.)  makes  a  con- 
venient quantity  to  mix,  especially  by  hand  methods. 

The  material  is  weighed,  dampened,  and  roughly  mixed  with 
a  trowel,  after  which  the  operation  is  completed  by  vigorously 
kneading  with  the  hand  for  ij  minutes. 

Moulding. — Having  worked  the  mortar  to  the  proper  con- 
sistency it  is  at  once  placed  in  the  mould  by  hand,  being  pressed 
in  firmly  with  the  fingers  and  smoothed  off  with  a  trowel  without 
ramming,  but  in  such  a  manner  as  to  exert  a  moderate  pressure. 
The  mould  should  be  turned  over  and  the  operation  repeated. 
The  briquettes  should  be  weighed  prior  to  immersion,  and  those 
which  vary  in  weight  more  than  3  per  cent  from  the  average 
should  be  rejected. 

Storage  of  the  Test-pieces. — During  the  first  twenty-four  hours 
after  moulding,  the  test-pieces  should  be  kept  in  moist  air  to 
prevent  them  from  drying  out.  A  moist  closet  or  chamber  is  so 
easily  devised  that  the  use  of  the  damp  cloth  should  be  abandoned 
if  possible.  Covering  the  test-pieces  with  a  damp  cloth  is  ob- 
jectionable, as  commonly  used,  because  the  cloth  may  dry  out 
unequally,  and,  in  consequence,  the  test-pieces  are  not  all  main- 
tained under  the  same  condition.  Where  a  moist  closet  is  not 
available,  a  cloth  may  be  used  and  kept  'uniformly  wet  by  im- 
mersing the  ends  in  water.  It  should  be  kept  from  direct  con- 
tact with  the  test-pieces  by  means  of  a  wire  screen  or  some  similar 
arrangement. 

A  moist  closet  consists  of  a  soapstone  or  slate  box,  or  a  metal- 
lined  wooden  box — the  metal  lining  being  covered  with  felt  and 
this  felt  kept  wet.  The  bottom  of  the  box  is  so  constructed  as 
to  hold  water,  and  the  sides  are  provided  with  cleats  for  holding 


§  I  1 9.].      TESTING   MATERIALS  OF  CONSTRUCTION.  189 

glass  shelves  on  which  to  place  the  briquettes.     Care  should  be 
taken  to  keep  the  air  in  the  closet  uniformly  moist. 

After  twenty- four  hours  in  moist  air  the  test-pieces  for  longer 
periods  of  time  should  be  immersed  in  water  maintained  as  near 
21°  C.  (70°  F.)  as  practicable;  they  may  be  stored  in  tanks  or 
pans,  which  should  be  of  non-corrodible  material. 

Tensile  Strength. — The  tests  may  be  made  on  any  standard 
machine.  A  solid  metal  clip,  as  shown  in  Fig.  93,  is  recommended. 
This  clip  is  to  be  used  without  cushioning  at  the  points  of  con- 
tact with  the  test  specimen.  The  bearing  at  each  point  of  con- 
tact should  be  \  inch  wide,  and  the  distance  between  the  centre 
of  contact  on  the  same  clip  should  be  i  J  inches. 

Test-pieces  should  be  broken  as  soon  as  they  are  removed 
from  the  water,  the  load  being  applied  uniformly  at  the  rate 
of  about  600  pounds  per  minute.  The  average  tests  of  the 
briquettes  of  each  sample  should  be  taken  as  the  strength,  ex- 
cluding any  results  which  are  manifestly  faulty. 

Constancy  o)  Volume. — The  object  is  to  develop  those  quali- 
ties which,  tend  to  destroy  the  strength  and  durability  of  a  cement. 
As  it  is  highly  essential  to  determine  such  qualities  at  once,  tests 
of  this  character  are  for  the  most  part  made  in  a  very  short  time, 
and  are  known,  therefore,  as  accelerated  tests.  Failure  is  re- 
vealed by  cracking,  checking,  swelling,  or  disintegration,  or  all 
of  these  phenomena.  A  cement  which  remains  perfectly  sound 
is  said  to  be  of  constant  volume. 

Tests  for  constancy  of  volume  are  divided  into  two  classes: 
(i)  normal  tests,  or  those  made  in  either  air  or  water  main- 
tained at  about  21°  C.  (70°  F.),  and  (2)  accelerated  tests,  or 
those  made  in  air,  steam,  or  water  at  a  temperature  of  45°  C. 
(115°  F.)  and  upward.  The  test-pieces  should  be  allowed  to  re- 
main twenty-four  hours  in  moist  air  before  immersion  in  water 
or  steam,  or  preservation  in  air. 

For  these  tests,  pats,  about  7^  cm.  (2.95  inches)  in  diameter, 
1}  cm.  (0.49  inch)  thick  at  the  centre,  and  tapering  to  a  thin 
edge,  should  be  made,  upon  a  clean  glass  plate  [about  10  cm. 
(3.94  inches)  square],  from  cement  paste  of  normal  consistency. 


190  EXPERIMENTAL  ENGINEERING.  [§  12O. 

Normal  Test. — A  pat  is  immersed  in  water  maintained  as 
near  21°  C.  (70°  F.)  as  possible  for  28  days,  and  observed  at 
intervals.  A  similar  pat  is  maintained  in  air  at  ordinary  tem- 
perature and  observed  at  intervals. 

Accelerated  Test. — A  pat  is  exposed  in  any  convenient  way 
in  an  atmosphere  of  steam,  above  boiling  water,  in  a  loosely 
closed  vessel  for  three  hours. 

To  pass  these  tests  satisfactorily,  the  pats  should  remain 
firm  and  hard,  and  show  no  signs  of  cracking,  distortion,  or 
disintegration.  Should  the  pat  leave  the  plate,  distortion  may  be 
detected  best  with  a  straight-edge  applied  to  the  surface  which 
was  in  contact  with  the  plate.  In  the  present  state  of  our 
knowledge  it  cannot  be  said  that  cement  should  necessarily  be 
condemned  simply  for  failure  to  pass  the  accelerated  tests, 
nor  can  it  be  considered  entirely  satisfactory  if  it  has  passed 
these  tests. 

120.  Specifications  for  Cement. — The  following  specifica- 
tions were  adopted  by  the  committee  of  the  American  Society  for 
Testing  Materials,  Nov.  14,  1904: 

General  Conditions. — i.  All  cement  shall  be  inspected. 

2.  Cement  may  be  inspected  either  at  the  place  of  manufacture  or  on 
the  work. 

3.  In  order  to  allow  ample  time  for  inspecting  and  testing,  the  cement 
should  be  stored  in  a  suitable  weather-tight  building  having  the  floor  properly 
blocked  or  raised  from  the  ground. 

4.  The  cement  shall  be  stored  in  such  a  manner  as  to  permit  easy  access 
for  proper  inspection  and  identification  of  each  shipment. 

5.  Every  facility  shall  be  provided  by  the  contractor  and  a  period  of  at 
least  twelve  days  allowed  for  the  inspection  and  necessary  tests. 

6.  Cement  shall  be  delivered  in  suitable  packages  with  the  brand  and 
name  of  manufacturer  plainly  marked  thereon. 

7.  A  bag  of  cement  shall  contain  94  pounds  of  cement  net.     Each  barrel 
of  Portland  cement  shall  contain  4  bags,  and  each  barrel  of  natural  cement 
shall  contain  3  bags  of  the  above  net  weight. 

8.  Cement  failing  to  meet  the  seven-day  requirements  may  be  held  await- 
ing the  results  of  the  twenty-eight-day  tests  before  rejection. 

9.  All  tests  shall  be  made  in  accordance  with  the  methods  proposed  by 
the  Committee  on  Uniform  Tes^s  of  Cement  of  the  American  Society  of 


§  I2O.]        TESTING   MATERIALS   OF  CONSTRUCTION.  191 

Civil  Engineers,  presented  to  the  Society  January  21,  1903,  and  amended 
January  20,  1904,  with  all  subsequent  amendments  thereto. 

10.  The  acceptance  or  rejection  shall  be  based  on  the  following  require- 
ments: 

11.  NATURAL  CEMENT. — Definition.— This  term  shall  be  applied  to  the 
finely  pulverized  product  resulting  from  the  calcination  of  an  argillaceous 
limestone  at  a  temperature  only  sufficient  to  drive  off  the  carbonic  acid  gas. 

12.  Specific   Gravity. — The   specific   gravity   of   the   cement   thoroughly 
dried  at  100°  C.  shall  be  not  less  that  2.8. 

13.  Fineness.— It  shall  leave  by  weight  a  residue  of  not  more  than  10% 
on  the  Nek  100  sieve,  and  30%  on  the  No.   200. 

14.  Time  of  Setting.— It  shall  develop  initial  set  in  not  less  than  ten  minutes, 
and  hard  set  in  not  less  than  thirty  minutes  nor  more  than  three  hours. 

15.  Tensile  Strength. — The  minimum  requirements  for  tensile  strength 
for  briquettes  one  inch  square  in  cross-section  shall  be  within  the  following 
limits,  and  shall  show  no  retrogression  in  strength  within  the  periods  specified:* 

NEAT   CEMENT. 
Age  Strength. 

24  hours  in  moist  air 50-100  Ibs. 

7  days    (i  day  in  moist  air,    6  days  in  water) 100-200    " 

28  days     (i  day  in  moist  air,  27  days  in  water) 200-300    " 

ONE   PART   CEMENT,    THREE    PARTS    STANDARD   SAND. 

7  days     (i  day  in  moist  air,    6  days  in  water) 25-75      " 

28  days     (i  day  in  moist  air,  27  days  in  water) 75~i5o    " 

1 6.  Constancy  of  Volume. — Pats  of  neat  cement  about  three  inches  in 
diameter,  one-half  inch  thick  at  centre,  tapering  to  a  thin  edge,  shall  be  kept 
in  moist  air  for  a  period  of  twenty-fours  hours. 

(a)  A  pat  is  then  kept  in  air  at  normal  temperature. 

(b)  Another  is  kept  in  water  maintained  as  near  70°  F.  as  practicable. 

17.  These  pats  are  observed  at  intervals  for  at  least  28    days,  and,  to 
satisfactorily  pass  the  tests,  should  remain  firm  and  hard  and  show  no  signs 
of  distortion,  checking,  cracking,  or  disintegrating. 

1 8.  PORTLAND  CEMENT. — Definition. — This  term  is  applied  to  the  finely 
pulverized  product  resulting  from  the  calcination  to  incipient  fusion  of  an 
intimate  mixture  of  properly  proportioned  argillaceous  and  calcareous  mate- 

*  For  example,  the  minimum  requirement  for  the  twenty-four-hour  neat-cement 
test  should  be  some  specified  value  within  the  limits  of  50  and  100  pounds,  and 
so  on  for  each  period  stated. 


192  EXPERIMENTAL   ENGINEERING.  [§  I2O 

rials,  and  to  which  no  addition  greater  than  3%  has  been  made  subsequent 
to  calcination. 

19.  Specific  Gravity. — The   specific  gravity  of  the   cement,   thoroughly 
dried  at  100°  C.,  shall  be  not  less  than  3.10. 

20.  Fineness. — It  shall  leave  by  weight  a  residue  of  not  more  than  8% 
on  the  No.  100  sieve,  and  not  more  than  25%  on  the  No.  200. 

21.  Time  of  Setting. — It  shall  develop  initial  set  in  not  less  than  thirty 
minutes,   but  must  develop  hard  set  in  not  less  than  one  hour  nor  more  than 
ten  hours. 

22.  Tensile  Strength. — The  minimum  requirements  for  tensile  strength 
for  briquettes  one  inch  square  in  section  shall  be  within  the  following  limits, 
and  shall  show  no  retrogression  in  strength  within  the  periods  specified:* 

NEAT   CEMENT. 
Age.  Strength. 

24  hours  in  moist  air 150-200  Ibs. 

7  days    (i  day  in  moist  air,    6  days  in  water) 450-550    " 

28  days    (i  day  in  moist  air,  27  days  in  water) 550-650    " 

ONE   PART   CEMENT,   THREE    PARTS   SAND. 


7  days    (i  day  in  moist  air,    6  days  in  water) 150-200 

28  days    (i  day  in  moist  air,  27  days  in  water) 200-300 


23.  Constancy  of  Volume. — Pats  of  neat  cement  about  three  inches  in 
diameter,  one-half  inch  thick  at  the  centre,  and  tapering  to  a  thin  edge,  shall 
be  kept  in  moist  air  for  a  period  of  twenty-four  hours. 

(a)  A  pat  is  then  kept  in  air  at  normal  temperature  and  observed  at 
intervals  for  at  least  28  days. 

(6)  Another  pat  is  kept  in  water  maintained  as  near  70°  F.  as  practicable, 
and  observed  at  intervals  for  at  least  28  days. 

(c)  A  third  pat  is  exposed  in  any  convenient  way  in  an  atmosphere  of 
steam,  above  boiling  water,  in  a  loosely  closed  vessel  for  five  hours. 

24.  These   pats,   to   satisfactorily   pass   the   requirements,   shall   remain 
firm  and  hard  and  show  no  signs  of  distortion,  checking,  cracking,  or  dis- 
integrating. 

25.  Sulphuric  Acid  and  Magnesia. — The  cement  shall  not  contain  more 
than  1.75%  of  anhydrous  sulphuric  acid  (SO3),  nor  more  than  4%  of  mag- 
nesia (MgO). 

*  For  example,  the  minimum  requirement  for  the  twenty-four-hour  neat-cement 
test  should  be  some  specified  value  within  the  limits  of  150  and  200  pounds,  and 
so  on  for  each  period  stated. 


§  120.]       TESTING  MATERIALS  OF  CONSTRUCTION.  193 

The  following  observations  are  taken  with  respect  to  each 
briquette : 


Brand  of  cement 

Temperature  of  air  at  mixing. . . 
Temperature  of  water  at  mixing. 

Percentage  of  sand 

"  water 

"          "  cement 

Date  of  mixing , 

Time  of  mixing 


In  the  log  of  the  tests  the  following  are  the  headings  for 
the  columns:  No.;  Time  of  Testing;  Weight  of  Water;  Ten 
sile  Strength ;  and  Remarks. 

Prof.  Lanza  of  Boston  requires  a  report  of  the  following 
form: 

CEMENT  TEST. 

Date  of  test, •    

Date  of  mixing, •    .     •     .... 

No.  of  days  set, 

Manner  of  setting  (in  air  or  in  water), 

Kind  of  cement, •    .    .    •    •    •    •    

Brand. •    •    •    •    •    •     •    • 


Cement.  Sand.  Water.  Lime. 

Mixture  (by  wt.), %        %        %        % 

Breaking-strength  per  sq.  in.  (tension),     . 

Crushing- load  (2-in.  cube),      

Signed 

The  cement-testing  laboratory  of  Berlin,  which  has  perhaps 
the  best  reputation  for  this  line  of  work,  makes  observations  as 
shown  on  the  following  schedule,  which  gives  the  results  of 
eleven  tests,  as  given  in  a  paper  by  P.  M.  Bruner,  before  the 
Engineers'  Club  of  St.  Louis: 


194 


EXPERIMENTAL   ENGINEERING. 


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§  121.]       TES TING  MA  TERIA L S   OF  CONSTR  UCTION.  1 9 5 

121.  Coefficients  of  Strength.— It  is  desirable  to  know  in 
advance  of  the  test  the  probable  load  the  material  under  in- 
vestigation will  safely  bear,  in  order  that  increments  of  stress 
may  be  so  proportioned  as  to  make  a  reasonable  number  of 
observations.  It  is  also  often  desirable  to  know  how  the 
results  obtained  compare  with  the  standard  values  for  the 
material  under  investigation.  To  provide  this  information  a 
brief  statement  of  the  results  of  various  tests  are  tabulated  in 
the  Appendix.  These  results  are  mainly  obtained  from  "  Ma- 
terials of  Construction,"  by  R.  H.  Thurston  (3  vols.;  N.  Y., 
Wiley  &  Son);  and  from  " Applied  Mechanics,"  by  Prof.  G. 
Lanza  (N.  Y.,  J.  Wiley  &  Son) ;  and  *'  Materials  of  Engineer 
ing,"  by  Prof.  W.  H.  Burr  (N.  Y.,  J.  Wiley  &  'Son).  These 
books  will  be  found  of  great  value  for  reference  in  the  testing- 
laboratory. 


CHAPTER  VI. 
FRICTION— TESTING  OF  LUBRICANTS. 

122.  Friction. — This  subject  is  of  great  importance  to  en- 
gineers, since  in  some  instances  it  causes  loss  of  useful  work, 
and  in  other  instances  it  is  utilized  in  transmission  of  power. 
The  subject  is  intimately  connected  with  that  of  measurement 
of  power  by  dynamometers,  treated  in  Chapter  VII.  ;  in  con- 
nection with  these  two  chapters,  the  student  is  advised  to  read 
"  Friction  and  Lost  Work  in  Machinery  and  Mill-work,"  by  R. 
H.  Thurston  ;  N.  Y.,  J.  Wiley  &  Sons. 

Definitions. — Friction,  denoted  by  F,'  is  the  resistance  to 
motion  offered  by  the  surfaces  of  bodies  in  contact  in  a  direc- 
tion parallel  to  those  surfaces. 

The  normal  force ',  denoted  by  R,  is  the  force  acting  perpen- 
dicular to  the  surfaces,  tending  to  press  them  together. 

The  coefficient  of  friction*  f,  is  the  ratio  of  the  friction,  F,  to 
the  normal  force,  R ;  that  is,f=F-t-R. 

The  total  pressure,  P,  is  the  resultant  of  the  normal  pressure, 
R,  and  of  the  friction,  F,  and  its  obliquity  or  inclination  to  the 
common  perpendicular  of  the  surfaces  is  the  angle  of  repose, 
or  friction,  whose  tangent  is  the  coefficient  of  friction. 

The  angle  of  repose  or  friction,  0,  is  the  inclination  at  which 
a  body  would«start  if  resting  on  an  inclined  plane.  It  is  easy  to 
show*  that  for  that  condition,  if  W\s  the  weight  of  the  body, 

>  =  R;     also,      Wsm</>  =  F; 


*  See  Mechanics,  by  I.  P.  Church;  p.  164. 

196 


§  1  24.]  FRICTION—  TESTING   OF  LUBRICANTS. 

and  since  /=  F  ~±-  Rt 


197 


/= 

J 


W  sin  0 
-—  -  ^ 
PFcos  0 


^tan  0. 


It  has  been  shown  by  experiment  that  for  sliding  friction 
(i)  the  coefficient /"is. independent  of  R  ;  (2)  it  is  greater  at  the 
instant  of  starting  than  after  it  is  in  motion ;  (3)  it  is  independ- 
ent of  the  area  of  rubbing  surfaces  ;  (4)  it  is  diminished  by 
lubrication  ;  (5)  it  is  independent  of  velocity. 

123.  Classification  and  Notation. — The  subject  of  friction 
is  naturally  divided  into  the  following  sub-heads,  all  of  which 
are  intimately  connected  with  methods  of  lubrication : 

A.  Friction  of  rest,  occurring  when  a  body.is  about  to  start. 
It  is  the  resistance  to  change  of  position. 

B.  Friction  of  motion,  occurring  during  uniform  motion,  and 
being  less  than  the  friction  of  rest. 

The  second  kind,  or  friction  of  motion,  is  of  principal  im- 
portance, and  consists  of — 

1.  Sliding  friction. 

a.  Bodies  sliding  on  a  plane. 

b.  Axles  or  journals  rolling  in  boxes. 

c.  Pivots  turning  on  a  plane  step. 

2.  Rolling  friction. 

a.  One  body  rolling  over  a  plane. 

b.  One  body  rolling  over  another. 

124.  Formulae  and  Notation. 


or  =  angle  of  inclination  of  plane; 
<f>  =  angle  of  friction; 
6  —  arc  of  contact  on  journal; 
ft  =  inclination  of  force  with  plane; 
JR  =  normal  force  on  a  plane; 
/=  coefficient  of  friction; 


r  =  radius  of  journal; 

/  =  length  of  journal; 

a  =  space  passed  through; 

/  .—  intensity  of  pressure  per  sq.  in.! 
P  =  total  pressure; 
W  =  weight  of  the  body. 


The  most  important  formulae  relating  to  friction  can  be 

tabulated  as  follows  : 


EXPERIMENTAL  ENGINEERING. 
TABLE  OF  USEFUL  FORMULAE. 


[§  126. 


V 

c 

ei 

cu 

rt 

O 

,1 

4J    3 

JO 
•—  > 
c 

F 

f 
±D 

F 

fW  =  Wtena^W  tan  0. 
Tan  a  =  tan  0  =  ^  W1  —  ^2 
W  (sin  a  ±  f  cos  a)  -*-  (cos 
sin  B\ 

+  X. 

0±S 

Square  of  reaction  of  bearing. 
Weight  on  journal  (squared)  .  . 
Moment  of  friction  

N* 
W1 

M 
U 

W*  —  F*  =  W\\  —  sin2  0) 

COS2  0. 

N*  +  F3  =  N\i  -f-/9)  =  F\ 

-*-/>. 
Fr  —  Wr  sin  0  —  fWr  -J-  4/T 

'-r-/2) 

+?• 
0  = 

Work  of  friction  per  minute.  .  . 

War    sin     0  =  zitnrW   sin 

2«nrflV+Vi+f>, 

Perfectly  fitting  Journal. 

Weight  on  journal  (general).  .  . 
Intensity  of  pressure  at  0=90° 
Weight,  perfect  fit  of  journal.  . 
Pressure  per  square  inch        . 

W 

w 
p 

P' 

F 

M 
U 

/+$ 
plr  cos  0*/0. 
9 

p  -5-  cos  0. 

/VSf 
cos2  QdQ  =  i.SJ/Sr. 
J^jTT 

0.64  W  cos  0  -f-  Ir. 

i*9 
0.64  W  I     cos  0</0  =  1.27  W. 

J  -  6 

fP'W—  1.2-jfW. 

P'fr=  -L.z-ifWr. 
Ma  =  \.l*ifWr  =  2.  ^qitfnr  IV. 

Maximum  pressure  per  sq.  inch 
Total  pressure  on  bearing  .... 

Work  of  friction  

Moment  of  friction  ....   ... 

Work  of  friction  per  minute  .  . 

Uniform  press- 
ure on  Journal. 

Maximum  pressure  per  sq.  inch 
Total  pressure  

P' 
P' 
F 

M 
U 

W  -*-  zlr. 

P'f=i.tffW. 
P'fr  =  ^lfWr. 
Ma  =  i.5-jafWr=  ntfWrn. 

Total  force  of  friction  

Work  of  friction  per  minute.  .  . 

125.  Friction  of  Journals  in  V  or  Triangular  Bearings. 

— Force  of  friction  F  =  P  cos  0  sin  0  -j-  cos  **,  in  which  /* 
equals  the  force  transmitted  through  the  shaft.  When  cos 
0=  i,  /?  =  P  sin  0-r-  cos  or. 

126.  Friction  of  Pivots  on  Flat  Rotating  Surfaces. — 
Intensity  of   pressure  =/;   total   pressure  =  P.     Moment  of 


§  128.]  FRICTION— TESTING   OF  LUBRICANTS.  199 

friction,  M  =  \fPr.     Work  of  friction,   U=  ^nnfPr.     For  a 
conical  pivot,  M  =  ^fPr  -j-  sin  a.     OL  =  \  angle  of  cone. 

For  Friction  on  a  Flat  Collar. — Moment  of  friction,  M  = 
lfP(r>-rn)+(r>—rn)  ;  r=  radius  of  collar  ;  r'=  radius  of  shaft 
on  which  it  is  fitted. 

127.  Friction  of  Teeth— Rolling  Friction.— Work  lost  in 
a  unit  of  time,  U=nFPs,  in  which  s  equals  the  sliding  or  slip- 
ping ;    n,  number  of  teeth ;   other  terms  as  before.     For  in 
volute  teeth,  in  which  C,  =  length  of  arc  of  approach,  £T2  that 
of  arc  of  recess,  0  the  obliquity  of  action,  rl  and  ra  respective 
pitch-radii,  we  have  for  involute  teeth 

U  =  nfPs  =  nfP(Q  +  C*)(-  +  -}  +  2  cos  9. 

r\      r-J 

This   is    nearly  accurate   for   any  teeth.      (See   article  "  Me- 
chanics," Encyc.  Britannica.) 

128.  Friction  of  Cords  and  Belts— Sliding  Friction.— 
Let  T,  be  the  tension  on  driving  side  of  belt,  Tt  on  the  loose 
side,  Tthe  tension  at  any  part  of  the  arc  of  contact';  let  6  be 
the  length  of  the  arc  of  contact  divided  by  the  radius,  i.e.,  ex- 
pressed in  circular  measure ;  let  c  equal  the  ratio  of  the  arc  of 
contact  to  the  entire  circumference ;  let  d  equal  the  number  of 
degrees  in  the  arc  of  contact,  e  the  base  of  the  Napierian 
logarithms  =  2.71828,  m  the  modulus  of  the  common  loga- 
rithms =  0.434295  ;  let  F  equal  the  force  of  friction. 

nr  d  _nd 


-£-=•  .......  « 

,  N 
=  360:.     ......    (c) 


The  tension  at  any  point,  dT,  is  equal  to  the  resistance  TfdQ. 

Hence 

dT=  TfdO,     .......    (d\ 

or 


2OO  EXPERIMENTAL  ENGINEERING.  [&  129. 

This  integrated  between  limits  Tt  and  7",  gives 

T        i  T 

fB  =  loge  ~  =  —  (common)  log  ^  ;    ....    (e) 

J.<t          rn  J-  s 

hence 


*a 

From  the  nature  of  the  stress, 


T 

•^  =  the  number  corresponding  to  the  logarithm,  which  is 

•*  2 

fndm  , 

equal   /ww,    or    —  ^  —  ,    or    27f/cm. 

Substituting  numerical  values, 

fOm  =  o.434/#,    ~^  =  o-  00758/4    and    2?r/h0  =  2.7288/7. 
From  equations  (/), 

common  log  ^~J  =  0434/9  =  2.7288/r. 
By  solving  equations  (/)  and  (^), 


129.  Friction  of  Fluids  (i)  is  independent  of  pressure  ; 
(2)  proportional  to  area  of  surface  ;  (3)  proportional  to  square 
of  velocity  for  moderate  and  high  speeds  and  to  velocity  for 
low  speeds  ;  (4)  is  independent  of  the  nature  of  the  surfaces  ; 
(5)  is  proportional  to  the  density  of  the  fluid,  and  is  related  to 
viscosity. 

The  resistance  to  relative  motion  in  case  of  fluid  friction, 

R=fAV*  =  2ghfA  = 


§  131.]  FRICTION—  TESTING  OF  LUBRICANTS.  2OI 

the  work  of  friction, 

U=  Rs  =  RVt  =A  V*t 


In  the  above  formulae  R  =  resistance  of  friction,  A  =  area 
of  surface,  V  •=•  velocity  of  slipping,  h  —  head  corresponding 
to  velocity,  w  =  weight,  f  fehe  resistance  per  unit  of  area  of 


surface,/"7  =  coefficient  of  liquid  friction,  f  =  -—  . 

Viscosity  and  density  of  fluids  do  not  affect  to  any  appreci- 
able extent  the  retardation  by  friction  in  the  rate  of  flow,  but 
have  some  influence  upon  the  total  expenditures  of  energy. 
Molecular  or  internal  friction  •also  exists. 

130.  Lubricated   Surfaces.  —  Lubricated    surfaces  are  no 
doubt  to  be  considered  as  solid  surfaces,  wholly  *or  partially 
separated  by  a  fluid,  and  the  friction  will  vary,  with  different 
conditions,  from  that  of  liquid  friction  to  that  of  sliding  fric- 
tion between  solids.     Dr.  Thurston  *  gives  the  following  laws, 
applicable  to  perfect  lubrication  only: 

1.  The  coefficient  of  friction  is  inversely  as  the  intensity  of 
the  pressure,  and  the  resistance  is  independent  of  the  pressure. 

2.  The  coefficient  varies  with  the  square  of  the  speed. 

3.  The  resistance  varies  directly  as  the  area  of  journal  and 
bearing. 

4.  The  friction  is  reduced  as  temperature  rises,  and  as  the 
viscosity  of  the  lubricant  is  thus  decreased. 

Perfect  lubrication  is  not  possible,  and  consequently  the 
laws  governing  the  actual  cases  are  likely  to  be  very  different 
from  the  above.  The  coefficient  of  friction  in  any  practical 
case  is  likely  to  be  made  up  of  the  sum  of  two  components, 
solid  and  fluid  friction. 

TESTING  OF  LUBRICANTS. 

131.  Determinations  required.  —  The  following  determina- 
tions are  required  in  a  complete  test  of  lubricants  : 

1.  The  composition,  and  detection  of  adulteration. 

2.  The  measurement  of  density. 

*  See  Friction  and  Lost  Work,  by  Thurston. 


202  EXPERIMENTAL   ENGINEERING.  [§ 

3.  The  determination  of  viscosity. 

4.  The  detection  of  tendency  to  gum. 

5.  The  determination  of  temperatures  of  decomposition, 
vaporization,  ignition,  and  solidification. 

6.  The  detection  of  acids. 

7.  The  measure  of  the  coefficient  of  friction. 

8.  The    determination    of    durability   and    heat-removing 
power. 

9.  The  determination  of  its  condition  as  to  grit  and  foreign 
matter. 

132.  Adulteration  of  Oils. — Adulteration  can  be  detected 
only  by  a  chemical  analysis.*       . 

Animal  oils  may  be  distinguished  from  vegetable  oils  by 
the  fact  thai  chlorine  turns  animal  oil  brown  and  vegetable  oil 
white. 

133.  Density  of  Oils. — The  density  or  specific  gravity  is 
usually  obtained  with  a  hydrometer  (see  Fig.  101)  adapted  for 
this  special  purpose,  and  termed  an  oleometer.     The  distance 

that  it  sinks  in  a  vessel  of  oil  of  known  temperature 
is  measured  by  the  graduation  on  the  stem ;  from 
this  the  specific  gravity  of  the  oil  may  be  found. 

The  density  is  usually  expressed  in  Beaume's  hy- 
drometer-scale, which  can  be  reduced  to  correspond- 
ing specific  gravities  as  compared  with  water  by  a 
table  given  in  the  Appendix. 

Beaume"'s  hydrometer  is  graduated  in  degrees  to 
accord  with  the  density  of  a  solution  of  common 
salt  in  water;  thus,  for  liquids  heavier  than  water 
the  zero  of  the  scale  is  obtained  by  immersing  in 
pure  water;  the  "five-degree  mark  by  immersing  in  a 
five-per-cent  solution  ;  the  ten-degree  mark  in  a  ten- 
FIG.  ioi.  per.cent  solution ;  etc.  For  liquids  lighter  than 

HYDROMETER.  r 

water  the  zero-mark  is  obtained  by  immersing  in  a 
ten-per-cent  solution  of  brine ;  the  ten-degree  mark  by  im- 
mersing in  pure  water.  After  obtaining  the  length  of  a 
degree  the  stem  is  graduated  by  measurement. 

*  See  Friction  and^Lost  Work,  by  R.  H.  Thurston. 


§  J35-]  FRICTION— TESTING   OF  LUBRICANTS.  2  03 

The  density  may  be  found  by  obtaining  the  loss  of 
weight  of  the  same  body  in  oil  and  in  distilled  water.  The 
ratio  of  loss  of  weights  will  be  the  density  compared  with 
water. 

It  may  also  be  obtained  by  weighing  a  given  volume  on  a 
pair  of  chemical  scales.  The  density  of  animal  oils  varies  from 
.62  to  .89 ;  sperm-oil  at  39°  F.  has  a  density  of  .8813  to  .8815  ; 
rape-seed  oil  has  a  density  of  .9168 ;  lard-oil  (winter)  has  a 
density  of  .9175  ;  cotton-seed  oil  a  density  of  .9224  to  .9231  for 
ordinary,  and  of  .9128  for  white  winter;  linseed-oil,  raw,  has  a 
density  of  .9299 ;  castor-oil,  pure  cold-pressed,  a  density  of 
.9667. 

134.  Method  of  finding  Density.— A.    With  Hydrometer 
Thermometer,  and  Hydrometer  Cylinder. 

Method. —  i.  Clean  the  cylinder  thoroughly,  using  benzine 
fill  first  with  distilled  water.  Set  the  whole  in  a  water-jacket, 
and  bring  the  temperature  to  60°  F.  Obtain  the  reading  of  the 
hydrometer  in  the  distilled  water  and  determine  its  error. 

2.  Clean  out  the  cylinder,  dry  it  thoroughly,  and  fill  with 
the  oil  to  be  tested  ;  heat  in  a  water-jacket  to  a  temperature  of 
60°  F.,  and  obtain  reading  of  hydrometer ;  also  obtain  reading, 
at  temperatures  of  40°,  80°,  100°,  125°,  and  150°,  and  plot  a 
curve  showing  relation  of  temperature  and  corrected  hydrome- 
ter-reading. 

Reduce  hydrometer-readings  to  corresponding  specific 
gravities,  by  table  given  in  Appendix. 

B.  Weigh  on  a  chemical  balance  the  same  volume  of  dis- 
tilled water  at  60°  F.,  and  of  the  oil  at  the  same  temperature; 
and  compute  the  specific  gravity. 

C.  Weigh  the  same  metallic  body  by  suspending  from  the 
bottom  of  a  scale-pan  of  a  balance:   I.  In  air;  2.   In  water;  3. 
In  the  oil  at  the   required  temperature.     Carefully  clean  the 
body  with  benzine  after  immersing  in  the  oil.     The  ratio  of  the 
loss  of  weight  in  oil  to  that  in  water  will  be  the  density. 

135.  Viscosity. —  Viscosity  of  oil  is  closely  related  but  not 
proportional  to  its  density.     It  is  also  closely  related,  and  in 
many  cases  it  is  inversely  proportional,  to  its  lubricating  prop- 


204 


EXPERIMENTAL   ENGINEERING. 


[§  136. 


erties.  The  relation  of  the  viscosities  at  ordinary  temperatures 
is  not  the  same  as  for  higher  temperatures,  and  tests  for  vis- 
cosity should  be  made  with  the  temperatures  the  same  as  those 
in  use.  The  less  the  viscosity,  consistent  with  the  pressure  to 
be  used,  the  less  the  friction. 

The  viscosity  test  is  considered  of  great  value  in  determin- 
ing the  lubricating  qualities  of  oils,  and  it  is  quite  probable 
that  by  means  of  it  alone  we  could  determine  the  lubricating 
qualities  to  such  an  extent  that  a  poor  oil  would  not  be  accepted 
nor  a  good  oil  rejected.  It  is,  however,  in  the  present  method 
of  performing  it,  to  be  considered  rather  as  giving  comparative 
than  absolute  results. 

There  are  several  methods  of  determining  the  viscosity 
It  is  usual  to  take  the  viscosity  as  inversely  proportional  to  its 

flow  through  a  standard  nozzle 
while  maintained  at  a  constant 
or  constantly  diminishing  head 
and  constant  temperature,  a 
comparison  to  be  made  with 
water  or  with  some  well-known 
oil,  as  sperm,  lard,  or  rape-seed, 
under  the  same  conditions  of 
pressure  and  temperature. 

136.  Viscosimeter. — A  pi- 
pette surrounded  by  a  water- 
jacket,  in  which  the  water  can 
be  heated  by  an  auxiliary  lamp 
and  maintained  at  any  desired 
temperature,  is  generally  used 
as  a  viscosirneter.  Fig.  72 
shows  the  usual  arrangement 
for  this  test.  E  is  the  heater 
for  the  jacket-water,  BB  the 
jacket,  A  the  pipette,  C  a  thermometer  for  determining  the 
temperature  of  the  jacket-water.  The  oil  is  usually  allowed  to 
run  partially  out  from  the  pipette,  in  which  case  the  head 
diminishes.  Time  for  the  whole  run  is  noted  with  a  stop-watch. 


FIG.  102. — VISCOSITY  OF  OILS. 


§  1 390 


FRICTION— TESTING   OF  LUBRICANTS. 


205 


In  the  oil-tests  made  by  the  Pennsylvania  R.  R.  Co.  the 
pipette  is  of  special  form,  holding  100  c.c.  between  two  marks, 
—  one  drawn  on  the  stem,  the  other  some  distance  from  the  end 
of  the  discharge-nozzle. 

137.  Tagliabue's  Viscosimeter.— In  Tagliabue's  viscosim- 
eter,  shown  in  Figs.  103  and  104,  the  oil  is 

supplied  in  a  basin  C,  and  trickles  down- 
ward through  a  metal  coil,  being  dis- 
charged at  the  faucet  on  the  side  into  a 
vessel  holding  50  c.c.  The  oil  is  main- 
tained at  any  desired  temperature  by 
heating  the  water  in  the  vessel  B  sur- 
rounding the  coil ;  cold  water  is  supplied 
from  the  vessel  A,  as  required  to  main- 
tain a  uniform  temperature.  The  tem- 
perature of  the  oil  is  taken  by  the  ther- 
mometer D. 

138.  Gibbs'  Viscosimeter.  —  In  the 
practical  use  of  viscosimeters  it  is  found 
that  the  time  of  flow  of  100  c.c.  of  the 
same  oil,  even  at  the  same  temperature,  , 

7    riG.  103. — TAGLIABUK  s  Visco- 

is  not  always  the  same, — which  is  probably  SIMETER. 

due  to  the  change  in  friction  of  the  oil  adhering  to  the  sides  of 

the  pipette. 

To  render  the  conditions  which  produce  flow  more  constant, 
Mr.  George  Gibbs  of  Chicago  surrounds  the  viscosimeter,  which 
is  of  the  pipette  form,  with  a  jacket  of  hot  oil.  A  circulation 
of  the  jacket-oil  is  maintained  by  a  force-pump.  The  oil  to 
be  tested  is  discharged  under  a  constant  head,  which  is  insured 
by  air-pressure  applied  by  a  pneumatic  trough.  The  tempera- 
ture of  the  discharged  oil  is  measured  near  the  point  of  dis- 
charge. 

139.  Perkins'   Viscosimeter. — The   Perkins  Viscosimeter 
consists  of  a  cylindrical  vessel  of  glass,  surrounded  by.  a  water  or 
oil  bath,  and  fitted  with  a  piston  and  rod  of  glass.     The  edges 
of  this  piston  are  rounded,  so  as  not  to  be  caught  by  a  slight 
angularity  of  motion.     The  diameter  is  one-thousandth  of  an 


206 


EXPERIMENTAL  ENGINEERING. 


inch  less  than  that  of  the  cylinder.     In  practice  the  cylinder  is 
filled  nearly  full  of  the  oil  to  be  tested,  and  the  piston  inserted. 


FIG.  104. — TAGLIABUE'S  VISCOSIMETER. 

The  time  required  for  the  piston  to  sink  a  certain  distance  into 
the  oil  is  taken  as  the  measure  of  the  viscosity.* 

140.  Stillman's  Viscosimeter. — Prof.  Thomas  B.  Stillman 
of  Stevens  Institute  uses  a  conical  vessel  of  copper,  6f  inches 
in  length   and    if   inches  greatest   diameter,  surrounded  by  a 
water-bath,  and  connected  to   a  small  branch  tube   of  glass, 
•^vhich  is  graduated  in  cubic  centimeters ;  the  time  taken  for 
25  c.c.  to  flow  through  a  bottom  orifice  -/%  of  an  inch  in  diam- 
eter is  taken  as  the  measure  of  the  viscosity,  during  which  time 
the  head  changes  from  6  to  5  inches.     Prof.  Stillman  makes  all 
comparisons  with  water,  which   is  the   most   convenient   and 
uniform   standard.     The   temperature   of  the  oil   is   taken   at 
about  the  centre  of  the  viscosimeter. 

141.  Viscosimeter  with  Constant  Head A   form   of 

viscosimeter  which  possesses  the  advantage  of  having  a  con- 
stant  head   for  flow  of   oil   regardless  of  the  quantity  in  the 
instrument,  as  made  by  Tinius  Olsen  &  Co.  of  Philadelphia, 

*  See   paper  by-Prof.  Denton,  Vol.   IX.,  Transactions   of  Am.    Society    of 
Mechanical  Engineers. 


FRICTION—  TJSS7VJVG  OF  LUBRICANTS. 


207 


is  shown  in  the  next  figure.  It  is  simple  in  form  and  can  be 
very  readily  cleaned.  It  is  provided  with  a  jacket,  and  oils 
may  be  tested  at  any  temperature.  This  instrument  is  now 
the  principal  standard  used  in  the 
Sibley  College  Laboratories. 

Description. — A  is  a  cup  similar  in 
construction  to  that  of  the  kerosene 
reservoir  of  a  students'  lamp,  with  a 
capacity  of  about  125  c.c.,  and  is  sur- 
rounded with  a  jacket  D,  in  which  may 
be  placed  insulating  materials  to  main- 
tain a  constant  temperature  while  the 
oil  is  flowing;  C  is  a  thermometer-cup, 
to  the  bottom  of  which  is  secured  a 
small  cap  containing  the  orifice  F ;  N 
is  a  channel  connecting  chamber  con- 
taining A  with  C\  B  is  one  of  four 
small  tubes  which  admit  air  to  the  in- 
terior of  the  cup  A  and  thus  maintain 
atmospheric  pressure  on  oil  in  it;  this 
action  secures  a  constant  level  of  the 
surface  of  the  oil  in  the  cup  C  and 
the  surrounding  space,  at  the  height  of  the  lower  opening 
in  the  tube  B.  H  is  a  valve  to  retain  oil  in  A  while  placing 
it  into  D.  M  and  N  are  brackets  serving  as  guides  for  valve- 
stem  K. 

The  mechanism  L,  G,  G  is  a  device  for  opening  and 
closing  the  orifice  F  readily,  and  is  held  in  a  closed  position 
by  spring  catch  L. 

The  instrument  is  supported  by  three  legs  about  eight 
inches  in  length. 

Operation. — Withdraw  cup  A,  fill  it  in  an  inverted  posi- 
tion with  the  oil,  hold  valve  H  on  its  seat  while  reinserting 
the  cup  into  its  former  place  as  seen  in  figure,  in  which  latter 
operation  the  valve  H  is  raised  and  the  oil  allowed  to  flow 
out  of  A  until  chambers  N  and  C  are  filled  a  little  above 


FlG.    105.—  VlSCOSIMETER. 


208  EXPERIMENTAL    ENGINEERING.  [§  141. 

lower  opening  of  tube  B.  A  beaker  graduated  in  c.c.'s,  of 
capacity  of  about  no  c.c.,  is  placed  under  F;  L  is  released 
and  G  allowed  to  drop,  permitting  oil  to  flow  through  F  freely 
into  the  beaker.  When  oil  in  C  falls  below  the  bottom  of 
tube  Bt  air  is  admitted  to  the  top  of  the  oil  in  A  and  oil  flows 
out  until  it  rises  a  little  above  tube  B  again,  when  flow  out 
of  A  is  stopped  until  the  level  falls  below  B  again.  This 
action  continues  throughout  entire  run,  intermittently  but  so 
rapidly  that  a  constant  head  is  maintained  at  F. 

In  C  a  thermometer  is  suspended  so  that  its  bulb  is 
immersed  in  the  oil,  by  which  means  the  temperature  of  oil 
can  be  observed  immediately  before  flowing  out  of  orifice  F, 
which  is  essential  in  ascertaining  the  viscosity  of  the  oil. 
The  oil  may  be  heated  in  the  viscosimeter  by  applying  a 
Bunsen  burner,  but  it  is  usually  more  conveniently  heated  in 
a  separate  vessel  until  it  has  attained  the  proper  temperature. 

Method  of  Conducting  a  Test. — Since  water  is  taken  as  the 
standard  of  comparison,  the  amount  of  flow  for  100  c.c.  is 
first  determined.  Clean  apparatus  thoroughly,  then  fill  A 
with  water,  allow  100  c.c.  to  flow  and  note  time;  similarly 
make  four  or  five  runs  so  as  to  get  a  fair  average. 

Wipe  apparatus  again  thoroughly  dry  and  proceed  in  a 
similar  manner,  using  oil  at  different  temperatures.  The 
jacket  should  be  heated  a  little  with  every  movement  of  tem- 
peratures. The  oil  should  be  heated  in  a  separate  vessel  and 
then  poured  into  A. 

The  ratio  of  time  of  flow  of  a  quantity  of  oil  to  time  of 
flow  of  an  equal  quantity  of  water  measures  the  relative 
viscosity  of  the  given  sample  of  oil  to  that  of  water  at  the 
given  temperature.  For  comparing  the  results  obtained  with 
this  instrument,  the  time  of  flow  of  100  c.c.  only  need  be 
known,  since  all  the  instruments  are  standardized. 

A  simple  form  of  viscosimeter  has  been  used  with  success 
by  the  author,  consisting  of  a  copper  cup  in  form  of  a  frustum 
of  a  cone,  having  dimensions  as  follows:  bottom  diameter 
1.25  inches,  top  diameter  1.95  inches,  depth  6  inches.  The 


FRICTION— TESTING  OF  LUBRICANTS. 


209 


flow  takes  place  through  a  sharp-edged  orifice  in  the  centre 
of  the  bottom  ^  inch  in  diameter.  The  whole  height  is  6£ 
inches.  The  instrument  when  made  of  copper  requires  a 
glass  oil-gauge,  showing  the  height  of  the  oil  in  the  viscosi- 
meter.  This  should  be  connected  to  the  viscosimeter  3 
inches  from  the  bottom.  The  time  for  the  flow  of  100  c.c. 
is  taken  as  the  measure  of  the  viscosity,  during  which  time 
the  head  changes  from  6  to  about  3.5  inches,  the  area  of 
exposed  surface  diminishes  at  almost  exactly  the  rate  of 
decrease  of  velocity  of  flow,  so  that  the  fall  of  level  is  very 
nearly  constant. 

The  comparative  number  of  vibrations  of  a  pendulum 
swinging  freely  in  the  air,  and  when  immersed  in  an  oil  dur- 
ing a  given  time,  is  also  said  to  afford  a  valuable  means  of 
determining  the  viscosity. 

142.  Viscosity  Determinations  of  Oil,  by  Prof.  Thomas 
B.  Stillman. 


Fluid. 

ime  of  Flow  in  Seconds  of  25 
c.  through  Orifice  as  explained. 

Viscosity 
compared 
with  water 
at  20°  C. 
(68°  F.). 

Water  

20°  C. 

68°  F. 
15 
55 
70 

50°  C. 

122°  F. 

100°  C. 
212°   F. 

150°  C. 
302°  F. 

I.O 

3-6 
4.6 

16.0 
4.6 

2.2 

2.6 

3-4 
3-8 
4.2 
4-7 

Prime  lard-oil  

29 
30 

19 

1  8 

16 
16 
360 

15 
14 

15 
16 

15 
15 
16 
16 

No    i      "     "  

240 
70 

33 
39 
5i 
57 
7i 
63 

80 
23 

22 

24 
26 

27 
26 

24 

19 
15 
16 

17 
27 
18 
20 
18 

"       "     2d  run  

Olive-oil  

143.  Method  of  measuring  Viscosity. — Apparatus'.  Stop- 
watch and  viscosimeter.  Fill  the  jacket  of  the  viscosimeter 
with  water  and  arrange  for  the  maintenance  of  the  same  at  any 
desired  temperature.  This  is  most  conveniently  done  by  cir- 
culation from  a  water-bath.  Fill  the  viscosimeter  with  the  oil 


210  EXPERIMENTAL  ENGINEERING.  [§  1 44- 

to  a  point  above  the  upper  or  initial  mark.  Allow  the  oil  to 
run  out,  noting  accurately  with  the  stop-watch  the  exact  time 
required  to  discharge  a  given  amount.  Make  determinations 
at  60°,  100°,  and  150°  F.,  two  for  each  temperature.  Clean 
the  apparatus  thoroughly  at  the  beginning  and  end  of  the  test, 
using  benzine  or  alkali  to  remove  any  traces  of  oil. 

143.  Gumming  or  Drying. — Gumming  or  drying  is  a  con- 
version of  the  oil  into  a  resin  by  a  process  of  oxidation,  and 
occurs  after  exposure  of  the  oils  to  the  air.     In  linseed  and  the 
drying  oils  it  occurs  very  rapidly,  and  in  the  mineral  oils  very 
slowly. 

Methods  of  Testing. — NasmytKs  Apparatus. — An  iron  plate 
six  feet  long,  four  inches  wide,  one  end  elevated  one  inch. 
Six  or  less  different  oils  are  started  by  means  of  brass  tubes  at 
the  same  instant  from  the  upper  end :  the  time  taken  until  the 
oil  reaches  the  bottom  of  the  plane  is  a  measure  of  its  gum- 
ming property. 

Bailey  s  Apparatus  consists  of  an  inclined  plane,  made  of  a 
glass  plate,  arranged  so  that  it  may  be  heated  by  boiling  water. 
A  scale  and  thermometer  is  attached  to  the  plane.  Its  use  is 
the  same  as  the  Nasmyth  apparatus. 

This  effect  may  also  be  tested  in  the  Standard  Oil-testing 
Machine  by  applying  fresh  oil,  making  a  run,  and  noting  the 
friction ;  then  exposing  the  axis  to  the  effect  of  the  air  for  a 
time,  and  noting  the  increase  of  friction.  In  all  cases  a  com- 
parison must  be  made  with  some  standard  oil. 

144.  The    Flash-test. —  The   effect  of   heat    is   in    nearly 
every  case  to  increase  the  fluidity  of  oils  and  to  lessen  the  vis- 
cosity ;  the   temperature  at  which  oils  ignite,   flash,    boil,    or 
congeal  is  often  of  importance. 

The  Flash-test  determines  the  temperature  at  which  oils 
discharge  by  distillation  vapors  which  may  be  ignited.  The 
test  is'  made  in  two  ways. 

Firstly.  With  the  open  cup. — In  this  case  the  oil  to  be  tested 
k  placed  in  an  open  cup  of  watch-glass  form,  which  rests  on  a 
sand-bath.  The  cup  is  so  arranged  that  a  thermometer  can 
be  kept  in  it.  Heat  is  applied  to  the  sand-bath,  and  as  the  oil 


§144-] 


FRICTION— TESTING   OF  LUBRICANTS. 


211 


becomes  heated  a  lighted  taper  or  match*  is  passed  at  intervals 
of  a  few  seconds  over  the  surface  of  the  oil,  and  at  a  distance 
of  about  one  half-inch  from  it.  At  the  instant  of  flashing  the 
temperature  of  the  water-bath  is  noted,  which  is  the  tempera- 
ture of  the  "  flash-point/' 

Fig.  1 06  shows  Tagliabue's  form  of  the  open  cup,  in  which 
heat  is  applied  by  a  spirit-lamp  to  a  water  or  sand  bath  sur- 
rounding the  cup  containing  the  oil. 

The  method  of  applying  the  match  is  found  to  a  have  great 
influence  on  the  temperature  of  the  flash-point,  and  should  be 
distinctly  stated  in  each  case.  When  the  vapor  is  heavier  than 


FIG.  106.— OPEN  CUP. 


FIG.  107.— CLOSED  CUP  FOR  FLASHING-POINT. 


air,  a  lower  flash-point  will  be  shown  by  holding  nsar  one  edge 
of  the  cup. 

Secondly.  With  the  closed  oil-cup. — Fig.  107  is  a  view  of  Tag- 
liabue's closed  cup  for  obtaining  the  flash-point ;  in  this  instru- 
ment the  oil  is  heated  by  a  sand-bath  above  a  lamp.  The 
thermometer  gives  the  temperature  of  the  oil,  and  the  match 


212  EXPERIMENTAL   ENGINEERING.  § 

applied  from  time  to  time  at  the  orifice  d,  which  in  the  inter- 
vals can  be  covered  with  a  valve,  determines  the  flash-point. 

The  open  cup  is  generally  preferred  to  the  closed  one  as 
giving  more  uniform  determinations,  and  it  is  also  more  con- 
venient and  less  likely  to  explode  than  the  closed  one. 

Method  of  Testing. — Put  some  dry  sand  or  water  in  the  outer 
cup  and  some  of  the  oil  to  be  tested  in  the  small  cup.  Light 
the  lamp  and  heat  the  oil  gently — at  the  rate  of  about  50°  F.  in 
a  quarter  of  an  hour.  At  intervals  of  half  a  minute  after  a 
temperature  of  100°  F.  is  attained,  pass  a  lighted  match  or 
taper  slowly  over  the  oil  at  a  distance  of  one  half  inch  at  the 
surface.  The  reading  of  the  thermometer  taken  immediately 
before  the  vapor  ignites  is  the  temperature  of  the  flash-point. 

With  the  closed  cup  the  method  is  essentially  the  same, 
The  lighted  taper  is  applied  to  the  tube  leading  from  the  oil 
vessel,  the  valve  being  opened  only  long  enough  for  this  pur- 
pose. 

145.  Method  of  Determining  the  Burning-point. — The 
burning-point  is  determined  by  heating  the  oil  to  such  a  tem- 
perature, that  when  the  match  is  applied  as  for  the  flasn-test 
the  whole  of  the  oil  will  take  fire.     The  reading  of  the  ther- 
mometer just  before  the  match  is  applied  is  the  burning-point. 

With  Open  Cup. — Apparatus:  Open  cup  of  watch-glass 
form  ;  thermometer  suspended  so  that  bulb  is  immersed  in 
cup  ;  outer  vessel  filled  with  sand  or  water,  on  which  the  open 
vessel  rests ;  lamp  to  heat  the  outer  vessel. 

Method. — The  burning-point  is  found  in  the  same  manner 
as  the  flash-point,  with  the  open  cup,  the  test  being  continued 
until  the  oil  takes  fire  when  the  match  is  applied.  The  last 
reading  of  the  thermometer  before  combustion  commences  is 
the  burning-point. 

146.  Evaporation. — Mineral  oil  will  lose  weight  by  evapo- 
ration, which  may  be  ascertained  by  placing  a  given  weight  in 
a  watch-glass  and  exposing  to  the  heat  of  a  water-bath  for  a 
given  time,  as  twelve  hours.     The  loss  denotes  the  existence 
of  volatile  vapors,  and  should  not  exceed  5  per  cent  in  good 
oil.     Other  oils  often  gainxweight  by  absorption  of  oxygen. 


§  1 47.]  FRICTION— TESTING   OF  LUBRICANTS. 


213 


147.  Cold  Tests. — Cold  tests  are  made  to  determine  the 
behavior  of  oils  and  greases  at  low  temperatures.  The  method 
of  test  is  to  expose  the  sample  while  in  a  wide-mouthed 
bottle  or  test-tube  to  the  action  of  a  freezing  mixture,  which 
surrounds  the  oil  to  be  tested.  Freezing  mixtures  may  be 
made  with  ice  and  common  salt,  with  ice  alone,  or  with  15 
parts  of  Glauber's  salts,  above  which  is  a  mixture  of  5  parts 
muriatic  acid  and  5  parts  of  cold  water.  The  temperature  is 
read  from  a  thermometer  immersed  in  the  oil.  The  melting- 
point  is  to  be  found  by  first  freezing,  then  melting. 

Tagliabue  has  a  special  apparatus  for  the  cold  test  of  oils 
shown  in  section  in  Fig.  108.  The  oil  is  placed  in  the  glass 


FIG.  108.— TAGLIABUE'S  COLD-TEST  APPARATUS. 

vessel,  which  is  surrounded  with  a  freezing  mixture.  The 
glass  containing  the  oil  can  be  rocked  backward  and  forward, 
to  insure  more  thorough  freezing.  A  thermometer  is  inserted 
into  the  oil  and  another  in  the  surrounding  air-chamber;  the 
oil  is  frozen,  then  permitted  to  melt,  and  the  temperature 
taken. 


214  EXPERIMENTAL   ENGINEERING.  [§  ISO. 

In  making  this  test  considerable  difficulty  may  be  experi- 
enced in  determining  the  melting-point,  since  many  of  the  oils 
do  not  suddenly  freeze  and  thaw  like  water,  but  gradually 
soften,  until  they  will  finally  run,  and  during  this  whole  change 
the  temperature  will  continue  to  rise.  This  is  no  doubt  due 
to  a  mixture  of  various  constituents,  with  different  melting- 
points.  In  such  a  case  it  is  recommended  that  an  arbitrary 
chill-point  be  assumed  at  the  temperature  that  is  indicated  by 
a  thermometer  inserted  in  the  oil,  when  it  has  attained  surru 
cient  fluidity  to  run  slowly  from  an  inverted  test-tube.  The 
temperature  at  the  beginning  and  end  of  the  process  of  melting 
is  to  be  observed. 

148.  Method  of  Finding  the  Chill-point. — Apparatus. — 
Test-tube  thermometer,  and  dish  containing  freezing  mixture. 

Method. — Pour  the  sample  to  be  tested  in  the  test-tube,  in 
which  insert  the  thermometer ;  surround  this  with  the  freezing 
mixture,  which  may  be  composed  of  small  particles  of  ice 
mixed  with  salt,  with  provision  for  draining  off  the  water. 
Allow  the  sample  to  congeal,  remove  the  test-tube  from  the 
freezing  mixture,  and  while  holding  it  in  the  hand  stir  it  gently 
with  the  thermometer.  The  temperature  indicated  when  the 
oil  is  melted  is  the  chill-point. 

In  case  the  operation  of  melting  is  accompanied  with  a  dis, 
tinct  rise  of  temperature,  note  the  temperature  at  the  begin- 
ning and  also  at  the  end  of  the  process  of  melting. 

In  report  describe  apparatus  used  and  the  methods  of  test- 
ing. 

149.  Oleography. — An  attempt  has  been  made  to  deter- 
mine  the  properties  of   oil   by  cohesion-figures,  by  allowing 
drops  of  oil  to  fall  on  the  surface  of  water,  noting  the  time  re- 
quired to  produce  certain  characteristic  figures,  also  by,noting 
the  peculiar  form  of  these  figures. 

Electrical  Conductivity  is  different  for  the  different  oils,  and 
this  has  been  proposed  as  a  test  for  adulteration. 

150.  Acid  Tests. —  Tests  for  acidity  may  be  made  by  ob- 
serving the  effects  on  blue  litmus-paper ;  or  better  by  th«  fol- 
lowing method  described  t?y  Dr.  C.  B.  Dudley :  Have  ready  (i) 


§  1 5 1 .]  FRICTION—  TESTING  OF  L  UBRICANTS.  2  I  5 

a  quantity  of  95  per  cent  alcohol,  to  which  a  few  grains  of  car- 
bonate  of  soda  have  been  added,  thoroughly  shaken  and  al. 
lowed  to  settle  ;  (2)  a  small  amount  of  turmeric  solution ;  (3) 
caustic-potash  solution  of  such  strength  that  31^  cubic  centi- 
meters exactly  neutralize  5  c.c.  of  a  solution  of  sulphuric  acid 
and  water,  containing  40  milligrams  HaSO4  per  c.c.  Now 
weigh  or  measure  into  any  suitable  closed  vessel — a  four-ounce 
sample  bottle,  for  example — 8.9  grams  of  the  oil  to  be  tested. 
To  this  add  about  two  ounces  No.  I,  then  add  a  few  drops 
No.  2,  and  shake  thoroughly.  The  color  becomes  yellow. 
Then  add  from  a  burette  graduated  to  c.c.,  solution  No.  3  un- 
til the  color  changes  to  red,  and  remains  so  after  shaking. 
The  acid  is  in  proportion  ,to  the  amount  of  solution  (3)  re- 
quired.  The  best  oils  will  require  only  from  4  to  30  c.c.  to  be 
neutralized  and  become  red. 


COEFFICIENT  OF  FRICTION  OF  LUBRICANTS. 

151.  Oil-testing  Machines. — Measurements  of  the  coefficients 
of  friction  are  made  on  oil-testing  machines,  of  which  various 
forms  have  been  built.  These  machines  are  all  species  o. 
dynamometers,  which  provide  (i)  means  of  measuring  the  total 
work  received  and  that  delivered,  the  difference  being  the  work 
of  friction  ;  or  (2)  means  of  measuring  the  work  of  friction 
directly.  Machines  of  the  latter  class  are  the  ones  commonly 
employed  for  this  especial  purpose. 

Rankines  Oil-testing  Machine. — Rankine  describes  two 
forms  of  apparatus  for  testing  the  lubricating  properties  of  oil 
and  grease. 

I.  Statical  Apparatus. — This  consists  of  a  short  cylindrical 
axle,  supported  on  two  bearings  and  driven  by  pulleys  at 
each  end.  In  the  middle  of  the  axle  a  plumber-block  was 
rigidly  connected  to  a  mass  of  heavy  material,  forming  a 
pendulum.  The  lubrirant  to  be  tested  was  inserted  in  the 
plumber-block  attached  to  the  pendulum,  and  the  coefficient 
of  friction  determined  by  its  deviation  from  a  vertical.  In  this 
machine  the  axle  was  provided  with  reversing-gears,  so  that  it 


2l6  EXPERIMENTAL  ENGINEERING.  [§  l$l- 

could  be  driven  first  in  one  direction  and  then  in  the  opposite. 
With  this  class  of  machine,  if  r  equal  the  radius  of  the  journal, 
R  the  effective  arm  of  the  pendulum,  P  the  total  force  acting 
on  the  journal,  0  the  angle  with  the  vertical,  we  shall  have 
.the  product  of  the  force  W  into  the  arm  R  sin  0  equal  to  the 
moment  of  resistance  Fr.  That  is, 

Fr  =  WR  sin  0, 
from  which 


p-         pr       ' 

* 

II.  Dynamic  or  Kinetic  Apparatus.  —  In  this  case  a  loose 
fly-wheel  of  the  required  weight  is  used  instead  of  the  pendu- 
lum. The  bearings  of  journals  and  of  fly-wheel  are  lubricated; 
then  the  machine  is  set  in  motion  at  a  speed  greater  than  the 
normal.  The  driving-power  is  then  disengaged,  and  the  fly- 
disk  rotates  on  the  stationary  axis  until  it  comes  to  rest.  The 
coefficient  of  friction  is  obtained  by  measuring  the  retardation 
in  a  given  time.  Thus,  let  W  equal  the  weight  of  the  fly- 
wheel, k  its  radius  of  gyration,  so  that  WJ?  —  g  equals  its 
moment  of  inertia.  Let  n  equal  number  of  revolutions  at 
beginning,  and  nf  at  end  of  period  /.  Then  the  retardation  in 
angular  velocity  per  second  is 


the  moment  producing  retardation, 


If  we  neglect  the  resistance  of  the  air,  this  must  equal  the 
moment  of  friction  fWr. 
Equating  these  values, 

_  27r(n  -  tt) 
*"    ~  ' 


§  152. 


FRICTION— TESTING  OF  LUBRICANTS. 


217 


In  case  the  moment  of  inertia  and  radius  of  gyration  are  un- 
known, they  may  be  found  as  in  Article  53,  page  80. 

152.  Thurston's  Standard  Oil-testing  Machine — This 
machine  permits  variation  in  speed  and  in  pressure  on  the 
journal ;  it  also  affords  means  of  supplying  oil  at  any  time,  of 
reading  the  pressure  on  the  journal,  and  the  friction  on  grad- 
uated scales  attached  to  the  instrument. 


FIG.  109  —SECTION  OF  THURSTON'S 
OIL-TESTING  MACHINE. 


FIG.  no.— PERSPECTIVE  VIEW  OF  THURSTON'S 
OIL-TESTING  MACHINE. 


This  machine,  as  shown  in  the  above  cuts,  Figs.  109  and  1 10, 
consists  of  a  cone  of  pulleys,  C,  for  various  speeds  carried  be- 
tween two  bearings,  B,  Bf,  and  connected  to  an  overhanging 
axis,  F\  on  this  overhanging  part  is  a  pendulum,  H,  with 
plumber-block  in  which  the  axis  is  free  to  turn  ;  the  pendulum 
is  supported  by  brasses  which  are  adjustable  and  which  may 
be  set  to  exert  any  given  pressure  by  means  of  an  adjusting 
screw,  K'y  acting  on  a  coiled  spring  within  the  penduljm. 
The  pressure  so  exerted  can  be  read  directly  by  the  scale  M, 
attached  to  the  pendulum  ;  a  thermometer,  Qt  in  the  upper 
brass  gives  the  temperature  of  the  bearings.  The  deviation 


21 8  EXPERIMENTAL  ENGINEERING.  [§  153. 

of  the  pendulum  is  measured  by  a  graduated  arc,  PP' ,  fastened 
to  the  frame  of  the  machine.  The  graduations  of  the  pendu- 
lum scale  M  show  on  one  side  the  total  pressure  on  the  jour- 
nal P,  and  on  the  other  the  pressure  per  square  inch,  / ;  those 
on  the  fixed  scale,  PP' ,  show  the  total  friction,  F\  this  divided 
by  the  total  pressure,  P,  gives/,  the  coefficient  of  friction. 

From  the  construction  of  the  machine,  it  is  at  once  per- 
ceived that  the  pressure  on  the  journal  is  made  up  of  equal 
pressures  due  to  action  of  the  spring  on  upper  and  lower 
brasses,  and  of  the  pressure  due  to  the  weight  of  the  pendu- 
lum, which  acts  only  on  the  upper  brass.  This  latter  weight 
is  often  very  small,  in  which  case  it  can  be  neglected  without 
sensible  error. 

153.  Thurston's  Railroad  Lubricant-tester.  —  The 
Thurston  machine  is  made  in  two  sizes ;  the  larger  one,  having 
axles  and  bearings  of  the  same  dimensions  as  those  used  in 
standard-car  construction,  is  termed  the  "  Railroad  Lubricant 
Testing-machine."  A  form  of  this  machine  is  shown  in  the 
following  cut,  arranged  for  testing  with  a  limited  supply  of 
lubricant.  (See  Fig.  ill.) 
Explanation  of  symbols : 

jT,  thermometer,  giving  temperature  of  bearings. 

R,  S,  rubber  tubes  for  circulation  of  water  through  the 
bearings. 

//,  burette,  furnishing  supply  of  oil. 

M,  siphon,  controlling  supply  of  oil. 

P,  candle-wicking,  for  feeding  the  oil. 

H,  copper  rod,  for  receiving  oil  from  G. 
The  Railroad  Testing-machine,  which  is  shown  in  section  in 
Fig.  1 1 2,  differs  from  the  Standard  Oil-testing  Machine  princi- 
pally in  the  construction  of  the  pendulum.  This  is  made  by 
screwing  a  wrought-iron  pipe,/,  which  is  shown  by  solid  black 
shading  in  Fig.  1 12, into  the  head  K,  which  embraces  the  jour- 
nal and  holds  the  bearings  aa  in  their  place.  In  this  pipe  a 
loose  piece,  b,  is  fitted,  which  bears  against  the  under  journal- 
bearing,  a' .  Into  the  lower  end  of  the  pipe  J  a  piece,  cc,  is 
screwed,  which  has  a  hole  drilled  in  the  centre,  through  which 


153-3 


FRICTION— TESTING   OF  LUBRICANTS. 


2I9 


a  rod,  /,  passes,  the  upper  end  of  which  is  screwed  into  a  cap, 
4\  between  this  cap  and  the  piece  cc  a  spiral  spring  is  placed. 
The  upper  end  of  the  rod  bears  against  the  piece  b,  which  in 
turn  bears  against  the  bearing  a'.  The  piece  b  has  a  key,  /, 
arhich  passes  through  it  and  the  pipe  J.  This  key  bears 


FIG.  in. — THURSTON'S  RAILROAD-LUBRICANT  TESTING-MACHINE. 


against  a  nut,  0,  screwed  on  the  pipe.  By  turning  the  nut  o 
the  stress  on  the  journal  produced  by  screwing  the  rod /can 
be  thrown  on  the  key  /,  and  the  bearing  relieved  of  pressure, 
without  changing  the  tension  on  the  spring.  A  counterbalance 
above  the  pendulum  is  used  when  accurate  readings  are  de- 


22O 


EXPERIMENTAL   ENGINEERING. 


[§154- 


sired.  The  "  brasses  "  are  cast  hollow,  and  when  necessary  a 
stream  of  water  can  be  passed  through  to  take  up  the  heat, 
and  maintain  them  at  an  even  temperature. 

The  graduations  on  the  machine  show  on  the  fixed  scale. 


FIG.  112. — SECTION  OF  RAILROAD  LUBRICANT  TESTING-MACHINE. 

as  in  the  standard  machine,  the  total  friction  ;  and  on  the 
pendulum,  the  total  pressures  (i)  on  the  upper  brasses,  (2)  on 
the  lower  brasses,  and  (3)  the  sum  of  these  pressures. 

154.  Theory  of  the  Thurston  Oil-testing  Machines. — 
The  mathematical  formulae  applying  to  these  machines  are  as 
follows  :  Let  P  equal  the  total  pressure  on  the  journal ;  /  the 
pressure  per  square  inch  on  projected  area  of  journal ;  T  the 
tension  of  the  spring;  W the  weight  of  the  pendulum;  r  the 
radius  of  the  journal ;  R  the  effective  arm  of  the  pendulum  ; 


§154-]  FRICTION— TESTING   OF  LUBRICANTS.  221 

Q  the  angle  of  deviation  of  the  pendulum  from  a  vertical  line  ; 
F  the  total  force  of  friction  ;  f  the  coefficient  of  friction ;  / 
the  length  of  bearing-surface  of  each  brass. 

Since  in  this  machine  both  brasses  are  loaded,  the  pro- 
jected area  of  the  journal  bearing-surface  is  2(2r)/=4/r.  We 
shall  evidently  have 


,     ........    (i) 

P      2T+  W 


By  definition  /=  F-f-  P. 

Since  the  moment  of  friction  is  equal  to  the  external  mo- 
ment  of  forces  acting, 


B..    .    .    (3) 
From  which 

F       WR  sin  8 


In  the  machines  WR  sin  0  H-  r  is  shown  on  the  fixed  scale* 
and  the  graduations  will  evidently  vary  with  sin  0,  since 
WR  -r-  r  is  constant. 

P,  the  total  pressure,  is  shown  on  the  scale  attached  to  the 
pendulum. 

In  the  standard  machine  the  weight  of  the  pendulum  is 
neglected,  and  P  =  2  T',  but  in  the  Railroad  Oil-testing  Machine 
the  weight  must  be  considered,  and  P=  2T  -\-  W,  as  in  equa- 
tion (i). 

Constants  of  the  Machine.  —  As  the  constants  of  the. 
machine  are  likely  to  change  with  use,  they  should  be  deter- 
mined before  every  important  test,  and  the  final  results  cor- 
rected accordingly. 


222  EXPERIMENTAL   ENGINEERING.  [§  155 

1.  To  determine  the  constant  WR,  swing  the  pendulum  to 
a  horizontal  position,  as  determined  by  a  spirit-level ;  support 
it  in  this  position  by  a  pointed  strut  resting  on  a  pair  of  scales. 
From  the  weight,  corrected  for  weight  of  strut,  get  the  value  of 
WR ;  this  should  be  repeated  several  times,  and  the  average 
of  these  products  obtained. 

2.  Obtain  the  weight  of  the  pendulum  by  a  number  of  care- 
ful  weighings. 

3.  Measure  the  length  and  radius  of  the  journal;  compute 
the  projected  bearing-surface  2(2  Ir). 

WR 

4.  Compute  the  constant ,  which  should   equal  twice 

the  reading  of  the  arc  showing  the  coefficient  of  friction  when 
the  pendulum  is  at  an  angle  of  30°,  since  sine  of  30°  equal  •£. 

The  following  are  special  directions  for  obtaining  the  co- 
efficient of  friction  with  the  Thurston  machine. 

155.  Directions  for  obtaining  Coefficient  of  Friction 
with  Thurston's  Oil-testing  Machines. — Cleaning. — In  the 
testing  of  oils  great  care  must  be  taken  to  prevent  the  mixing 
of  different  samples,  and  in  changing  from  one  oil  to  another 
the  machine  must  be  thoroughly  cleaned  by  the  use  of  alkali 
or  benzine. 

In  the  test  for  coefficient  of  friction  the  loads,  velocity,  and 
temperature  are  kept  constant  for  each  run  ;  the  oil-supply  is 
sufficient  to  keep  temperature  constant,  the  journals  being 
generally  flooded.  The  load  is  changed  for  each  run. 

The  following  are  the  special  directions  for  the  test  of 
Coefficient  of  Friction,  as  followed  in  the  Sibley  College  Engi- 
neering Laboratory. 

Apparatus. — Thurston's  Standard  Lubricant  Testing-ma- 
chine; thermometer;  attached  speed-counter.  (See  Art.  151, 
page  2 1 7.) 

Method. — Remove  and  thoroughly  clean  the  brasses  and 
the  steel  sleeve  or  journal  by  the  use  of  benzine.  Put  the 
sleeve  on  the  mandrel ;  place  the  brasses  in  the  head  of  the 
pendulum  and  see  that  the  pressure  spring  is  set  for  zero  and 
pressure  as  indicated  by  the  pointer  on  the  scale.  Slide  the 


§  1 55.]  FRICTION— TESTING   OF  LUBRICANTS.  22$ 

pendulum  carefully  over  the  sleeve,  put  on  the  washer,  and 
secure  it  with  the  nut.  See  that  the  feeding  apparatus  is  in 
running  order.  Belt  up  the  machine  for  the  high  speed  and 
throw  on  the  power,  at  the  same  time  supplying  the  oil  at  a 
rate  calculated  to  maintain  a  free  supply.  By  deflecting  the 
pendulum  and  using  a  wrench  on  the  nut  at  the  bottom  in- 
crease the  pressure  on  the  brasses  gradually  until  the  pointer 
indicates  50  Ibs.  per  square  inch. 

Determine  the  constants  of  the  machine  as  explained  in 
Article  I54tpage  222;  measure  the  projected  area  of  journal 
bearing-surface,  and  the  weight  and  moment  of  the  pendulum. 
Ascertain  the  error,  if  any,  in  the  graduation  of  the  machine, 
and  correct  the  results  obtained  accordingly. 

Make  a  run  at  this  pressure,  and  also  foi  pressures  of  100, 
150,  and  200  Ibs.;  but  do  not  in  general  permit  the  maximum 
pressure  in  pounds  per  square  inch  to  exceed  44,800  -+•  (v  +  20). 
Begin  by  noting  the  time  and  the  reading  of  the  revolution- 
counter  ;  take  readings,  at  intervals  of  one  minute,  of  the  arc 
and  the  temperature  until  both  are  constant.  At  the  end  of 
the  run  read  the  revolution-counter  and  note  the  time. 

The  velocity,  v,  in  rubbing  surface  in  feet  per  minute  should 
be  computed  from  the  number  of  revolutions  and  circumfer- 
ence of  the  journal. 

Make  a  second  series  of  runs,  with  constant  pressure  and 
variable  speed. 

In  report  of  the  test  state  clearly  the  objects,  describe 
apparatus  used  and  method  of  testing. 

Tabulate  data,  and  make  record  of  tests  on  the  forms  given. 

Draw  a  series  of  curves  on  the  same  sheet,  showing  results 
of  the  various  tests  as  follows  : 

1.  With  total  friction  as  abscissae,  and  pressure  per  square 
inch  as  ordinates;  for  constant  speed. 

2.  With  coefficient  of  friction  as  abscissae,  and  pressure  per 
square  inch  as  ordinates ;  for  constant  speed. 

3.  With  coefficient  of  friction  as  abscissae,  and  velocity  of 
tubbing  in  feet  per  minute  as  ordinates;  pressure  constant. 


224  EXPERIMENTAL  ENGINEERING.  [§  157- 

156.  Instructions  for  Use  of  Thurston's  R.  R.  Lubricant- 
tester.     (See  Article  152,  page  218.) — Follow  same  directions 
for  coefficient  of  friction-test  as  given  for  the  standard  machine, 
applying  the  pressure  as  explained  in  Article  155,  page  222. 

Water  or  oil  of  any  desired  temperature  can  be  forced 
through  the  hollow  boxes  by  connecting  as  shown  in  Fig.  80, 
page  191,  and  the  temperature  of  the  bearings  thus  maintained 
at  any  desired  point.  With  this  arrangement  the  machine  may 
be  used  for  testing  cylinder-stocks,  as  explained  in  directions 
for  using  Boult's  machine  (see  Article  161,  page  231).  The  con- 
cise directions  are : 

1.  Clean  the  machine. 

2.  Obtain  the  constants  of  the  machine ;  do  not  trust  to  the 
graduations. 

3.  Make  run  under  required  conditions,  which  may  be  with 
*ach  rate  of  speed. 

a.  With  flooded  bearings,  temperature  variable. 

b.  With  flooded  bearings,  temperature  regulated  by 

forcing  oil  or  water  through  hollow  brasses. 

c.  Feed  limited,  temperature  variable  or  temperature 

regulated. 

In  all  cases  the  object  will  be  to  ascertain  the  coefficient  of 
friction. 

157.  Richie's  Oil-testing  Machine.— This  machine  con- 
sists of  an  axis  revolving  in  two  brass  boxes,  which  may  be 
clamped  more  or  less  tightly  together.    The  machine  as  shown 
in  Fig.  1 13  has  two  scale-beams, — the  lower  one  for  the  purpose 
of  weighing  the  pressure  put  upon  the  journal  by  the  hand- 
screw  on  the  opposite  side  of  the  machine,  the  upper  one  for 
measuring  the  tendency  of  the  journal  to  rotate.     The  upper 
scale-beam  shows  the  total  friction,  or  coefficient  of  friction,  as 
the  graduations  may  be  arranged.     A  thermometer  gives  the 
temperature  of  the  journal;  a  counter  the  number  of  revolu- 
tions. 

Let  P  equal  the  total  pressure  applied  to  the  bearings. 
Let  B  equal  the  projected  area  of  the  journal-bearings,/  equal 


§  1 57.]  FRICTION— TESTING   OF  LUBRICANTS.  22$ 

the  pressure  per  square  inch  ;  F  equal  the  total  friction ;  /  equal 


FIG.  113.— RiEHifi's  OIL-TESTING  MACHINE, 

the  coefficient  of  friction;   n  equal  the  arm  of  the  bearing; 
a  the  arm  of  the  total  pressure.     Then  do  we  have 


Fn  =  aP  =  aBp, 
Bfn  =  aP9 


and 


- 

Bn~  »' 


226  EXPERIMENTAL   ENGINEERING.  [§  158. 

If  /  be  maintained  constant,  and  a  -f-  n  be  made  the  value 
of  the  unit  of  graduation  on  the  scale-beam 


f=  graduation. 

158.  Durability  of  Lubricants. — In  this  case  the  amount 
of  oil  supplied  is  limited,  and  it  is  to  be  used  for  as  long  a  time 
as  it  will  continue  to  cover  and  lubricate  the  journal  and  pre- 
vent abrasion.  To  give  satisfactory  results,  this  requires  a 
limited  supply  or  a  perfectly  constant  rate  of  feed,  an  even  dis- 
tribution of  the  oil,  and  the  restoration  of  any  oil  that  is  not 
used  to  destruction ;  these  difficulties  are  serious,  and  present 
methods  do  not  give  uniform  results.*  The  method  at  present 
used  is  to  consider  the  endurance  or  durability  proportional  to 
the  time  in  which  a  limited  amount,  as  one  fourth  c.c.  will  con- 
tinue to  cover  and  lubricate  the  journal  without  assuming  a 
pasty  or  gummy  condition,  and  without  giving  a  high  coefficient 
of  friction.  The  average  of  a  number  of  runs  is  taken  as  the 
correct  determination.  In  this  test  care  must  be  taken  not  to 
injure  the  journal,  and  it  must  be  put  in  good  condition  at  the 
end  of  the  run. 

The  time  or  number  of  revolutions  required  to  raise  the 
temperature  to  a  fixed  point — for  instance,  160  F. — is  in  some 
instances  considered  proportional  to  the  durability. 

The  Ashcroft  (see  Article  159,  page  227)  and  the  Boult  (see 
Article  160,  page  228)  machines  are  especially  designed  for  de- 
termining the  durability  of  oils — from  the  former  by  noting  the 
rise  in  temperature,  from  the  latter  by  noting  the  change  in  the 
coefficient  of  friction.  The  difficulty  of  properly  making  this 
test  no  doubt  lies  in  the  loss  of  a  very  slight  amount  of  oil 
from  the  journals,  which  is  sufficient,  however,  to  make  the 
results  very  uncertain. 


*See  paper  by  Professor  Denton,  Vol.  XI.,  p.  1013,  Transactions  of  Am: 
can  Society  of  Mechanical  Engineers. 


§160.] 


FRICTION— TESTING   OF  LUBRICANTS. 


227 


159.  Ashcroft's  Oil-testing  Machine.— This  machina 
(Fig,  I  I4)consists  of  an  axle  revolving  in  two  brass  boxes  ;  the 
pressure  on  the  axle  is  regulated  by  the  heavy  overhanging 
counterpoise  shown  in  the  engraving.  The  tendency  to  rotate 
is  resisted  by  a  lever  which  is  connected  to  the  attached  gauge. 
The  gauge  is  graduated  to  show  coefficient  of  friction. 


FIG.  114.— ASHCROFT'S  OIL-TESTING  MACHINE. 

The  temperature  is  taken  by  an  attached  thermometer,  and 
the  number  of  revolutions  by  a  counter,  as  shown  in  the  figure. 

In  this  machine  the  weights  and  levers  are  constant,  the 
Variables  being  the  temperature  and  coefficient  of  friction. 

It  is  used  exclusively  with  a  limited  supply  of  oil,  the  value 
of  the  oil  being  supposed  to  vary  with  the  total  number  of 
revolutions  required  to  raise  the  temperature  to  a  given  degree, 
—for  instance,  to  1 60°  F. 

160.  Boult's  Lubricant-testing  Machine. — This  machine, 
designed  by  W.  S.  Boult  of  Liverpool,  is  a  modification  of 


228 


EXPERIMEN  TA  L   ENGINEERING. 


L 


the  Thurston  oil-tester,  yet  it  differs  in  several  essential  feat- 
ures. A  general  view  of  the  machine  is  shown  in  Fig  115, 
and  a  section  of  its  boxes  and  the  surrounding  bushin  Fig.  1 16. 


FIG.  115.— BOULT'S  LUBRICANT-TESTER. 

The  machine  is  designed  to  accomplish  the  following  pur- 
poses: I.  Maintaining  the  testing  journal  at  any  desired  tem- 
perature. 2.  Complete  retention  on  the  rubbing  surfaces  of 
the  oil  under  test.  3.  Application  of  suitable  pressure  to  the 
rubbing  surfaces.  4.  Measurement  of  the  friction  between  the 
rubbing  surfaces. 


§  i6o.] 


FRICTION— TESTING   OF  LUBRICANTS. 


229 


To  secure  the  complete  retention  of  the  oil,  a  complete  bush 
with  internal  flanges  is  used  instead  of  the  brasses  employed  in 
other  oil-testing  machines.  On 
the  inside  of  the  bush  is  an  ex- 
panding journal,  DD,  Fig.  I  i6,the 
parts  of  which  are  pressed  outward 
against  the  surrounding  bush  by 
the  springs  E,  or  they  may  be 
drawn  together  by  the  set-screws 
BB,  compressing  the  springs  £.  A 
limited  amount  of  oil  is  fed  from 
a  pipette  or  graduated  cylinder 
on  the  journal,  with  the  bush 
removed.  This  oil,  it  is  claimed, 
will  be  maintained  on  the  outer 
surface  of  the  journal  and  on  the 
interior  surface  of  the  metallic 
bush,  so  that  it  may  be  used  to 
destruction.  The  bush  is  hollow, 
and  can  be  filled  with  water,  oil, 
or  melting  ice  and  brine. 

The  oil  to  be  tested   can  be 


FiG.n6. — SECTION  OF  BOULT'S  LUBRICANT* 

TESTER. 


maintained  at  any  desired  tem- 
perature by  a  burner,  F,  which  heats  the  liquid  CC  in  the  sur- 
rounding bush.  The  temperature  of  the  journal  can  be  read 
by  a  thermometer  whose  bulb  is  inserted  in  the  liquid  CC. 

The  friction  tends  to  rotate  the  bush  ;  this  tendency  is  re- 
sisted by  a  lever  connected  by  a  chain  to  an  axis  carrying  a 
weighted  pendulum,  G,  Fig.  115. 

The  motion  of  the  pendulum  is  communicated  by  gearing 
to  a  hand,  passing  over  a  dial  graduated  to  show  the  total  fric- 
tion on  the  rubbing  surfaces. 

The  formulae  for  use  of  the  instrument  would  be  as  follows : 
Let  f  equal  coefficient  of  friction ;  G  the  weight  of  the  bob 
on  the  pendulum,  R  its  lever  arm ;  a  the  angle  made  by  the 
pendulum  with  the  vertical;  a  the  length  of  the  connecting 
lever;  c  the  radius  of  the  axis  to  which  the  pendulum  is 


230  EXPERIMENTAL   ENGINEERING.  _     l6l> 

attached  ;  r  the  radius  of  the  journal ;  A  the  projected  area  of 
the  journal ;  Pthe  total  pressure  on  the  journal.     Then 

-.-'Gs'ma  =/AP, 
r    c 

from  which 

aGR  sin  a       sin  a 
/=      rcAp-       —p->  (constant.) 

In  this  instrument  the  total  pressure  P  is  usually  constant 
and  equal  to  68  Ibs.,  so  that  the  graduations  on  the  dial  must 
be  proportional  to  sin  a. 

If  the  graduations  are  correct,  the  coefficient  is  found  by 
dividing  the  readings  of  the  dial  by  P  (68  Ibs.).  The  work  of 
friction  is  the  product  of  the  total  space  travelled  into  the  total 
friction,  and  this  space  in  the  Boult  instrument  is  two  thirds  of 
a  foot  for  each  revolution,  or  two  thirds  of  the  number  of 
revolutions. 

The  instrument  cannot  be  used  with  a  constant  feed  of  oil, 
nor  can  the  pressures  be  varied  except  by  changing  the 
springs  E. 

161.  Directions  for  Durability  Test  of  Oils  with  Boult's 
Oil-testing  Machine. — To  fill  cylindrical  oil-bath,  take  out 
the  small  thumb-screw  in  cylindrical  bath  and  insert  a  bent 
funnel.  Pour  in  oil — any  sort  of  heavy  oil  may  be  used — until 
it  overflows  from  the  hole  in  which  funnel  is  inserted,  and  re- 
place thumb-screw. 

i.  See  that  the  friction  surfaces  are  perfectly  clean.  These 
can  be  examined  by  tightening  the  set-screws  in  order  to  de- 
press the  spring.  This  will  enable  the  cylindrical  bath  to  be 
lifted  away.  After  seeing  that  the  surfaces  are  perfectly  clean, 
pour  on  a  measured  quantity  of  the  lubricant  to  be  tested, 
and  reset  the  cylinder-bath  in  position.  Slacken  set-screws 
so  as  to  allow  the  spring  to  have  full  pressure.  The  set-screws 
should  not  be  removed  entirely  when  slackening. 


§  I6~2.J  FRICTION— TESTING   OF  LUBRICANTS. 

2.  Light  the  Bunsen  burner. 

3.  The   thermometer  indicates   the  temperature  to  which 
the  lubricant  has  to  be  subjected  in  the  steam-cylinder,  being 
graduated  in  degrees  Fahrenheit,  and  their  equivalent  in  pounds 
pressure.     Thus,  if  the  working  steam-pressure  is  60  Ibs.,  the 
thermometer  shows  that  the  heat  of  steam  at  that  pressure  is 
307°  Fahr.;  whilst  at  100  Ibs.  pressure  its  temperature  is  358° 
Fahr.,  etc.     Run  the  tester,  say,  until  there  is  a  rise  of  50  per 
cent ;  in  some  cases  it  is  preferable  to  run    the    tester   until 
there  is  a  rise  of  100  per  cent  of  the  friction  first  indicated. 
There  does  not  appear  to  be  any  advantage  in  going  beyond 
this,  as  the  oil  is  then  practically  unfit  for  further  use,  and 
there  is  danger  of  roughening  the  friction  surfaces. 

4.  When  it  is  considered  desirable  to  ascertain  the  distance 
travelled  by  the  friction   surfaces  during  a  test,  read  off  the 
counting-indicator  before  and  after  the  test,  and  subtract  the 
lesser  from  the  greater  total,  and  the  difference  will  represent 
the  number  of  revolutions  made  during  the  test.     As  the  fric- 
tion surfaces  travel  two  thirds  of  a  foot  during  each  revolution, 
the  number  of  feet  travelled  is  arrived  at  by  simply  deducting 
from  the  number  of  revolutions  made,  one  third  thereof. 

The  value  of  the  oil  is  proportional  to  the  number  of  feet 
travelled  by  the  rubbing  surfaces. 

The  speed  at  which  the  tester  should  be  run  should  be 
about  five  to  six  hundred  revolutions  per  minute.  For  quick- 
speed  engine-oil  the  speed  may  be  increased  to  about  a  thou- 
sand per  minute. 

162.  Experiment  with  Limited  Feed.— The  object  of  this 
experiment  is  to  ascertain  the  variation  in  the  coefficient  of 
friction  due  to  a  change  in  the  rate  of  feed. 

The  experiment  is  to  be  made  with  the  feeding  apparatus 
arranged  so  that  the  supply  can  be  regulated.  Different  runs 
are  made  with  different  rates  of  feed,  and  the  variation  in 
the  coefficient  of  friction  determined.  Fig.  1 1 1,  p.  2 19,  repre- 
sents the  Thurston  R.  R.  Lubricant-tester  as  arranged  for  the 
experiment,  with  a  constantly  diminishing  rate  of  feed,  by  Pro- 
fessor G.  W.  Bissel.  In  this  case  oil  is  obtained  by  the  siphon 


232 


EXPERIMENTAL   ENGINEERING. 


[§  162. 


M  from  the  burette  N,  and  conveyed  by  the  candle-wicking  P 
to  a  copper  rod  H  inserted  in  the  bearings.  The  rate  of  flow 
will  depend  upon  the  height  of  the  oil  in  the  burette  N  above 
the  end  of  the  siphon-tube  M,  and  as  the  head  gradually  di- 
minishes from  loss  of  oil,  the  rate  of  flow  will  decrease. 

The  quantity  of  oil  used  is  to  be  determined  by  gradua- 
tions on  the  burette.  The  increase  in  coefficient  of  friction 
due  to  the  constantly  diminishing  rate  of  feed  is  shown  in  Fig. 
86,  the  coefficients  of  friction  being  shown  by  the  dotted 
lines,  corresponding  to  a  given  rate  of  feed  and  a  given  time 
in  minutes. 


.009 
.008 


.001 


.002  .003 

Coefficient  of.Frict.ion 


.001 


.005 


FIG. 


117. 


The  experiment  with  head  and  feed  maintained  constant 
during  each  run  would  represent  very  closely  the  usual  condi- 
tions of  supplying  lubricants. 

In  this  case,  provided  there  was  no  loss  of  oil  from  the 
journals,  the  experiment  might  show — 

1.  The  laws  of  friction  for  ordinary  lubrication. 

2.  The  most  economical  rate  of  feed  for  a  given  lubricant. 


FRICTION— TESTING   OF  LUBRICANTS. 


233 


3.  The  value  of  the  lubricants  on  the  joint  basis  of  amount 
consumed  and  coefficient  of  friction. 

A  few  tables  showing  coefficients  of  friction  which  has  been 
obtained  in  various  trials  are  given  in  the  Appendix  for  refer- 
ence. 

163.  Forms  for  Report. — The  following  are  the  forms  used 
in  Sibley  College  for  data  and  results  of  lubricant  test: 

REPORT   OF   LUBRICANT   TEST. 


Name  of  Lubricant  

Mark Lab.  No Date... 

Source Observer. 

Investigation 


No   of  feet  travelled  by  rubbing  surface 

Time. 
Min- 
utes. 

Total 
Revolu- 
tions. 

Temper- 
ature. 

Read- 
ing on 
Arc. 

Coeffi- 
cient of 
Friction. 

Time. 
Min- 
utes. 

Total 
Revolu- 
tions. 

Temper- 
ature. 

Read- 
ing on 
Arc. 

Coeffi- 
cient of 
Friction. 

VISCOSITY   AND   RESULTS  OF  OIL  TEST. 

Kind  of  oil Date . .    189. ... 

Received  from 

Color Ash * 

Specific  gravity °  B.  Tar % 

"  "      Waterloo.        Chill-pt *  F. 

Flashing  pt °  F.      Loss  at °  F.  for  3  hrs % 

Burning-pt °  F.  Acid.  '. 


234 


EXPERIMENTAL  ENGINEERING. 
VISCOSITY   TEST. 


[§  163- 


No. 

Time  of  Flow  of  100  c.c.  in  Seconds. 

Temperature 
Degrees  F. 

Lubricating 
Value  Lard-oil 
xoo. 

Sample, 

Lard-oil. 

Water, 

RESULTS  OF  FRICTION   TEST. 


Date. 

I 

• 

I] 

L".- 

I] 

I. 

...180  . 

Temp. 

Arc. 

Temp. 

Arc. 

Temp. 

Arc. 

Speed  : 

Pressure: 
Total  Ibs  

Coefficient  of  friction.  . 

TEST  FOR   RESINS. 

Flow  on  plane  inclined degrees. 

Kind  of  plane Tempt,  room. 

Time  in  hrs.,  Sample ,  Lard-oil Water. 


CHAPTER  VIL 

MEASUREMENT    OF    POWER— DYNAMOMETERS— BELT- 
TESTING  MACHINES. 

164,  Classes. — Dynamometers  are  instruments  for  measur- 
ing power.     They  are  of  two  classes  :  I.  Absorption;  2.    Trans- 
mission.     In  the  first  class  the  work  received  is  transformed 
by  friction  into  heat  and  dissipated  ;  in  the  second  class  the 
dynamometer  absorbs  only  so   much  force  as  is  necessary  to 
overcome  its  own  friction,  the  remainder  being  transmitted. 

165.  Absorption  Dynamometer.— The  Prony  Brake.* — 
The  Prony  brake  is  the  most  common  form  of  absorption  dy- 
namometer.    This  brake  is  so  constructed  as  to  absorb  the 
work  done  by  the  machine  in  friction,  this  friction  being  pro- 
duced by  some  kind  of  a  surface  connected  to  a  stationary 
part,  and  which  rubs  on  the  revolving  surface  of  the  wheel 
with  which  it  is  used.     The  brake  usually  consists  of  a  por- 
tion which  can  be  clamped  on  to  a  wheel  (see  Fig.  n8,page 
2 39), with  more  or  less  pressure,  and  an  arm  or  its  equivalent. 
The  part  exerting  pressure  on  the  wheel  is  termed  the  brake- 
strap  ;  the  perpendicular  distance  from  the  line  of  action  of 
the  weight,  G,  to  the  centre  of  the  wheel  is  termed  the  arm  of 
the  brake.     The  brake  is  prevented  from  turning  by  a  definite 
load  which  we  term  G,  applied  at  a  distance  equal  to  the 
length  of  the  arm  (a)  from  centre  of  motion.     The  work  of 
resistance  would  then  evidently  be  equal  to  the  product  of  the 
weight  of  resistance,  G,  into  the  distance  it  would  pass  through 

*See  Engine  and  Boiler  Trials,  by  R.  H.  Thurston,  page  157;  Mechanics  of 
Materials,  by  I.  P.  Church,  page  269;  Du  Bois*  Weisbach's  Mechanics  of  En* 
gineeting,  page  13. 

235 


236  EXPERIMENTAL   ENGINEERING.  [§  167,, 

if  free  to  move.     If  n  be  the  number  of  revolutions  per  minute, 
the  horse-power  shown  by  the  brake  would  evidently  be 

2nGan  -r-  33000  ........     (i) 

Brakes  are  made  with  various  rubbing  surfaces,  and  with 
various  devices  to  maintain  a  constant  resistance. 

166.  Stresses  on  the  Brake-strap.  —  Formula.  —  The 
strains  on  the  brake-strap  are  essentially  the  same  as  those 
on  a  belt,  as  given  in  Article  128,  page  199. 

That  is,  if  7^  represent  the  greatest  tension,  7J,  the  least 
tension,  c  the  percentage  that  the  arc  of  contact  bears  to  the 
whole  circumference,  N  the  normal  pressure,  F  the  resistance 
of  the  brake,  /  coefficient  of  friction, 


T 

_L  =  I02-7288/<=  Number  whose  log  is  2.7288/c  =  B. 


FB 


167.  Designing  a  Brake.* — The  actual  process  of  designing 
a  brake  is  as  follows  :  There  is  given  the  power  to  be  absorbed, 
number  of  revolutions,  diameter  and  face  of  the  brake-wheel. 
In  case  a  special  brake-wheel  is  to  be  designed,  the  area  of 
bearing  surface  is  to  be  taken  so  that  the  number  obtained  by 
multiplying  the  width  w  of  the  brake  in  inches  by  the  velocity 
of  the  periphery  v  of  the  wheel  in  feet  per  minute,  divided  by 


*See  "  Engine  and   Boiler  Trials,"  by  R.   H.  Thurston,  pages  260  to  282; 
also,  "  Friction  and  Lubrication." 


§  167.]  MEASUREMENT  OF  POWER.  237 

the  horse-power  H,  shall  not  exceed  500  to  1000.*     Call  this 
result  K.     Then 

*-?• 


400  to  500  is  considered  a  good  average  value  of  K. 

The  value  of  the  coefficient  of  friction  f  should  be  taken 
as  the  lowest  value  for  the  surfaces  in  contact  (see  table  of  co- 
efficient of  friction  in  Appendix).  This  coefficient  is  about  0.2 
for  wood  or  leather  on  metal,  and  about  0.15  for  metal  on  metal. 

Let  H  be  the  work  to  be  transmitted  in  horse-power,  n  the 
number  of  revolutions  of  the  brake-wheel,  D  its  diamete«-r 
then  the  resistance  F  of  the  brake  must  be 


The  arc  of  contact  is  known  or  assumed,  and  may  be  expressed 
as  convenient  (see  Article  128)  in  circular  measure  6,  degrees 
a,  or  in  percentage  of  the  whole  circumference  c. 

Example.  —  Assume  the  arc  of  contact  as  180  degrees 
(£  =  0.5),  the  diameter  of  brake-wheel  4  feet,  coefficient  of 
friction  (y=o.  15),  face  of  brake-wheel  10  inches,  revolutions 
90,  horse-power  70.  Find  the  safe  dimensions  of  the  brake- 
strap  and  working  parts  of  the  brake. 

Then,  from  page  236, 


B  =  io2-7288^  = 

That  is,  B  equals  the  number  whose  logarithm  is  0.2046  ;  or, 

B  =  1.602. 

*See  also  "  Engine  and  Boiler  Trials,"  by  R.  H.  Thurston,  pp.  272  and  279. 


238  EXPERIMENTAL   ENGINEERING.  [§  l6/. 

Thus  if  the  brake-wheel  is  4  feet  diameter  revolving  at  90 
revolutions  per  minute :  from  equation  (4) 

'=i^i=2043pounds- 

Taking  B  as  above,  and  substituting  in  equations  (2)  and  (3). 
we  have 

i.6o2\  _ 


.  =  2°43  fi         =  "36; 


=         =  13620. 


From  the  value  of  7", ,  the  maximum  tension,  we  compute  the 
required  area  of  the  brake-straps,  using  10,000  pounds  as  the 
safe-working  strain. 

Section  of  brake-straps  =  5436-7-  10000  =  0.55  square  inch. 
The  assumed  width  of  brake-wheel  is  10  inches ;  this  gives 
for  the  value  of  Ky  by  equation  page  237. 

K  =  (10)  (i  132)  -f-  70  =  162 ;    a  low  value. 

If  it  is  proposed  in  this  brake  to  use  3  straps,  each  2  inches 
wide,  the  thickness  will  then  be 

0.55  -r-  6  =  0.091  inch. 

To  determine  a  convenient  length  of  the  brake-arm,  con* 
sider  equation  (i)  for  work  delivered  in  horse-power. 

H  =F  27tGan  ~  33000. 


§  169.]  MEASUREMENT  OF  POWER.  239 

By  dividing  both  terms  by  2?r, 

H=  Gan-±  5252; 

G-=5_252 
H    '   an  ' 

168.  Brake  Horse-power. — The  following  table  will  often 
be  convenient  for  determining  the  delivered  horse-power  from 
a  brake. 

HORSE-POWER  PER  100  REVOLUTIONS  FROM  A  BRAKE. 


Length  of  Brake-arm, 
feet. 

Factor  to  multiply 
scale-reading  to  give 
horse-power,  H-*-G. 

Ratio  of  scale-read- 
ing to  horse-  power, 

I 

O.OI9 

52.52 

2 

.038 

26.26 

3 

•057 

17.51 

4 

.076 

I3-I3 

5 

.090 

10.50 

5.252 

.100 

IO.OO 

6 

.114 

8.75 

7 

.133 

7-50 

8 

.152 

6.56 

9 

.172 

5-83 

10.504 

.200 

5.00 

169.  Different  Forms  of  Prony  Brakes. — Various  forms 
of  brakes  are  made.     Fig.  118  shows  a  very  simple  form  of 


FIG.  118. — PRONY  BRAKE. 


Prony  brake,  in  which  the  rubbing  surfaces  are  made  by  two 
wooden  beams  clamped  together  by  the  bolts  C  C.  Weight  is 
applied  to  the  arm  E  at  the  point  G ;  the  stops  D  D  prevent  a 
great  range  of  motion  of  the  arm  ;  the  projection  F  is  used  to 
hang  on  sufficient  counterbalance  to  prevent  the  brake  from 


240 


EXPERIMENTAL  ENGINEERING. 


[ 


revolving  by  its  own  arm-weight  when  the  screws  C  C  are  very 
loose.  The  net  load  acting  on  the  brake-arm  is  the  difference 
between  the  weight  at  G  and  that  at  F,  reduced  to  an  equiva- 
lent weight  acting  at  G. 

Brakes  are  usually  constructed  by  fastening  blocks  of  wood, 
on  the  inside  of  flexible  bands  of  iron,  so  as  to  encircle  a 
wheel.  The  inside  of  the  blocks  should  be  fitted  to  the  wheel, 
and  the  spaces  between  the  blocks  should  be  at  least  equal  to 
one  third  the  area  of  the  block.  The  iron  bands  are  connected 
to  the  brake-arm  in  such  a  manner  that  the  tension  on  the 
wheel  can  readily  be  changed.  The  form  of  such  a  brake  is 
shown  in  Fig.  119  attached  to  a  portable  engine. 


FKJ.  ii9w— BRAKE  APPLIED  TO  PORTABLE  ENGINE. 

170.  Strap-brakes.— Brakes  are  sometimes  made  by  taking 
one  or  more  turns  of  a  rope  or  strap  around  a  wheel,  as  shown 


Fie.  120. — STRAP-BRAKE. 


in  Fig.  1 20.  In  this  case  weights  must  be  hung  on  both  sides, 
and   since  the   arm   of  action   is   equal,  the  resultant  force 


§  1 75.]  MEASUREMENT  OF  POWER.  241 

acting  is  the  difference  between  the  two  weights :  that  is,  in 
the  figure  the  resultant  force  is  A  —  B ;  the  equivalent  space 
passed  through  is  the  distance  travelled  by  any  point  of  the 
circumference  of  the  wheel  in  a  given  time.  The  work  done 
is  the  product  of  these  quantities. 

171.  Self- regulating   Brakes. — Brakes    with    automatic 
regulating  devices  are  often  made  ;  in  this  case  the  direction  of 
motion  of  the  wheel  must  be  such  as  to  lift  the  brake-arm.     If 
the  tension  is  too  great  the  brake-arm  rises  a  short  distance, 
and  this  motion  is  made  to  operate  a  regulating  device  of  some 
sort,  lessening  the  tension  on  the  brake- 
wheel  ;  if  the  tension  is  not  great  enough, 

the  brake-beam  falls,  producing  the  oppo- 
site effect. 

172.  Brake  with  oblique  Arm. — A 
very  simple  form  of  self -regulating  brake 
is   shown    in    Fig.  121:  in  this  case  the 
arm  is  maintained  at  an  angle  with  the 
horizontal.     If  the  friction  becomes  too 
great,  the  weight  G  rises,  and  the  arm  of 

the  brake  swings  from  A  to  E,  thus  in-  FIG  ial>^EU,REGULA™c» 
creasing  the  lever-arm  from  BC  to  LC\  if  BRAKE. 

the  friction  diminishes,  the  lever-arm  is  correspondingly  dimin- 
ished, thus  tending  to  maintain  the  brake  in  equilibrium. 

173.  Alden  Brake The  Alden  brake  (see Figs.  122  to  12  5) 

is  an  absorption  dynamometer  in  which  the  rubbing  surfaces 
are  separated  by  a  film  of  oil,  and  the  heat   is  absorbed  by 
water  under  pressure,  which  produces  the  friction.     It  is  con- 
structed by  fastening  a  disk  of  cast-iron,  A,  Fig.  1 22,  to  the 
power-shaft ;  this  disk  revolves  between  two  sheets  of  thin 
copper  E  E  joined  at  their  outer  edges,  from  which  it  is  sepa- 
rated by  a  bath  of  oil.     Outside  the  copper  sheets  on  either 
side  is  a  chamber  which  is  connected  with  the  water-supply  at 
G.  The  water  is  received  at  G  and  discharged  at  H,  thus  main- 
taining a  moderate  temperature.     Any  pressure  in  the  chamber 
causes  the  copper  disks  to  press  against  the  revolving  plate,  pro- 
ducing friction  which  tends  to  turn  the  copper  disks.     As  these 


242 


EXPERIMEN  TA  L   ENGINEERING. 


[§  174. 


are  rigidly  connected  to  the  outside  cast-iron  casing  and  brake, 
arm  Pt  the  turning  effect  can  be  balanced  and  measured  the 
same  as  in  the  ordinary  Prony  brake.  The  pressure  of  water 
is  automatically  regulated  by  a  valve  V,  Fig.  1 2 5,  which  is  par- 


FIG.  122. — SECTION. 


FIG.  125.— VALVE. 

tially  closed  if  the  brake-arm  rises  above  the  horizontal,  and  is 
partially  opened  if  it  falls  below  ;  this  brake  with  a  constant 
head  gives  exceedingly  close  regulation. 

174.  Hydraulic  Friction-brake. — The  author  has  designed 
a  hydraulic  friction-brake  that  can  be  applied  to  the  surface 
of  an  ordinary  brake-wheel.  The  brake  consists  of  .a  tube  of 
copper  with  an  oval  or  rectangular  cross-section,  which  very 
nearly  encircles  the  brake-wheel,  and  has  both  ends  closed. 
The  greatest  dimension  in  its  cross-section  is  equal  to  the 
width  of  the  brake-wheel,  and  its  least  dimension  is  one  half  to 
three  fourths  of  an  inch.  One  end  of  the  tube  is  connected 
with  the  water-supply,  the  other  to  the  discharge,  which  can 
be  throttled  as  required.  Outside  is  a  band  of  iron  completely 
encircling  the  tube  and  the  brake-wheel,  and  held  rigidly  to- 
gether by  means  of  bolts.  To  this  band  is  fastened  the  brake- 
arm,  and  also  one  end  of  the  copper  tube.  When  water-pres- 


UNIVERSITY 


§  i;6.]  MEASUREMENT  OF  POWER.  243 

sure  is  applied  to  the  tube,  it  tends  to  assume  a  round  cross- 
section,  the  shorter  diameter  increasing  and  the  greater 
diameter  diminishing.  As  these  changes  cannot  take  place 
because  of  the  outer  band  of  iron,  pressure  is  exerted  on  the 
surface  of  the  brake-wheel,  and  motion  of  the  brake-wheel 
tends  to  revolve  the  tube  and  band  of  iron.  This  is  resisted 
by  the  weight  on  the  arm  of  the  brake.  The  water-pressure  is 
regulated  automatically  by  a  slight  motion  of  the  brake-arm, 
which  closes  or  opens  the  supply-valve  as  is  required.  The 
arm  may  be  permitted  to  act  downward  on  a  pair  of  scales,  by 
interposing  a  spring  of  the  requisite  stiffness  between  it  and 
the  platform  of  the  scales.  To  prevent  wear  of  the  copper 
tube  thin  sheets  of  iron  may  be  interposed.  A  lubricant  is 
applied  by  means  of  lubricators  fixed  near  the  ends  of  the 
tube. 

175.  Removal  of  the  Heat  generated  by  the  Brake.— 
Various  devices  have  been  adopted  to  secure  the  removal  of 
the  heat.     One  method   is  to  cast  the  outer  rim  of  the  brake- 
wheel  hollow,  and  connect  this  by  a  tube  with  a  cavity  in  the 
centre  of  the  axis,  so  that  water  can  be  received  at  one  end  of 
the  axis  and  discharged  at  the  other.     Another  way  is  to  leave 
a  deep  internal  flange  on  the  brake-wheel,  and   in   using  the 
brake,  to  supply  water  by  means  of  a  crooked  pipe  on  one  side 
and  to  scoop  it  out  by  a  pipe  with  a  funnel-shaped-mouth  bent 
to  meet  the  current  of  water  near  the  opposite  side  of  the 
wheel.     Water  is  sometimes  run  on  to  the  surface  through  a 
hose,  but  aside  from  the  inconvenience   due  to  flying  water, 
if  any  of  the  rubbing  surfaces  are  of  wood  it  is  likely  to  make 
sudden  and  irregular  variations  in  the   coefficient  of  friction 
that  are  difficult  to  control. 

176.  Applying  Load.—  In  applying  the  load,  care  must  be 
taken  that  its  direction  is  tangent  to  the  circle  that  would  be 
described   by  the  brake-arm  were  it  free  to  move.     In  other 
words,  the  virtual  brake-arm  must  be  considered  as  perpendic- 
ular to  this  force.     If  a  vertical  load  or  weight  is  applied,  the 
brake-arm  must  be  horizontal,  and  equal  in  length  to  the  dis- 
tance from  this  vertical  line  to  the  centre  of  the  motion. 


244  EXPERIMENTAL   ENGINEERING.  [§  I/8- 

It  will  be  found  in  general  safer  and  more  satisfactory  to 
have  the  motion  of  the  brake-wheel  such  as  to  produce  a 
downward  force,  which  may  be  measured  by  a  pair  of  scales, 
rather  than  the  reverse,  which  requires  a  weight  to  be  sus- 
pended on  the  brake-arm.  There  should  be  a  knife-edge 
between  the  brake-arm  and  the  load  ;  in  case  of  downward 
motion,  the  support  upon  the  scales,  should  be  made  the  proper 
length  to  hold  the  brake-arm  horizontal. 

177.  Constants  of  Brake.— All  brakes  with  unbalanced 
arms  have  a  tendency  to  turn,  due  to  weight  of  the  arm. 
This  amount  must  be  ascertained  and  added  to  or  taken  from 
the  scale  or  load  readings  as  required  by  the  rotation,  in  order 
to  give  the  correct  load.  To  ascertain  this  amount,  the  brake 
may  be  balanced  on  a  knife-edge,  with  a  bearing  point  directly 
over  the  centre  of  the  wheel,  and  the  correction  to  the  weight 
obtained  by  readings  on  the  scale.  It  is  obtained  more  accu- 
rately by  making  the  brake  loose  enough  to  move  easily  on  the 
wheel ;  then  apply  a  spring-balance  at  the  end  of  the  arm  ;  first 
pull  the  arm  upward  through  an  arc  of  about  3°  either  side  of 
its  central  position,  moving  it  very  slowly  and  gradually :  the 
reading  will  be  the  weight  plus  the  friction.  Then  let  it  back 
through  the  same  arc  very  slowly  and  gradually,  and  the  read- 
ing will  be  the  weight  less  the  friction.  The  sum  of  these  two 
results  will  be  twice  the  correction  for  the  brake-arm.  Repeat 
this  three  times  for  an  average  result.  In  case  the  friction  is 
greater  than  the  weight  this  second  result  will  be  negative,  but 
the  method  will  remain  the  same. 

The  weight  of  the  brake,  as  generally  mounted,  is  carried 
on  the  main  bearings  of  the  wheel,  from  which  the  power  is 
obtained,  and  virtually  increases  its  weight.  This  may  in  some 
instances  increase  perceptibly  the  friction  of  the  journals  of 
the  wheel,  but  is  generally  an  imperceptible  amount.  This 
weight  can  be  reduced  when  desired,  by  a  counterbalance  con- 
nected to  the  brake  by  means  of  guide-pulleys. 

178.  Directions  for  Using  the   Prony   Brake. — i.    See 
that  the  brake-wheel  is  rigidly  fastened  to  the  main  shaft. 
2.   Provide  ample  means  of  lubrication. 


§  l8o.j  MEASUREMENT  OF  POWER.  24$ 

3.  If  the  brake-wheel  has  an  internal  rim,  provide  means 
for  supplying  and  removing  water  from  this  rim. 

4.  Find  the  equivalent  weight  of  brake-arm   to  be  taken 
from   or  added   to   the  load,   depending  on  the  direction  of 
motion  of  the  wheel. 

5.  In    applying   the   load,    tighten    the   brake-strap   \erji 
slowly,  and  give  time  for  the  friction  to  become  constant  be«' 
fore  noting  readings  of  the  result. 

6.  Note  the  time,  number  of  revolutions,  length  of  brake* 
Arm,  corresponding  load,  and  calculate  the  results. 

179.  Pump  Brakes.  —  A  rotary  pump  which  delivers  water 
through  an  orifice  that  can  be  throttled  or  enlarged  at  will,  has 
been  used  with  success  for  absorbing  power. 

If  the  casing  of  the  pump  is  mounted  so  as  to  be  free  to 
revolve,  it  can  be  held  stationary  by  a  weighted  arm,  and  the 
absorbed  power  measured,  as  in  the  case  of  the  Prony  brake. 
If  the  casing  of  the  pump  is  stationary,  the  work  done  can  be 
measured  by  the  weight  of  water  discharged  multiplied  by  the 
height  due  to  the  greatest  velocity  of  its  particles  multiplied 
by  a  coefficient  to  be  determined  by  trial.* 

A  special  form  of  the  pump-brake,  with  casing  mounted  so 
that  it  is  free  to  revolve,  has  been  used  with  success  on  the 
Owens  College  experimental  engine  by  Osborne  Reynolds. 
In  this  case  the  brake  is  practically  an  inverted  turbine,  the 
wheel  delivering  water  to  the  guides  so  as  to  produce  the 
maximum  resistance.  The  water  forced  through  the  guides 
at  one  point  is  discharged  so  as  to  oppose  the  motion  Df  the 
wheel  at  anothei  point. 

180.  Fan-brakes.  —  A  fan  or  wheel  with  vanes  revolved  in 
water,  oil,  or  air  will  absorb  work,  and  in  many  instances  forms 
a  valuable  absorption-dynamometer. 

The  resistance  to  be  obtained  from  a  fan-brake  is  expressed 
by  the  formula  f 


*  See  Rankine,  Machinery  and  Mill-work,  page  404. 
\  Ibid.,  page  406. 


246 


EXPERIMENTAL   ENGINEERING, 


in  which  ^/equals  the  moment 
of  resistance,  V  the  velocity  in 
feet  per  second  of  the  centre 
of  vane,  A  the  area  of  the  vane 
in  square  feet.  /  equals  the 
distance  from  centre  of  vane 
to  axis  in  feet,  D  the  weight 
per  cubic  foot,  of  fluid  in  which 
the  vane  moves,  K  a  coefficient, 
found  by  experiment  by  Pon- 
celet  to  have  the  value 


A*  =1.254 


1.62441/3" 


n  which  s  is  the  distance  in 
feet  from  the  centre  of  the 
entire  vane  to  the  centre  of 
':hat  half  nearest  the  axis. 
iVhen  set  at  an  angle  i  with 
the  direction  of  motion  the 
value  for  Rl  must  be  multi- 


plied  by 


2  sin 

:  —  r-  5 
sma 


181.  Traction-dynamome- 
ters. —  Dynamometers  for  sim- 
ple traction  or  pulling  are 
usually  constructed  as  in  Fig. 
126.  Stress  is  applied  at  the 
two  ends  of  the  spring,  which 
rotates  a  hand  in  proportion 
to  the  force  exerted. 


FIG.  146. — DYNAMOMETER  FOR  TRACTION. 


§  183.]  MEASUREMENT  OF  POWER.  247 

Recording  Traction-dynamometers. — These  are  constructed 
in  various  forms.  Fig.  127  shows  a  simple  form  of  a  recording 
traction-dynamometer,  designed  by  C.  M.  Giddings.  Paper  is 
placed  on  the  reel  A,  which  is  operated  by  clock-work;  a 
pencil  is  connected  at  K  to  the  band,  and  this  draws  a  diagramv 
as  shown  in  Fig.  128,  the  ordinates  of  which  represent  pounds 


500  — 


Olbsr 


FIG.  128.— DIAGRAM  FROM  TRACTION-DYNAMOMETER. 


of  pull,  the  abscissae  the  time.  The  drum  may  be  arranged 
to  be  operated  by  a  wheel  in  contact  with  the  ground  :  then  the 
abscissa  will  be  proportional  to  the  space,  and  the  area  of  the 
diagram  will  represent  work  done. 

182.  General  Types  of  Transmission-dynamometers.* 
— Transmission-dynamometers  are  of  different  types,  the  ob- 
ject   in    each   case   being   to    measure   the   power   which   is 
received  without  absorbing  any  greater  portion  than  is  neces- 
sary to  move  the  dynamometer.     They  all  consist  of  a  set  of 
pulleys  or  gear-wheels,  so  arranged  that  they  may  be  placed 
between  the  prime  movers  and  machinery  to  be  driven,  while 
the  power  that  is  transmitted  is  generally  measured  by  the 
flexure  of  springs  or  by  the  tendency  to  rotate  a  set  of  gears, 
which  may  be  resisted  by  a  lever. 

183.  Morin's  Rotation-dynamometer. — In    Morin's   dy- 
namometer, which  is  shown  in  Fig.  129,  the  power  is  trans- 
mitted  through   springs,   FG,  which   are   thereby   flexed    an 
amount  proportional  to  the  power.     The  flexure  of  the  springs 
is  recorded  on  paper  by  a  pencil  z  fastened  to  the  rim  of  the 

*  See  Thurston's  Engine   and    Boiler   Trials,   page   264 ;   also  Weisbach'9 
Mechanics,  Vol.  II.,  pages  39-73  ;  also  Rankine's  Steam-engine,  page  42. 


248 


EXPERIMENTAL  ENGINEERING. 


wheel.  A  second  pencil  is  stationary  with  reference  to  the 
frame  carrying  the  paper.  The  paper  is  made  to  pass  under 
the  pencil  by  means  of  clock-work  driven  by  the  shafting, 
which  can  be  engaged  or  disengaged  at  any  instant  by  operating 
the  lever  R.  The  springs  are  fastened  at  one  end  rigidly  to 
the  main  axle,  which  is  in  communication  with  the  prime 
mover,  and  at  the  other  end  to  the  rim  of  the  pulley,  which 
otherwise  is  free  to  turn  on  the  main  shaft.  The  power  is 
taken  from  this  last  pulley,  and  this  force  acts  to  bend  the 


FIG.  129-^MoRiN  ROTATION-DYNAMOMETERS. 


springs  as  already  described.     In  the  figure  A  is  a  loose  pulley 
B  is  fixed  to  the  shaft. 

The  autographic  recording  apparatus  of  the  Morin  dyna- 
mometer consists  essentially  of  a  drum,  which  is  rotated  by 
means  of  a  worm-gear,  UK,  cut  on  a  sleeve,  which  is  concentric 
with  the  main  axis.  This  sleeve  slides  longitudinally  on  the 
axis,  and  may  be  engaged  with  or  disengaged  from  the  frame  at 
any  instant  by  means  of  a  lever.  When  this  sleeve  is  engaged 
with  the  frame  and  made  stationary  the  recording  apparatus 
is  put  in  motion  by  the  concentric  motion  of  the  gearing,  SV, 
with  respect  to  the  axis.  The  pencil  attached  to  the  spring 
will  at  this  instant  trace  a/  diagram  on  the  paper  whose  ordi- 


§  184.]  MEASUREMENT  OF  POWER.  249 

nates  are  proportional  to  the  force  transmitted.  The  rate  of 
rotation  of  the  drums  carrying  the  paper,  with  respect  to  the 
main  axis,  is  determined  in  the  same  manner  as  though  the 
gears  were  at  rest — by  finding  the  ratios  of  the  radii  of  the 
respective  wheels.  Thus  the  amount  of  paper  which  passes 
off  from  one  drum  on  to  the  other  can  be  proportioned  to  the 
space  passed  through,  so  that  the  area  of  the  diagram  may  be 
proportional  to  the  work  transmitted. 

To  find  the  value  of  the  ordinates  in  pounds  the  dyna- 
mometer must  be  calibrated  ;•  this  may  be  done  by  a  dead  pull 
of  a  given  weight  against  the  springs,  thus  obtaining  the 
deflections  for  a  given  force ;  or,  better,  connect  a  Prony  brake 
directly  to  the  rim  of  the  fixed  pulley  B,  and  make  a  series  of 
runs  with  different  loads  on  the  brake,  and  find  the  correspond- 
ing  values  of  the  ordinates  of  the  card. 

184.  Calibration  of  the  Morin  Dynamometer. — Appara- 
tus. — Speed-indicator,  dynamometer-paper,  and  Prony  brake. 

1.  Fasten  paper  on  the  receiving  drum,  wind  off  enough 
to  pass  over  the  recording  drum,  and  fasten  the  end  securely 
to  the  winding  drum.     See  that  the  gears  for  the  autographic 
apparatus  are  in  perfect   order,  and  that  both  pencils  give 
legible  lines.     Adjust  the  pencil  fixed  to  the  frame  of  the 
clock-work,  so  that  it  will  draw  the  same  line  as  the  movable 
pencil,  when  no  load  is  applied. 

2.  With  the  apparatus  out  of  gear  apply  the  power.     Take 
a  card  with  no  load.    This  card  will  be  the  friction  work  of 
the  dynamometer. 

3.  Apply  power  and  load,  take  cards  at   intervals:  these 
cards  will  represent  the  total  work  done.     This,  less  the  fric- 
tion work,  will  be   the  power  transmitted.     The  line  traced 
by  the  pencil  affixed  to  the  frame  of  the  clock-work  must  in 
all  cases  be  considered  the  zero-line,  or  line  of  no  work. 

4.  To  calibrate  the  dynamometer,  attach  a  Prony  brake  to 
the  same  shaft  and  absorb  the  work  transmitted.     This  trans- 
mitted work   must   equal   that   shown   by  the  Prony  brake. 
Find  constants  of  brake  as  explained  Article  177,  page  211. 

5.  Draw  a  calibration-curve,  with  pounds  on  a  brake-arm, 


-- 


EXPERIMENTAL 


[§186. 


reduced  to  an  equivalent  amount  acting  at  a  distance  equal  to 
the  radius  of  the  driving-pulley  of  the  dynamometer,  as 
abscissae,  and  with  ordinate  of  the  diagram  as  ordinate. 
Work  up  the  equation  of  this  curve. 

<x  In  report  of  calibration  make  record  of  time,  number  o! 
revolutions  brake-arm,  equivalent  brake-load  for  arm  equal  to 
radius  of  dynamometer-pulley,  length  of  ordinate,  scale  o' 
ordinate.  Describe  the  apparatus. 

7.  In  using  it,  insert  it  between  the  prime  mover  and  re- 
ststance  to  be  measured.  Deteonine  the  power  transmitted 
from  the  calibration. 

185.  Form  of  Report— The  following  form  is  useful  in 
calibrating  this  dynamometer* 


CALIBRATION  OF  MORIN  DYNAMOMETER. 


Kind  of  brake  used 

Weight  of  brake-arm Iba. 

of  driving-pulley. ....... .ft. 


....     Length  of  brake-arm 
Zero-reading  of  scales.... 


..ft. 

.Ibs. 


.189.. 


Ordinate,  Inches. 


Up.      Down.    Mean. 


Bnta 

K.  P. 


EquatJonof  Curve, 


X  = 


1861  Steelyard-dynamometer. — In  this  dynamometei  the 
pressure  of  the  axle  of  a  revolving  shaft  is  determined  by 
shifting  die  weight  G  on  the  graduated  scale-beam  AC. 

The  power  is  applied  at  P,  putting  in  motion  the  train  of 
gear-wheels,  and  is  delivered  at  Q. 

Denote  the  applied  force  by  P,  the  delivered  force  by  Q 


I  1  86.]  MEASUREMENT  OP  POWER. 

the  radios  KM  by  a,  KE  by  r,  LF  by  r,,  JV£  by  &  the  force 
delivered  atEbyfi,  that  at  ^"by  R+ 
We  shall  have 

Rr  =  Pa,    also 
But 


and  since  ED  =  FD, 

R  =  R>. 

The  resultant  force  Z=  R+  R^ 


If  we  know  the  number  of  revolutions,  the  space  passed 
through  by  each  force  can  be  readily  calculated,  and  the  work 
found  by  taking  the  product  of  the  force  into  the  space 
passed  through. 


Consideration  of  Friction.— The  friction  of  the  axle  and 
gear-teeth  will  increase  the  force  ^  and  decrease  the  force  R+ 
Let  ;*  be  the  experimental  coefficient  expressing  this  friction, 


Then 


Par,  -  Qbr 


252 


EXPERIMENTAL  ENGINEERING. 


[§  1 88 


187.  Pillow-block  Dynamometer.  —  The  pillow-block  dy. 
namometer  operates  on  the  same  principle  as  the  steelyard 

dynamometer,  but  no  intermediate 
wheel  is  used.  This  dynamometer, 
shown  in  Fig.  131,  consists  of  the 
fixed  shaft  Lt  which  is  rotated  by 
the  power  Q  applied  at  N.  The 
power  rotates  the  gear-wheel  ELt 
which  communicates  motion  to  the 
wheel  KE  on  the  same  shaft  with 
the  wheel  KM.  This  shaft  is  sup 
ported  on  a  pair  of  weighing-scales  so  that  the  downward  force 
Z  acting  on  the  bearing  can  be  weighed.  Let  P  equal  the 
force  delivered,  let  a  equal  the  angle  this  force  makes  with  the 
horizontal,  let  KM  equal  a  and  KE  equal  r  ,  G  equal  the  weight 
of  shaft  and  wheel  The  weight  on  the  pillow-block  at  K 
must  be 


FIG.  131.— PILLOW-BLOCK  DYNA 

AIOMETER. 


Z=G  +  P*in 
Fran  which 


a 


Z-G 

sin  a  -) 


When  the  belt  is  horizontal, 


a=&0    and    />=(£—£)-. 

188.  The  Lewis  Dynamometer.* — This  transmission-dy 
namometer  is  a  modified  form  of  the  pillow-block  dyna- 
mometer, arranged  in  such  a  manner  that  the  friction  of  the 
gearing  or  journals  will  not  affect  the  reading  on  the  weighing, 
scales.  This  dynamometer  is  shown  in  Fig.  1 32 ,  and  also  in  Fig. 
139,  Article  195,  page  265.  The  dynamometer  consists  of  two 


*See  Voi,  VII.,  page  276,  Trans.  Am.  Society  Mechanical  Engineers. 


1 88.] 


MEASUREMENT  OF  POWER. 


253. 


^-ear-wheels  A  and  Ct  whose  pitch-circles  are  tangent  at  B\ 
the  gear-wheel  A  is  carried  by  the  fixed  frame  T,  the  wheel  Cls 
carried  on  the  lever  BD :  the  lever  BD  is  connected  to  the 
sixed  frame  T  by  a  thin  steel  fulcrum,  as  used  in  the  Emery 
Testing-machines  (Article  67,  page  105).  The  point  D,  the 
centre  of  wheel  C9  and  the  fulcrum  are  in  the  same  right  line. 
The  fulcrum  B  permits  vertical  motion  only  of  the  point  D. 
The  point  D  rests  on  a  pillar,  which  in  turn  is  supported  by 
a  pair  of  scales.  The  shaft  leading  from  the  wheel  C  is  fur- 
nished  with  a  universal  joint  (see  Fig.  139),  so  that  its  weight 
does  not  affect  that  on  the  journal  C.  In  Fig.  132,  A  is  the 


FIG.  132.— THE  LEWIS  DYNAMOMBTBS. 

driving  and  C  the  driven  wheel,  the  force  to  be  measured  being 
received  on  a  pulley  on  the  shaft  a,  transmitted  through  the 
dynamometer,  and  delivered  from  a  pulley  on  the  shaft  c, 
From  this  construction  it  follows,  that  no  matter  how  great 
the  friction  on  the  journals  of  the  shaft  c,  there  will  be  no 
pressure  at  the  point  D  except  what  results  from  torsio» 
of  the  shaft  c.  This  will  be  readily  seen  by  considering: 

1.  That  any  downward  force  acting  at  B  will  be  resisted  by 
the  fixed  frame   T,  and  will  not  increase  the  pressure  at  D. 

2.  A  downward  force  acting  on  the  lever  between  B  and  D 
will  produce  a  pressure  proportional  to  its  distance  from  B. 

3.  If  the  driven  wheel  C  were  firmly  clamped  to  its  frame,  no 
force  acting  at  B  would  change  the  pressure  at  D ;  and  since 


254  EXPERIMENTAL  ENGINEERING.  |_§ 

journal-friction  would  have  the  effect  of  partially  clamping  the 
wheel  to  the  journal  c,  it  would  have  no  effect  on  the  scale- 
reading  at  D. 

Denote  the  transmitted  torsional  force  by  Z;  the  radius  of 
the  driven  pulley  by  r  ;  the  length  of  lever  BD  by  a  ;  the  scale- 
reading  at  D  by  W.  Then  from  equality  of  moments 


The  effective  lever-arm  BD  is  to  be  obtained  experimen- 
tally as  follows  :  Disconnect  the  universal  joint,  shown  in  Fig. 
108,  so  as  to  leave  the  wheel  C,  free  to  turn  ;  block  the  driving- 
pulley  A  ;  fasten  a  horizontal  arm,  ^/"(dotted  lines,  Fig.  101), 
to  the  shaft  c,  parallel  to  the  line  DB  and  carrying  a  weight 
G  ;  balance  the  scales  in  this  position,  then  move  the  weight 
out  on  the  lever,  until  the  reading  of  the  scales  is  increased  an 
amount  equal  to  the  weight  moved.  The  distance  moved  by 
the  weight  will  equal  length  of  the  lever  DB. 

Thus  let  ef,  shown  in  dotted  lines,  represent  the  lever 
clamped  to  the  axis  c  ;  let  e  represent  the  first  position  of  the 
weight  Gt  and  /the  second  position;  let  Wand  W  represent 
the  corresponding  scale-readings,  after  balancing  scales  without 
G  on  the  lever,  ef. 

Then  we  have 


G  =  W  = 
Hence 


Then  will 

DB  =  ef. 


§  189.]  MEASUREMENT  OF  POWER.  255 

189.  The  Differential  Dynamometer. — This  is  often 
called  the  Bachelder,  Francis,  or  Webber  dynamometer ;  was 
invented  by  Samuel  White,  of  England,  in  1780,  and  brought 
to  this  country  by  Mr.  Bachelder  in  1836. 

The  dynamometer  portion  consists  of  four  bevel-gears, 
shown  in  plan  in  Fig.  133. 

Power  is  applied  to  the  pulley  M,  which  carries  the  bevel- 
x 


FIG.  133.— THE  DIFFERENTIAL  DYNAMOMETER. 

wheel  EEj ;  the  resistance  is  overcome  by  the  pulley  Nt  which 
carries  the  bevel-wheel  FFl .  Both  wheels  run  loosely  upon 
the  fixed  shaft  XXlt  and  are  connected  by  the  wheels  EFand 
E^F^ .  By  the  action  of  the  force  P  and  the  resistance  (2,  the 
pressure  of  the  wheels  EEl  and  FF^  is  downward  at  E  and  /% 
and  upward  at  El  and  Fl ,  tending  to  swing  the  lever  GGl 
around  the  axis  XX^ ,  one  half  as  fast  as  the  pulley  M.  The 
weight  which  holds  the  lever-arm  stationary,  multiplied  by  the 
space  it  would  pass  through  if  free  to  move,  is  the  measure  of 
the  work  of  the  force  P.  A  dashpot  is  usually  attached  to  the 
lever  GGl  at  Gl ,  to  lessen  vibrations  and  act  as  a  counterbal- 
ance. Let  Z  equal  the  vertical  force  acting  at  B  and  Bl ;  R, 
the  vertical  pressure  between  the  teeth  at  each  point  of  con^ 
tact ;  b,  the  distance  of  B  and  Bl  from  the  centre  C\  a,  the 
distance,  AC,  to  the  weight. 
Then  we  have  evidently 

2Z  =  4#,     or    Z  =  2R ; 
also 

Ga  =  2Zb  = 


256  EXPERIMENTAL   ENGINEERING.  [§ 

If  a'  is  the  radius  of  the  driving-pulley  M,  and  r  the  radius 
of  each  bevel-gear, 

2Rr      G  r  a 

Pa'  =  2Rr,     or     P  =  -—  =  —  r  -7. 
a'         2  b  a' 

If  friction  is  considered, 


The  mechanical  work  received  is  equal  to  /'multiplied  by 
the  space  passed  through  in  the  given  time. 

This  instrument  has  been  improved  by  Mr.  S.  Webber,  as 
shown  in  Fig.  134. 


FIG.  134.— THE  WEBBER  DYNAMOMETER. 

These  dynamometers  are  used  in  substantially  the  same 
way  as  the  Morin  dynamometers. 

190.   Calibration  of  the   Differential   Dynamometer. — 

I.  See  that  it  is  well  oiled,  in  good  condition,  its  axis  horizon- 
tal, and  also  that  the  weighing  arm  is  horizontal  for  no  load. 

2.  Observe  constants  of  the  apparatus ;  obtain  weight  of 
small  poise*  of  large  poise;  of  amount  to  balance  beam  We. 
Measure  the  arm  of  each,  and  calculate  the  foot-pounds  per 
IOO  revolutions  corresponding  to  weights  and  graduations. 


MEASUREMENT  OF  POWER. 

3.  Make  a  preliminary  run  without   load,  and   note   the 
reading  of  the  poise  required  to  balance  the  arm.     This  will 
determine   the   friction    of  the   dynamometer   without    load. 
Determine  the  length  of  the  arm,  and  the  value  of  each  sub- 
division in  foot-pounds. 

4.  Attach  a  strap-brake  (see  Art.  169,  p.  239)  to  the  delivery 
pulley  of  the  dynamometer,  and  absorb  all  the  force  trans- 
mitted.    Make  a  series  of  ten  runs,  each  ten  minutes  in  length, 
and  during  each  of  which  the  load  on  the  Prony  brake-arm  is 
kept  as  constant  as  possible,  but  which  is  increased  by  equal 
increments,  in  the  different   runs.     Take   observations  each 
minute  during  the  run. 

5.  The  difference  between  the  work  absorbed  by  the  brake 
and  that  shown  by  the  dynamometer  should  be  carefully  de- 
termined.    It  is  the  error  of  the  dynamometer. 

6.  Note  whether  this  error  is  a  constant  quantity,  or  is  a 
percentage  of  the  work  delivered. 

7.  In  your  report,  describe  the  apparatus,  give  the  results 
of  the  calibration,  and  draw  a  curve,  using  brake  foot-pounds 
as  ordinates,  and  dynamometer  foot-pounds  as  abscissae. 

8.  To  use  the  dynamometer  insert  it  between  the  prime 
mover  and  the  machinery  to  be  run. 

Special  Directions  for  Calibrating  the  Webber  Differential 

Dynamometer. 
Apparatus  required : 

I.  Ten  small  tension-weights.     2.  Spring-balance  or  plat- 
form-scales.   3.  Measuring-scale.    4.  Calipers.    5.  Stop-watch. 
Measurements  : 

a.  Weight  of  small  tension-weights. 

b.  "         "  fixed  poise-weights. 

c.  "        "  dynamometer-arm. 

d.  "        "  sliding  poise. 

e.  Length  of  dynamometer-arm  to  fixed  poise. 
/.  Length  of  dynamometer-arm  to  sliding  poise. 
g.  Diameter  of  brake-pulley. 

k.  Thickness  of  brake-strap. 


258 


EXPERIMENTAL   ENGINEERING. 


[ 


I.  Friction-run. — Remove   brake.     Find  time,   in  seconds, 
of  IOOO  revolutions  (10  rings  of  bell).     Balance  dynamometer, 
arm  ;  the  reading  is  the  "  zero-reading"  by  the  beam,  and  must 
be  corrected  to  get  the  true  friction-reading. 

II.  Test-runs. — Put   on    brake ;    hang   one   weight   on    its 
slack  side.     Time,  IOOO  revs.     Read  simultaneously  dynamom- 
eter-arm and  platform  jcales.     Repeat  the  same  with  succes- 
sive weights  added. 

III.  To  Weigh  Dynamometer-arm. — Run  by  hand,  first  for- 
ward and  then   backward,  weighing  in  each  case  the  turning 
effect,  with  the  platform-scale  applied  at  the  knife-edge  of  the 
dynamometer-arm,  and  sliding-poise  set  at  the  zero-mark. 

191.  Form  of  Report. — The  following  blank  is  used  in  the 
exercises  with  the  differential  dynamometer  in  Sibley  College : 

MECHANICAL  LABORATORY,  SIBLEY   COLLEGE,  CORNELL   UNI- 

VERSITY. 

Calibration  of Differential  Dynamometer. 

Kind  of  Brake  used 

Length  of  Brake-arm ft.     Weight  of  Brake-arm Ibs. 

Zero-reading  of  Brake-scales Ibs. 

Date., 189. .     Observers- 


Number. 

Time  of  100  Revolutions' 
Seconds. 

Brake-tensions,  Lbs. 

Work  in  ft.-lbs.  per  100  Revolutions. 

Brake  Horse-power. 

Tight  Side. 

Slack  Side. 

Effective  Load.^ 

Dynamometer-readings. 

Obtained  from 
Brake. 

Error  of  the 
Dynamometer. 

Observed  on 
Dynamome- 
ter-beam. 

Calculated 
from 
Machine 
Constants. 

Transmitted 
as  shown  by 
Beam,  =  Wt 

?! 

T9 

T-j-T, 

wd 

»i 

wd-w^ 

»"» 

Wt-W 

D.H.P. 

I 
2 

3 

4 

•6 

I 

9 

10 

I93-J 


MEASUREMENT  OF  POWER. 
CONSTANTS   OF   MACHINE. 


259 


Moment  i 

^rm....ft. 

Sliding 
Weight 

I  Poise, 
....Ibs. 

Loads  at  Knife-edge. 

Weight, 
Ibs. 

Value,  ft.- 
Ibs.  per 
100  Revs. 

Moment 
Arm, 
Feet. 

Value,  ft.. 
Ibs.  per 
100  Revs. 

First  Notch  

Last  Notch  

Dynamometer-beam 

...~We 

Increase  per  Notch. 

= Zero-reading  by  Beam ft.-lbs. 


. .  .ft.-lbs. 


192.  Emerson's  Power-scale. — One  of  the  most  complete 
transmission-dynamometers  is  shown  in  Fig.  135,  with  attached 
numbers  showing  the  dimensions  of  the  various  sizes  manu- 
factured.    In  this  instrument  the  wheel  C  is  keyed  or  fastened 
to  the  shaft ;  the  wheel  B  is  connected  with  the  wheel  C  near 
its  outer  circumference  by  projecting  studs;  the  amount  of 
pressure  on  these  studs  is  conveyed  by  bent  levers  to  a  collar, 
which  in  turn  is  connected  with  weighing-levers.   Small  weights 
are  read  off  from  the  scale  D,  and  larger  ones  by  the  weights 
in  the  scale-pan  N.     A  dash-pot  is  used  to  prevent  sudden 
fluctuations  of  the  weighing-lever. 

193.  Form  of  Report. — The   following  forms  for  report 
and  log  of  tests   on  Webber   Dynamometer  and   Emerson's 
Power-scale  are  used  by  the  Massachusetts  Institute  of  Tech- 
nology. 


REPORT. 


Test  on., 


No. 


Date. 


No.  of  test 

Ft.-lbs.  per seconds 


WEBBER  DYNAMOMETER. 
X 


.'. I. 


No.  of  test 

Duration  of  test 

Revolutions  per  minute.. 
Load 


EMERSON  POWER-SCALE. 

I 


260 


EXPERIMENTAL   ENGINEERING. 


[8 


FIG.  135 —EMERSON'S  POWER-SCALE!*. 


I94-] 


MEASUREMENT  OF  POWER. 


26l 


BRAKE. 


I 

2 

c 

i 

2 

q 

1-2 

I_o        2—3 

_ 

H.  P.  bv  brake..                       

LOG. 

No.. 

Date.   . 

1 

•3 
1 

Webber  Dynamometer. 

Emerson  Power-scale. 

Brake. 

\ 

H 

Time  of 
Revolutions. 

Ft.-lbs.  per 
Revolutions. 

i 

H 

Readings  of  Counter. 

Revolutions  per 
Minute. 

' 

I 
H 

Readings  of  Counter. 

oj 
3 
g 

i 

s, 

i 

.2 
^ 

rt 

Test  Number  i. 

Test  nu 

H.  P.  b 
H.  P.  b 
H.  P.  b 

I 

2 

3 

1-2 

i-3 

2-3 

y  dynamo 
y  power-s< 
y  brake.  .  . 

:ale  

Constants  and  Remarks. 


194.  The  Van  Winkle  Power-meter. — The  Van  Winkle 
Power-meter  is  shown  in  Fig.  136,  complete,  and  with  its  parts 


262 


EXPERIMENTAL   ENGINEERING. 


[§.  194. 


separated,  in  Fig.  137.  It  consists  of  a  sleeve  with  attached 
plate,  B,  that  can  be  fastened  rigidly  to  the  shaft;  and  a 
plate,  *4,  which  is  revolved  by  the  force  communicated  through 


36. —  TAN  WINKLE  POWER-METER. 


the  springs  s s.  The  angular  position  of  the  plate  A  with  refer- 
ence to  B  will  vary  with  the  force  transmitted.  This  angular 
motiim  is  utilized  to  operate  levers,  and  move  a  loose  sleeve 


FIG.  137.— PARTS  OF  THE  VAN  WINKLE  POWER-METER. 

longitudinally  on  the  shaft.  The  amount  of  motion  of  the 
sleeve,  which  is  proportional  to  the  force  transmitted,  is  indi- 
cated by  a  hand  moving  over  a  graduated  dial.  The  dial  is 
graduated  to  show  horse-power  per  100  revolutions. 


MEASUREMENT  OF  POWER. 


263 


195.  Belt-dynamometers.— Belts  ha-e  been  used  in  some 
instances   instead  of   gearing   in    transmission-dynamometers, 
but  because  of  the  great  loss  of  power  due  to  stiffness  of  the 
belts,  and  to  the  uncertainty  caused 
by   slipping,  they  have   not   been 
extensively  used.      The   following 
form,   from    Church's    "  Mechanics 
of  Materials,"  is  probably  as  suc- 
cessful as   any  that   has   been  de- 
vised.     It    consists   of    a   vertical 
plate,  carrying  four  pulleys  and  a 
scale-pan,   as   shown    in    Fig.    138. 
The   scale-beam    is    balanced,   the 

belt  then  adjusted,  and  power  turned  on  ;  a  sufficient  weight, 
G,  is  placed  in  the  scale-pan  to  balance  the  plate  again.  Let 
b  be  the  arm  of  the  scale-pan,  and  a  that  of  the  forces  P  and 
P'.  Then,  for  equilibrium, 


FIG.  138. — A  BELT-DYNAMOMETER. 


(i) 


since  P  and  P'  on  the  right  have  no  leverage  about  C,  as  the 
line  of  the  belts  produced  intersects  C.    From  (i) 


(2) 


The  work  transmitted  in  foot-pounds  per  minute  is  equal 
to  (P  —  P')vt  in  which  v  is  the  velocity  of  the  belt  in  feet  per 
minute  to  be  obtained  by  counting.  Another  form  employs 
two  quarter-twist  belts  to  revolve  a  shaft  at  right  angles  to  the 
main  shaft.  (See  Vol.  XII.,  Transactions  Am.  Soc.  Mechan- 
ical Engineers.) 

196.  Method  of  Testing  Belts.* — The  object  of  this  test 
is  to  determine  the  coefficient  of  friction,  and  the  power  trans- 
mitted by  various  kinds  of  belting  running  under  different 
conditions. 


264  EXPERIMENTAL  ENGINEERING.  [§  IQ7- 

The  required  formulae  are  given  in  Article  128,  page  199, 
as  follows  :  7",  ,  maximum  tension  ;  7a  ,  minimum  tension  ;  Ft 
the  force  of  friction  ;  c,  the  percentage  of  arc  of  contact  to 
whole  circumference  ;  0,  the  arc  of  contact  in  circular  measure 
We  have 


T 


T 

Common  log  -~  =  0434/0  =  2.7288/2;. 
•*» 


From  which 


or 

/=  Napierian  log  1-^ 


Belt-testing  machines  must  be  arranged  so  that  measures 
of  Tlt  T9,  0,  and  c  can  be  made.  To  determine  loss  due  to 
resistance,  it  is  necessary  to  supply  the  power  by  a  transmis- 
sion-dynamometer, and  absorb  that  delivered  by  a  brake. 

197.  The  Sibley  College  Belt-testing  Machine.—  The 
belt-testing  machine  illustrated  in  Fig.  139  is  used  in  the 
Mechanical  Laboratory  of  Sibley  College.  It  was  designed  by 
Wilfred  Lewis  of  Philadelphia,  and  used  in  the  tests  described 
in  Vol.  VII.  of  Transactions  of  American  Society  of  Mechanical 
Engineers. 

The  belt  to  be  tested  is  placed  on  the  pulleys  E,  F\  power  is 
transmitted  through  the  pulleys  P  to  the  Lewis  transmitting- 

*  The  student  is  referred  to  papers  in  Transactions  of  American  Society  of 
Mechanical  Engineers,  Vol.  VII.,  by  Wilfred  Lewis  and  Prof.  G.  Lanza;  also 
to  paper  in  Vol.  XII.,  by  Prof.  G.  Alden  ;  and  to  the  Holman  tests  in  the  Join 
nal  of  the  Franklin  Institute,  1885. 


i  w 


MEASUREMENT  OF  POWER. 


265 


266  EXPERIMENTAL  ENGINEERING.  [§  198. 

dynamometer  (see  Article  188,  page  252),  and  thence  through 
the  shaft  //"to  the  pulley  E.  The  power  transmitted  is  absorbed 
by  a  Prony  brake  on  the  shaft  M.  The  slip  of  the  belt  is 
measured  by  transmitting  the  motion  of  the  pulley  E  by  gearing 
to  the  shaft  /,  and  thence  to  a  disk  S,  whose  edge  is  graduated. 
The  pulley  F  is  connected  to  the  gear-wheel  Z,  shown  in  a 
larger  scale  in  centre  of  Fig.  96.  The  wheel  L  is  so  proportioned 
that  if  there  is  no  slip  it  will  revolve  at  the  same  rate  as  the 
disk  S\  if  there  is  slip  it  will  fall  behind  5.  The  amount  that 
it  falls  behind  is  read  by  the  scale  V,  which  may  be  clamped 
to  the  hub  of  L  by  the  screw  T.  As  this  device  moves  only 
one  one-hundredth  as  fast  as  the  main  shafts,  the  amount  of 
slip  can  be  easily  read.  The  pulley  F  and  the  brake  M  are 
mounted  on  a  carriage,  which  can  be  drawn  back  by  the  screw 
N.  The  pulley  E  is  mounted  in  a  frame,  supported  on  knife- 
edges  below,  R.  The  shaft  H  is  fitted  with  a  universal  joint, 
to  eliminate  the  effect  of  transverse  strains  on  the  dynamom- 
eter. 

Weighing-scales  are  placed  at  A,  By  and  C,  respectively, 
that  at  A  is  termed  the  dynamometer-scales ;  that  at  B,  the  brake- 
scales  that  at  C,  the  tension-scales.  The  reading  on  the  tension- 
scales  C,  multiplied  by  the  horizontal  arm  K,  divided  by  the 
height  d  of  the  pulley  E  upon  the  knife-edge,  gives  the  total 
tension  on  the  belts  7",  -f-  7"2.  The  reading  on  brake-scales 
B,  divided  by  the  arm  b  of  the  brake,  and  multiplied  by  the 
radius  D  of  the  pulley  F,  gives  the  difference  of  tensions 
Tt—T9.  The  brake-scale  reading,  multiplied  by  the  brake-arm 
£,'and  by  27rn,  n  being  the  number  of  revolutions,  gives  tht 
delivered  work  in  foot-pounds.  The  dynamometer  scale-read- 
ing A,  multiplied  by  the  equivalent  dynamometer-arm  a  and 
by  27TW,  gives  the  work  received  in  foot-pounds.  The  dyna- 
mometer-arm a  is  to  be  found  as  described  in  Article  188, 
page  2 5 3. 

198.  Directions  for  Belt-test. 

I.  Before  starting: 

(a)  Get  speed-indicator  and  log-blanks. 

(b}  Oil  all  bearings  and  loose  pulley  under  main  belt. 


§  108.]  MEASUREMENT  OF  POWER.  26? 

(c)  Balance   scales  A  and   C,  and  note  their   "zero- 
readings." 

2.  With  test-belt  off : 

(d)  Take  friction-reading  on  scales  A  for  driving-shaft, 
counting  its  revolutions. 

(e)  Weigh    brake-arm   (see   note  below)  to   get  zero- 
reading  of  scale  B  and  then  remove  brake  from  brake-pulley. 

3.  With  brake  off : 

(/)  Put  on  test-belt  (while  loose),  first  moving  brake- 
shaft  frame  by  unscrewing  hand-wheel  next  the  floor.  Tighten 
belt  to  read  while  at  rest  75  Ibs.  net,  on  scales  C. 

(<£")  Take  friction-reading  again  on  scales  A.  Count 
revolutions  of  driving-shaft  and  read  "  per  cent  of  slip,"  from 
which  the  speed  of  brake-shaft  can  be  calculated. 

4.  Run  I. 

(/i)  For  tension  of  belt :  Set  scales  C  to  read  50  Ibs.  net 
with  belt  at  rest,  by  screwing  up  hand-wheel  next  the  floor, 
which  should  not  be  changed  during  the  run. .  Take  reading 
of  scales  C  for  each  load  added  on  brake-scales  B. 

(i)  For  power  given  out  by  belt :  Set  scales  B  to  read  5 
Ibs.  "  net "  or  effective  "  load,"  and  balance  by  tightening 
brake  while  running.  Feed  a  light  stream  of  water  into  rim 
of  brake-pulley.  Count  its  revolutions. 

(k)  For  power  put  into  .belt  :  Read  scales  A  and  take 
speed  of  driving-shaft. 

(/)  For  slip  of  belt :  Read  graduated  "  slip-disk/*  which 
has  100  equal  divisions.  When  vernier  is  set,  it  turns  with  the 
disk,  and  shows  one  per  cent  of  slip  when  falling  back  one 
division  during  one  turn  of  the  slip-disk. 

(m)  Thus  continue  to  increase  brake-load  by  5  Ibs.  of 
increments  on  scales  B.  Each  time  keep  it  carefully  balanced, 
and  take  simultaneous  readings  on  scales  A,  scales  ^/scales  Ct 
slip-disk,  and  revolution-counter. 

5.  Runs  II.,  III.,  and  IV. 

(n)  For  run  II.,  set  tension-scales  to  read  75  Ibs.  net 
with  belt  at  rest,  and  proceed  as  in  run  I.  Increase  this  initial 
tension-reading  by  25  Ibs.  each,  for  runs  III.  and  IV. 


268 


EXPERIMENTAL  ENGINEERING. 


6.  Measurement  of  machine-constants : 

(o)  Get  length  in  feet  of  (i)  brake-arm,  (2)  dynamom- 
eter-arm, (3)  arms  of  bell-crank  acting  on  tension-scales,  and 
(4)  circumferences  of  test-belt  pulleys, — latter  with  steel  tape. 
Calculate  diameters. 

(/)  If  the  pulleys  differ  in  diameter,  the  reading  on 
slip-disk,  obtained  while  running  "  light "  (see  (g),  above),  wii! 
be  the  "  zero"  of  all  the  slip-readings. 

N.B.  Shut  off  water  at  brake-pulley  when  it  stops. 

Note. — To  weigh  brake-arm :  Loosen  brake  and  oil  face  of 
pulley.  Balance  arm  on  scales  while  turning  pulley  first  back- 
ward and  again  forward.  The  mean  of  the  two  readings  will 
be  the  weight  required. 

199.  Form  of  Log  and  Reports  as  used  in  Sibley  Col- 
lege. 

Test  of  Belting  by 189 .. 

Description  of  Belt,  Material Made  by 

Length feet.  Width inches.  Thickness inches. 

Condition 


Nuntfier 

4) 

B 

Revolutions, 
Driving  pulley. 

Slip,  per  cent. 

Arc  of  Contact, 
per  cent. 

Scale-readings, 
Ibs. 

i 
* 

a 

Tension  on  Belt, 
Driving  side 

Tension  on  Belt, 
Driven  side. 

Ratio  of  Ten- 
sions. 

Coefficient  of 
Friction. 

Dynamometer, 
Horse-power. 

brake  H.  P.  | 

a 
I, 

P 

1 

Tension. 

n 

-y 

C 

A 

B 

C 

r,-ra 

T-j-r-T^, 

TI 

T9 

Tj-i-T-a 

/ 

I 

2 

3 

4 

5 

6 

8 

II 

' 

12 

13 

14 

15 

16 

17 

IS 

19 

20 

Avg 

1 99.] 


MEASUREMENT  OF  POWER. 
CONSTANTS   OF   MACHINE. 


269 


Symbol. 


Results. 


b 
k 
d 

r> 


Arm  of  transmission-dynamometer 

Arm  of  Prony  brake 

Hor.  arm  on  tension-scales 

Ver.  arm  on  tension-scales 

Diameter  driving  pulley 

Diameter  driven  pulley 

Face  driving  pulley 

Face  driven  pulley 

Area  of  bearings,  driving  wheel  . . . 

"     "          "         driven  wheel.. .. 

Weight  on  bearings,  driving  wheel.. 

"       "         "         driven  wheel .. 

Kind  of  pulley  used 


in 


sq.  in. 
.  Ibs. 


FORM  OF   REPORT. 

Results  of  Test  of Belting. 

Made  by 190.. 


Average  of  Results. 

Test  No. 

Test  No. 
II. 

Test  No. 
III. 

Test  No. 
IV. 

Ti  —  Ti  o  ... 

T^  4-  T* 

CHAPTER   VIII. 

MEASUREMENT  OF  LIQUIDS  AND  GASES. 

200.  Theory  of  the  Flow  of  Water. — General  Formula  of 

Discharge. — The  theory  of  the  flow  of  water  is  fully  investigated 
in  Weisbach's  Mechanics,  Vol.  I.;  in  Church's  Mechanics  of 
Engineering;  and  in  the  article  "  Hydromechanics,"  Encyclo- 
paedia Britannica.  A  very  concise  statement  of  the  principles 
involved  and  formulae  required  are  given  here,  preceding  the 
actual  methods  of  measurement  of  the  flow,  but  students  are  ad- 
vised to  consult  the  foregoing  works.  In  the  flow  of  water  the 
particles  are  urged  onward  by  gravity,  or  an  equivalent  force, 
and  move  with  the  same  velocity  as  bodies  falling  through  a 
height  equal  to  the  head  of  water  exerting  the  pressure.  If 
this  head  be  represented  by  ^,  and  the  corresponding  velocity 
in  feet  per  second  by  vy  we  have,  neglecting  friction  losses, 

v—  V2gk (i) 

If  we  denote  the  area  in  square  feet  of  the  discharge  ori- 
fice by  F,  the  quantity  discharged  in  cubic  feet  per  second  by 
Qy  then,  neglecting  contraction. 

Q  —  vF=F^fTgh (2) 

It  is  found,  however,  in  the  actual  discharge  of  water,  that, 
except  in  rare  cases,  I.  The  actual  velocity  of  discharge  is  less 
,:nan  the  theoretical ;  2.  The  area  of  the  stream  discharged  is 
less  than  the  area  of  the  orifice  through  which  it  passes.  These 
losses  are  corrected  by  introducing  coefficients.  The  coefficient 

270 


§  2OO.]        MEASUREMENT  OF  LIQUIDS  AND   GASES.  2?  I 

of  velocity  is  the  ratio  of  the  actual  to  the  theoretical  velocity, 
and  is  represented  by  cv  .  The  coefficient  of  contraction  is  the  ratio 
of  the  least  area  of  cross-section  of  the  discharged  stre'am  to 
the  area  of  orifice  of  discharge,  and  is  denoted  by  ce.  The 
coefficient  of  efflux  or  discharge  is  the  product  of  these  two 
quantities,  and  is  represented  by  c. 

If  va  denotes  the  actual  velocity  of  discharge,  we  shall  have 


(3) 


The  coefficient  c,  is  to  be  determined  by  experiment ;  it  is 
nearly  constant  for  different  heads  with  well-formed  simple 
orifices.  It  often  has  the  value  0.97.  The  difference  between 
the  velocity  of  discharge  and  that  due  to  the  head  may  be 
expressed  in  terms  of  the  equivalent  loss  of  head.  Thus  the 
total  head  producing  outflow  consists  of  a  part,  haj  producing 
the  actual  velocity  va\  and  a  second  part,  hrj  expended  in 
overcoming  velocity  and  friction.  Denote  the  ratio  of  these 
parts  by  cr .  Then 

&,  =  *A (4) 

We  also  have 

^  =  ^  +  ^  =  ^+1). (5) 

Hence 


Since  ha  is  the  head-producing  velocity, 


2/2  EXPERIMENTAL  ENGINEERING.  [§  2OI. 

By  equating  (7)  and  (3)  we  obtain  the  relation  of  cr  to  c9 
as  follows: 

^  =  4-1  ........    (8) 

*f» 

Tke  actual  discharge 


(9) 
Since  c  ^ 


.    (10) 
From  equation  (9), 

c  -  0.  -J-  Q. 

201.  Formulae  for  Flow  of  Water  over  Weirs.*  —  A  weir 
is  primarily  a  dam  or  obstruction  over  which  the  water  is  made 
to  pass  ;  but  the  term  is  often  applied  to  a  notch  opening  to 
the  air  on  one  side,  through  which  the  water  flows.  In  cases 
where  the  opening  is  entirely  below  the  surface,  it  is  spoken  of 
as  a  submerged  weir.  The  head  of  water  producing  the  flow 
is  the  distance  to  the  surface  of  still  water  from  the  centre  of 
pressure  of  the  issuing  stream.  The  depth  of  the  iveir  is  meas- 
ured from  the  surface  of  still  water  to  the  bottom  or  sill  of  the 
notch. 

Rectangular  Notch.  —  Denote  the  coefficient  of  efflux  by  c, 
the  depth  of  the  weir  in  feet  by  k,  the  area  in  sq.  feet  enclosed 
by  the  wetted  perimeter  by  F9  and  the  number  of  cubic  feet 
per  second  by  Q.  We  have,  as  a  formula  applicable  to  open 
rectangular  notches, 

.    (ii) 


*  See  Church's  Mechanics,  page  684;  Rankine's  Steam-engine,  p.  90;  Encyc. 
Britannica,  Vol.  XII.  p.  470;  Bulletin  on  Irrigation  and  Use  of  Weirs,  by  Prof. 
L.  G.  Carpenter,  Fort  Collins,  Colorado. 


§  2OI.]       MEASUREMENT  OF  LIQUIDS  AND   GASES.  273 

With  most  areas  c  increases  slightly  with  the  length  and 
diminishes  with  the  head  ;  it  probably  depends  on  the  ratio  of 
wetted  perimeter  to  area,  although  it  is  not  quite  constant  for 
triangular  notches,  in  which  this  ratio  is  a  constant  one.  Very 
complete  and  extensive  experiments  were  conducted  by  J.  B. 
Francis  at  Lowell,  Mass.,  anji  from  these  experiments  he  de- 
duced the  value  of  the  coefficient  of  contraction  to  equal  one 
tenth  the  head,  and  consequently  for  rectangular  weirs 


Q  —  \c(b  —  Q.inh)h  V2ght      ....     (12) 

in  which  n  =  number  of  contractions.  Applying  this  correc 
tion  to  an  ordinary  rectangular  notch  with  two  contractions. 
we  have  the  well-known  Francis  formula  for  rectangular  weirs, 

Q  =  \c(b  —  o.2h)h  \f2gh  =  5.35<£  —  o.2h)h*.    .    (13) 


For  heads  ranging  from  three  inches  to  two  feet  it  has  been 
found  by  experiment  that 

£  =  0.62    and        =  *b  —  o. 


Triangular  Notch.  —  For  the  triangular  notch  in  which  apex 
is  down,  b  the  base  at  water-level,  h  the  depth, 


4.28^*.    .    .    .     (14) 
If  the  angle  is  60°, 

b  =  2h  tan  30°  =  1.1547^    and    Q 

If  the  angle  is  90°, 

b  =  2h    and     Q  = 

Trapezoidal  Notch.  —  To  avoid  the  corrections  for  contrac- 
tions, Cippoletti  of  Milan  in  1886  proposed  to  use  a  trape- 


274 


EXPERIMENTAL   ENGINEERING. 


[§202 


zoidal  notch  of  such  dimensions  that  the  area  of  the  stream 
flowing  through  the  triangular  portion  should  be  just  sufficient 
to  correct  for  the  contraction  of  the  stream  in  a  rectangular 
weir.  The  proportions  of  such  a  weir,  in  terms  of  the  length 
at  bottom  of  the  notch,  is  as  follows  :  height  equal  to  six  tenths 
the  bottom  length,  width  of  top  equal  to  the  bottom  plus 
one  fourth  the  height  added  to  either  side  ;  the  tangent  of  the 
angle  of  inclination  of  the  sides  equal  to  0.25.  It  is  asserted 
that  such  a  weir  will  give  the  discharge  with  an  error  less  than 
one  half  of  one  per  cent.  The  formula  for  the  use  of  such  a 
notch  would  be  simply 

....     (15) 


Submerged  orifices,  rectangular  or  circular,  are  sometimes 
used  for  the  measurement  of  water.  The  required  formulae 
are  given  in  the  table  following. 

From  table  in  Weisbach's  Mechanics,  c  =  on  the  average 
O.6.  For  small  areas  it  diminishes  with  increase  of  head  from 
0.7  to  0.6,  and  for  large  areas  it  increases  with  increase  of  head 
from  0.57  to  0.60. 

These  formulae  are  conveniently  tabulated  as  follows  : 

202.  Table  of  Formulae  for  Flow  over  Weirs. 


ij 

11. 

°| 

||| 

Form  of  Notch. 

0.0 

4n          O 

4-1 

A  rt 

&|1 

Formula  for  discharge  in  cubic 
feet  per  second. 

fl 

ill 

5«M2 

gioo 

Rectangular: 

Usual  form  .  .  . 

h 

0 

b 

.63  to  .58 

$cbh  ^2gh 

Francis       .... 

h 

O 

b 

.622 

%ch  ^~2gh(b  —  O.ink) 

Submerged..  . 

h 

fl 

b 

%cb  ^^Tg($  —  h'  ') 

r 

h 

h' 

b 

.62 

cb(h  -  h'}  \/g(h  -[-  ^> 

Triangular:  \ 

h 

O 

b' 

.617 

•facb'h  ^2gh 

I 

h 

0 

2h  tan  a 

.617 

•fabh*  tan  a  \/2gh 

Ang.  at  b.    60° 

h 

0 

1.1547^ 

.617 

2.47^' 

Ang.  at  b.    90° 

h 

0 

2h 

.617 

T8F^/^2  ^2gh 

Trapezoidal; 

Cippoletti's.  .  . 

h 

0 

*  +  \h 

0.629 

*bh^k 

§  204-}        MEASUREMENT  OF  LIQUIDS  AND   GASES.  2?$ 

When  still  water  cannot  be  found  above  the  weir,  and  we 
have  a  velocity  of  approach  that  can  be  measured  and  is  equal 
«»'  =  V2gk't  we  can  compute  k  '.  Then 

*')«-  **]  »    ....    (16) 


In  above  formula  Q  =  discharge  in  cubic  feet  per  second, 
b  the  length  of  sill  at  bottom  of  notch. 

203.  Efflux  of  Water  through  Nozzles,  or  Conical  Con- 
verging Orifices.*—  In  this  case,  if  we  denote  least  area  in 
square  feet  by  7%  in  which  c"  is  the  coefficient  of  contraction, 
c'  that  of  velocity,  and  c  that  of  discharge, 


(17) 


In  this  case  the  head  is  to  be  measured  by  a  pressure-gauge 
attached  close  to  the  nozzle. 

The  value  of  c  is  a  maximum  when  the  sides  of  the  nozzle 
make  an  angle  of  13°  24',  attaining  a  value  of  0.946.  When  the 
angle  of  the  nozzle  is  3°  10',  c  =  0.895,  and  when  49°,  c  =  0.895. 
(See  Church's  Mechanics,  page  692  ;  "  Hydromechanics," 
Encyc.  Brit.,  page  475.) 

204.  Efflux  of  Water  through  Venturi  Tubes  or  Bell- 
mouthed  Orifices.  —  A  conically  divergent  orifice,  with 
rounded  entrance  to  conform  to  the  shape  of  the  contracted 
vein,  is  now  termed,  from  the  first  experimenter,  Venturis  tube. 
The  dimensions  of  such  a  tube,  as  given  in  Encyc.  Britannica, 
Vol.  XII.,  page  463,  are  as  follows,  in  terms  of  the  small 
diameter  (d).  Large  diameter  (D)  at  opening  equals  1.25^; 
length  equals  .625^,  or  .$D.  The  sides  are  in  section  a  circular 
arc,  struck  with  a  radius  of  1.625^,  from  a  centre  in  the  line  of 
(a)  produced. 

*  Rankine's  Steam-engine.     Hamilton  Smith  writes  formula 


2/6  EXPERIMENTAL  ENGINEERING.  [§  205. 

The  formula  of  discharge  is 

~  (18) 


in  which  F  is  the  least  area,  h  the  head  to  be  measured  by  a 
pressure-gauge  attached  to  the  pipe  before  the  area  of  cross. 
section  is  reduced,  c'  the  coefficient  of  velocity.  The  coeffi- 
cient of  contraction  in  this  case  is  equal  to  one.  Weisbach 
gives  the  value  of  c'  as  .959,  -975,  and  .994  for  heads  respec* 
tively  2  feet,  40  feet,  and  160  to  1000  feet. 

Prof.  Church,  in  his  Mechanics,  page  694,  describes  an  ex- 
periment on  a  conically  divergent  tube  3  inches  long,  .8  inch 
diameter  at  least  section. 

Coefficient  of  discharge  with  heads  from  2  to  4  feet  varied 
from  .901  to  .914. 

205.  Flow  of  Water  under  Pressure.  —  The  pressure  ex- 
erted by  flowing  water  in  pipes  is  very  different  from  that  due 
to  still  water  under  the  same  head.  The  pressure  follows  more 
or  less  closely  the  law  enunciated  in-the  theorem  of  Bernouilli, 
which  may  be  stated  in  a  general  form  as  follows  :  "  The  exter* 
nal  and  internal  work  done  on  a  mass  is  equal  to  the  change  of 
kinetic  energy  produced  ;"  that  is,  the  total  energy  of  a  flowing 
stream  remains  constant  except  for  losses  due  to  friction. 

In  the  flow  of  water  through  a  pipe  with  varying  cross- 
section  the  velocity  of  flow  will  be  very  nearly  inversely  as  the 
area  of  cross-section.  Since  the  energy  or  product  of  pressure 
and  velocity  is  nearly  constant  by  Bernoulli's  theorem,  as  the 
velocity  increases  the  pressure  must  diminish,  and  we  shall 
find  least  pressuie  at  the  points  where  the  cross-sections  are 
least.  From  some  experiments  made  by  the  author,  the  same 
law  of  varying  pressure  with  varying  cross-section  applies  in  a 
less  degree  to  the  flow  of  steam  through  a  pipe.*  The  formula 
expressing  Bernouilli's  theorem,  neglecting  friction,  is 

i?       p 

^+-  +  *  =  constant; 

*See  "Hydromechanics,"  Encyc.  Britannica,  page  468. 


§  206.]        MEASUREMENT  OF  LIQUIDS  AND   GASES. 

in  which  v*  -f-  2g  is  the  velocity-head,  /  is  the  pressure  per 
square  foot,  y  the  weight  per  cubic  foot  ;  so  that  p  -r-  y  is  the 
pressure-head,  and  z  the  potential  head,  or  vertical  distance 
from  any  horizontal  reference  line. 

206.  Flow  of  Water  in  Circular  Pipes.*—  In  this  dase 
there  is  a  loss  of  head,  /*',  due  to  friction.  Denote  the  sine  of 
the  angle  of  inclination  by  i,  diameter  by  d,  length  by  L,  loss 
of  head  by  ht'9  all  in  feet  coefficient  of  loss  of  head  by  £. 


=**~  .......    09) 


From  experiments  of  Darcy, 

C  =  0.005^1  -|  --  -0     for  clean  pipes; 
C  •=  o.oi  f  i  -|  --  %J     for  incrusted  pipes  ; 


(20) 


Loss  of  Head  at  Elbows. — In  this  case  the  loss  is  principally 
due  to  contraction.     Weisbach  gives  the  following  formulae : 


See  "  Hydromechanics,  "  Encyc.  Britannica. 


2/8  EXPERIMENTAL   ENGINEERING. 

If  0  equal  the  exterior  angle, 


[§206. 


=  0.9457  sin8  —  +  2.047  sin4  y 


(23) 


From  this  are  deduced  the  following  values : 


0 
& 

20° 
0.046 

40° 
0.139 

60° 
0.364 

80° 
0.740 

90° 
0.984 

100° 

1.26 

110° 

1.556 

120° 

1.861 

I3°; 

2.158 

For  pipes  neatly  bent  the  value  of  £e  is  much  less. 

By  equating  hp'  and  ke'  in  equations  (19)  and  (22),  a  length 
of  pipe  can  be  found  which  will  produce  a  loss  of  head  equiva- 
lent to  that  produced  by  any  given  elbow.  We  shall  have 
this  additional  length : 


(24) 


On  substituting  the  values  of  C*  as  above,  and  C  as  equal  to 
0.006,  this  additional  length  will  be  found  not  to  vary  much 
trom  40  diameters  for  each  90°  elbow,  and  7  diameters  for  each 
45°  elbow. 

Loss  of  Head  on  entering  a  Pipe. — This  loss  is  very  small 
when  a  special  bell-mouthed  entrance  is  used,  but  is  great  in 
other  cases.  The  loss  of  head  in  entering  a  straight  tube  is 
expressed  by  the  formula 


. 


(25) 


§  20^.]        MEASUREMENT  OF  LIQUIDS  AND   GASES. 


279 


Weisbach  found  £.  =  0.505.  By  making  hj  of  equation  (19) 
equal  to  /fca',  and  reducing,  we  find  the  additional  length,  L,  of 
straight  pip«  producing  the  same  loss  of  head. 


cx 

4C' 


Assuming  C  has  an  average  value  of  0.006,  and  Ctf  as  above, 


Loss  of  Head  by  abrupt  Contraction  of  Pipe.  —  In  this  case 
Weisbach  found 


=  0. 


which  would  correspond  to  an  additional  length  of  pipe  equal 
to  about  13  diameters.  When  the  mouth  of  the  contracted 
pipe  is  .reduced  by  an  aperture  smaller  than  the  pipe,  Weis- 
bach found  the  following  values  of  Cc.  In  the  table,  Fl  is  area 
of  orifice,  Ft  that  of  pipe  into  which  the  flow  takes  place. 


F>  -f-  F*    .    .     .    . 

O.I 

0.016 

0.2 
O.6I4 

0-3 

0.612 

0.4 

0.610 

0.5 

0.607 

0.6 
o  60^ 

0.8 
o  601 

I.O 

Oc  06 

L 

271.7 

CO.QQ 

10.78 

9.612 

e    2^6 

3O77 

i  160 

£         

050^ 

2l2d 

ted 

4od 

22d 

13^ 

5^ 

2d 

Globe  valves  produce  about  one  half  more  resistance  than 
a  right-angled  elbow,  or  an  amount  equal  to  an  additional 
length  of  about  60  diameters. 

207.  Loss  of  Head  in  flowing  through  a  Perforated 
Diaphragm  in  a  Tube  of  Uniform  Section. — Let  ^.be  the 
area  of  the  orifice,  .Fthat  of  the  pipe  in  square  feet,  C  the  co- 
efficient of  discharge,  c  the  coefficient  of  contraction. 


280        .  EXPERIMENTAL  ENGINEERING. 

The  loss  of  head  in  feet 


[§  208. 


(26) 


Weisbach  gives  the  following  values  as  the  results  of  ex- 
periments : 


Pi 

"F 

O.I 

0.2 

0.3 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

I.O 

Cc 

0.624 

0.632 

0.643 

0.659 

0.681 

0.712 

0-755 

0.813 

0.892 

I.O 

c 

225.9 

47-77 

30.83 

7.801 

1-753 

1.796 

0.797 

0.290 

0.060 

0.0 

208.  Volume  flowing  through  a  Perforated  Diaphragm. 
—  Let  Ha  represent  the  head  in  feet  on  side  of  greatest  press- 
ure, and  Hb  that  on  the  opposite  side. 

The  loss  of  head 

hc  =  Ha  —  Hb. 


From  equation  (26),  by  transposing  and  substituting, 


(27) 


The  quantity  discharged  in  cubic  feet  per  second, 


(28) 


From  this 


(28a) 


g  210.]        MEASUREMENT  OF  LIQUIDS  AND   GASES.  28 1 

209.  Measurements  of  the   Flow  of  Water. — General 
Methods. — -The  measurement  of  the  flow  of  water  is  of  import- 
ance in  connection  with  efficiency-tests  of  pumps,  water-meters, 
and  steam-engines,  as  well  as  in  determining  the  amount  of  water 
that  can  be  obtained  from  a  given  stream, 

The  methods  used  for  measurement  of  the  flow  usually  con- 
sist  in  making  the  water  pass  through  open  notches  over  weirs, 
through  standard  orifices  or  nozzles,  or  through  meters. 

The  coefficients  that  have  been  given  are  in  every  case  to  be 
considered  approximations  only,  and  should  be  tested  by  actual 
measurement  under  the  conditions  of  use. 

The  head  of  water  is  the  distance  from  the  centre  of  press- 
ure  to  the  surface  of  still  water  under  atmospheric  pressure.  In 
case  the  water  is  under  pressure  and  at  rest,  this  head  can  be 
measured  by  a  calibrated  pressure-gauge.  The  gauge  is  usually 
graduated  to  show  pressure  in  pounds  per  square  inch,  each 
pound  being  equivalent  to  a  head  of  2.307  feet  of  water  at  a 
temperature  of  70°  Fahr.,  or  to  2.037  inches  of  mercury. 

In  case  the  water-pressure  is  read  in  inches  of  mercury,  one 
inch  of  mercury  corresponds  to  a  head  equal  to  1.113  ^eet- 

A  convenient  table,  showing  relation  of  pounds  of  pressure- 
head  in  feet  of  water  or  inches  of  mercury,  will  be  found  in 
Article  260. 

210.  Flow  of  Water  over  Weirs. — Methods  of  measuring 
the  Head. — The  head  is  measured  most  accurately  by  the  use  of 
the  hook-gauge,  used  first  by  Mr.  U.  Boyden   of  Boston   in 
1840.  Many  of  the  English  engineers  still  depend  on  the  use 
of  floats.     The  head  in  all  cases  is  to  be  measured  at  a  distance 
sufficiently  back  from  the  weir  to  insure  a  surface  which  is  un- 
affected by  the  flow.     The  channel  above  the  weir  must  be  of 
sufficient  depth  and  width  to  secure  comparatively  still  water. 
The  addition  of  baffle-plates,  some  near  the  surface  and  some 
near  the  bottom,  under  or  over  which  the  water  must  flow,  or 
the  introduction  of  screens  of  wire-netting,  serves  to  check  the 
current  to  great  extent.     Such  an  arrangement  is  sometimes 
called  a  tumbling-bay. 

The  object  of  the  baffle-plates  is  to  secure  still  water  for  the 


282 


EXPERIMENTAL   ENGINEERING. 


[ 


accurate  measurement  of  height  of  the  surface  above  the  sill  of 
the  weir.  The  same  object  can  be  accomplished  by  connecting 
a  box  or  vessel  to  the  water  above  the  weir  by  a  small  pipe 
entering  near  the  bottom  of  the  vessel ;  the  water 
will  stand  in  this  vessel  at  the  same  height  as  that 
above  the  weir,  and  will  be  disturbed  but  little  by 
waves  or  eddies  in  the  main  channel.  The  height 
of  water  is  then  obtained  from  that  in  the  vessel. 
Prof.  I.  P.  Church  has  the  connecting-pipe  pass  over 
the  top  of  the  vessel  and  arranged  so  as  to  act  as  a 
siphon. 

The  Hook-gauge. — This  consists  of  a  sharp- 
pointed  hook  attached  to  a  vernier  scale,  as  shown 
inFig.  i4O,in  such  a  manner  that  the  amount  it  is 
raised  or  lowered  can  be  accurately  measured.  To 
use  it,  the  hook  is  submerged,  then  slowly  raised  to 
break  the  surface.  The  correct  height  is  the  read- 
ing the  instant  the  hook  pierces  the  surface.  To 
obtain  the  head 'of  water  flowing  over  the  weir,  set 
the  point  of  the  hook  at  the  same  level  as  the  sill 
of  the  weir.  The  reading  taken  in  this  position 
will  correspond  to  the  zero-head,  and  is  to  be  sub- 
tracted from  all  other  readings  to  give  the  head  of 
the  water  flowing  over  the  weir. 

In  some  forms  of  the  hook-gauge  the  zero  of 
the  main  scale  can  be  adjusted  to  correspond  to 
HOOK-GAUGE.  the  zero_head,  or  level  of  the  sill  of  the  weir. 

Floats. — Floats  are  sometimes  used  :  they  are  made  of  hol- 
low metallic  vessels,  or  painted  blocks  of  wood  or  cork,  and 
carry  a  vertical  stem ;  on  the  stem  is  an  index-hand  or  pointer 
that  moves  over  a  graduated  scale. 

211.  Conditions  affecting  the  Accuracy  of  Weirs.— 
I.  The  weir  must  be  preceded  by  a  straight  channel  of  con- 
stant cross-section,  with  its  axis  passing  through  the  middle  of 
the  weir  and  perpendicular  to  it,  of  sufficient  length  to  secure 
uniform  velocity  without  internal  agitation  or  eddies. 

2.  The  opening  itself  must  have  a  sharp  edge  on  the  up- 


FlG. 


§  2I3-J        MEASUREMENT  OF  LIQUIDS  AND   GASES.  283 

stream  face,  and  the  walls  cut  away  so  that  the  thickness  shall 
not  exceed  one  tenth  the  depth  of  the  overflow. 

3.  The  distance  of  the  sill  or  bottom  of  the  weir  from  the 
bottom  of  the  canal  shall  be  at  least  three  times  the  depth  on 
the  weir,  and  the  ends  of  the  sill  must  be  at  least  twice  the 
depth  on  the  weir  from  the  sides  of  the  canal. 

4.  The  length  of  the  weir  perpendicular  to  the  current  shall 
be  three  or  four  times  the  depth  of  the  water. 

5.  The  velocity  of  approach  must  be  small ;  for  small  weirs 
it  should  be  less  than  6  inches  per  second.     This  requires  the 
channel  of  approach  to  be  much  longer  than  the  weir  opening. 

4.  The  layer  of  falling  water  should  be  perfectly  free  from 
the  walls  below  the  weir,  in  order  that  air  may  freely  circulate 
underneath. 

5.  The  depth  of  the  water  should  be  measured  with  accuracy, 
at  a  point  back  from  the  weir  unaffected  by  the  suction  of  the 
flow  and  by  the  action  of  waves  or  winds. 

6.  The  sill  should  be  horizontal,  the  plane  of  the  notch 
vertical. 

212.  Effect  of  Disturbing  Causes  and  Error  in  Weir 
Measurements. —  i.    Incorrect   measurement   of   head.     This 
may  increase  or  decrease  the  computed  flow,  as  the  error  is  a 
positive  or  negative  quantity. 

2.  Obliquity  of  weir ;  the  effect  of  this  or  of  eddies  is  to 
retard  the  flow. 

3.  Velocity  of  approach  too  great,  sides  and  bottom  too 
near   the   crest,  contraction    incomplete,   crest   not   perfectly 
sharp,  or  water  clinging  to  the  outside  of  the  weir,  tend  in  each 
case  to  increase  the  discharge. 

The  causes  tending  to  increase  the  discharge  evidently  out- 
number those  decreasing  jt,  and  are,  all  things  being  taken  into 
account,  more  difficult  to  overcome. 

213.  Water-meters. — The  water-meter  is  an   instrument 
for  measuring  the  amount  of  water  flowing  through  a  pipe. 
Knight  makes  seven  distinct  classes  of  water-meters,  as  follows:* 

*  Knight's  Mechanical  Dictionary,  Vol.  III. 


284  EXPERIMENTAL   ENGINEERING.  [§  2I4- 

i.  Those  in  which  the  water  rotates  a  horizontal  case,  or  a 
horizontal  wheel  in  a  fixed  case,  delivering  a  definite  amount 
at  each  rotation. 

*  2.  A  piston  or  wheel  made  to  rotate  by  the  pressure  of  the 
water,  the  meter  in  this  case  being  the  converse  of  the  rotary 
engine  or  pump. 

3.  A  screw  made  to  rotate  by  the  motion  of  the  water. 

4.  A  reciprocating  piston  in  a  cylinder  of  known  capacity 
driven  backward  and  forward  by  the  pressure  of  the  water. 

5.  The  pulsating  diaphragm,  in  a  vessel  of  known  capacity, 
which  is  moved  alternately  as  the  side  chambers  are  filled  and 
emptied. 

6.  The  bucket  and  balance-beam,  in  which  the  buckets  of 
known  capacity  on  the  ends  of  the  beam,  are  alternately  pre- 
sented to  catch  the  water  and  are  depressed  and  emptied  as  they 
become  filled. 

7.  The  meter-wheel,  in  which  chambers  of  known  capacity 
are  alternately  filled  and  discharged  as  the  wheel  rotates. 

Besides  these  seven  classes,  it  is  evident  that  any  machine 
may  be  used  in  which  the  motion  is  proportional  to  the  velocity 
of  flow  of  water. 

These  classes  can  be  united  into  two  general  classes:  I.  Posi- 
tive; II.  Inferential.  In  class  I.  the  water  cannot  pass  without 
moving  the  mechanism,  and  meters  of  this  kind  are  considered 
more  delicate  and  accurate  than  those  in  class  II. 

Each  class  of  meter  has  a  registering  apparatus,  which  in 
general  consists  of  a  series  of  gear-wheels,  so  arranged  as  to 
move  a  hand  continuously  around  a  graduated  dial,  from  which 
the  volume  can  be  read. 

214.  Errors  of  Water-meters. — In  addition  to  the  constant 
errors  of  graduation,  meters  are  liable  to  be  clogged  by  dirt,  to 
be  affected  by  air  in  the  water,  and  by  change  in  the  tempera- 
ture, head,  or  quantity  of  discharge  of  the  water  passing 
through. 

While  the  meter  is  no  doubt  of  sufficient  accuracy  for  com- 
mercial purposes,  it  should  be  used  with  caution  in  the  measure- 
ment of  water  for  tests  or  for  purposes  of  scientific  investiga- 


§  2 1 5-]        MEASUREMENT  OF  LIQUIDS  AND   GASES.  285 

tion.  Before  and  after  such  tests  a  careful  calibration  of  the 
meter  should  be  made  tfnder  the  exact  conditions  of  the  test. 

The  following  directions  explain  the  method  of  calibrating 
the  weir  notch  and  meter,  arranged  in  series.  In  this  experi- 
ment the  water  is  to  be  weighed.  Either  instrument  may  be 
calibrated  separately.  In  case  the  weir  has  been  calibrated,  the 
meter  could  be  calibrated  by  direct  comparison,  without  the 
use  of  weighing-scales. 

215.  Directions  for  Calibrating  the  Weir  Notch  and 
jy[eter. — The  object  of  this  experiment  is  to  determine  the 
coefficient  c  of  formula  (9),  Article  20 1,  page  272,  and  the  ac- 
curacy of  previous  determinations. 

Apparatus  needed. —  Hook-gauge,  pair  of  scales,  thermom- 
eter, spirit-level,  pressure-gauge,  weir,  and  meter. 

1.  Accurately  level  the  sill  of  the  weir,  and  see  that  the 
notch  is  in  a  truly  vertical  plane. 

2.  Take  the  zero-reading  of  the  hook-gauge,  by  setting  the 
point  of  the  hook  with  a  spirit-level,  at  the  same  height  as  the 
sill  of  the  notch.     In  case  the  form  of  the  notch  is  such  as  to 
prevent  the  use  of  the  spirit-level,  grease  the  edge  of  the  notch 
and  set  the  hook  by  the  water-level ;  being  sure  that  the  water 
surface  does    not,  through    capillary   action,    rise    above   the 
lower  edge  of  the  notch. 

3.  Start  the  water  flowing,  and  after  it  has  obtained  a  con- 
stant rate,  take  measurements  of  weights  and  of  head.     The 
commencement  of  the  experiment  to  be  determined  by  the 
rising  of  the  poise  on  the  scale-beam,  which  previously  must  be 
set  at  a  given  weight.    Note  the  time,  scale  reading,  thermom- 
eter-reading, reading  of  the  hook-gauge  at  the  beginning  and 
once  in  five  minutes  during  the  run.     As  the  experiment  ap- 
proaches the  end  set  the  poise  of  the  scale-beam  in  advance  of 
the  weight,  terminate  the  run  when  the  beam  rises,  accurately 
noting  the  time,  weight,  thermometer-reading,  and  reading  of 
the  hook-gauge.    Make  direct  measurements  of  the  coefficient 
of  contraction.     Calculate  coefficient  of  discharge, 

4.  If  the  water  to  the  weir  first  passes  through  a  meter,  take 
corresponding  readings  of  the  meter-dial,     Note  the  pressure 


286 


EXPERIMENTAL   ENGINEERING. 


[§216. 


and  temperature  at  the  meter.  Calculate  the  number  of  cubic 
feet. 

5.  Draw  on  cross-section  paper  a  curve  of  discharge,  in 
which  cubic  feet  per  second  are  taken  as  abscissae  and  the  cor- 
responding heads  as  ordinates.  Also  draw  in  dotted  lines  on 
the  same  sheet  a  curve  of  coefficients,  of  discharge  in  which  co- 
efficients are  taken  as  abscissa,  and  corresponding  heads  as 
ordinates.  Also,  draw  a  curve  showing  error  of  meter  for  each 
head. 

2l6.  Form  of  Report. — The  following  form  has  been 
used  by  the  author  for  calibration  of  the  weir  notch  and  meter : 

CALIBRATION  OF  WEIR  NOTCH  AND  METER. 

Made  by „ 

at..  -       Date.. 


Number  of  Run. 

I. 

II. 

III. 

IV. 

V. 

Temperature   discharge    deg    F           

Max  ft. 

Min  ft. 

"                "          "         Av         .      .     ft 

\Veight  cf  water  —  Beginning  (tare)  Ibs 

•'           "        Total               Ibs 

Cubic  feet  per  second  .  .  .•  Q 

"         End     .                          ft 

Area  —  Wetted  orifice     so    ft 

Coefficients  —  Contraction    Cc  •  •  «              .... 

"              Loss  of  head   c?      

Constants  of  Weir,  Form   Length ft.     Angle  of  sides .... 

Remarks 

Meter,  manf.  by General  class .    No. . . . 


Remarks. 


Formulae:   c 


§  2I8.J        MEASUREMENT  OF  LIQUIDS  AND   GASES.  287 

217.  Calibration  of  Nozzles  and  Venturi  Tubes.  —  These 
are  often  more  convenient  to  use  than  weir-notches,  in  the 
measurement  of  the  efflux  of  water.  Before  using  these  they 
should  be  carefully  calibrated  by  measurements  of  the  head 
and  discharge.  The  Venturi  tube  is  sometimes  inserted  in  a 
length  of  pipe;  in  this  case  the  pressure  should  be  observed 
on  either  side  of  the  tube,  and  the  discharge  measured.  The 
special  directions  for  calibrating  when  discharging  into  the  air 
would  be  as  follows  : 

1.  Arrange  the  nozzle  or  Venturi  tube,  so  that  the  discharge 
can  be  caught  in  tanks  and  measured  or  weighed. 

2.  Attach  a  pressure-gauge,  which  has  been  previously  cali 
brated,  to  the  pipe  near  the  nozzle.     Since  the  pressure  is  a 
function  of  the  area  of  cross-section,  the  position  ot  the  gauge 
should  be  described  and  the  area  of  the  cross-section  at  that 
point  measured. 

3.  Make  careful  measurements  of  least  and  greatest  inter- 
nal diameters  of  nozzles,  of  length  of  nozzle,  and  note  condition 
of  interior  surface.     Make  sketch  showing  the  form. 

4.  Make  five  runs,  as  explained  in  directions  for  calibrating 
weir-notches,  Article  215,  page  285,  obtaining  weight  of  water 
by  the  same  method.    In  case  it  is  not  convenient  to  weigh  the 
water,  discharge  into  tanks  which  have  been  carefully  calibrated 
by  weighing,  arranged  so  that  one  is  emptying  while  the  other 
is  filling. 

5.  Observe  during  run,  reading  of  pressure-gauge,  temper- 
ature  of  discharge-water,  weight   of  discharged  water.     Com- 
pute corresponding  head  producing  flow,  volume  of  discharged 
water,  and  the  coefficient  of  discharge  in  the  formula 


6.  Draw  a  curve  showing  relation  of  discharge  in  cubic 
feet  to  head,  as  explained  for  weir-notches,  page  285  ;  also  one 
showing  relation  of  coefficient  to  head. 

218.  Measurement  of  Efflux  of  Water  through  an  Ori- 
fice in  End  of  Tube  of  Uniform  Section.  —  A  cap  can  often 


288  EXPERIMENTAL   ENGINEERING.  [§  219. 

be  arranged  over  the  end  of  a  tube,  and  an  orifice  made  in, 
this  cap  with  a  sharp  edge  on  the  side  toward  the  current. 
This  will  be  found  to  give  very  uniform  coefficients  of  dis- 
charge. The  special  method  of  calibrating  this  orifice  would 
be  as  follows : 

1.  Arrange  the  tube  with  a  cap  in  which  is  an  orifice,  the 
area  of  which  is  one  third  that  of  the  pipe.     Ream  the  sides  of 
the  orifice  so  that  a  sharp  edge  will  be  presented  to  the  out- 
flowing water.     Attach  a  calibrated  gauge  at  a  distance  of  two 
diameters  of  the  pipe  back  from  the  orifice.     Arrange  to  weigh 
or  measure  the  discharged  water.     Measure  the  orifice. 

2.  Make   runs  as  explained  for  other  calibrations  with  five 
different  heads,  and  note  reading  of  pressure-gauge,  temperature 
of  discharged  water,  weight  or  volume  of  discharged  water,  and 
least  diameter  of  stream  discharged.    The  least  diameter  of  the 
discharged  stream  can  be  measured  by  arranging  two  sharp- 
pointed  set-screws  in  a    frame,  so  that  they  can  be  screwed 
toward  each  other.     These  screws  can  be  made  to  touch  the 
outflowing  stream,  and  the  distance  between  their  points  meas- 
ured. 

3.  Compute  head  producing  the  flow,  coefficient  of   con- 
traction, which  is  ratio  of  area  of  stream  to  area  of  orifice, 
coefficient  of  discharge,  and  loss  of  head.     See  equations  (i) 
to  (10),  Article  200,  page  272. 

4.  Draw  curves  on  cross-section  paper  showing  the  relations 
of  these  various  quantities. 

5.  Repeat  the  experiment  with  orifices  of  different  sizes. 
219.  Measurement  of  the  Flow  of  Water  in  Pipes  by 

use  of  a  Perforated  Diaphragm  or  of  a  Venturi  Tube. — In 
this  case  the  loss  of  head  flowing  through  the  orifice  in  the 
diaphragm  or  the  Venturi  tube  must  be  measured ;  then,  know- 
ing  the  coefficient  of  efflux  and  area  of  cross-section,  the  vol- 
ume discharged  can  be  computed  by  equation  (28),  Article 
208,  page  280;  also  Art.  204,  p.  275. 


(28) 


^  22O.]        MEASUREMENT  OF  LIQUIDS  AND   GASES.  289 

The  difference  of  head  is  measured  accurately  by  inserting 
tubes  at  a  distance  of  two  diameters  on  each  side  of  the  orifice, 
connecting  each  of  these  tubes  to  a  U-shaped  glass  tube  partly 
filled  with  water,  very  much  as  shown  :n  Fig.  145,  page  294, 
except  that  the  ends  of  the  tubes  A  and  B  are  in  each  case 
perpendicular  to  the  pipe,  and  are  on  opposite  sides  of  the 
diaphragm.  The  difference  in  the  height  of  the  water  in  the 
two  branches  of  the  U-shaped  tube  will  be  the  loss  of  head 
(Ha  —  Hb)  caused  by  the  orifice.  It  is  essential  that  the  tubes 
be  connected  into  pipes  having  equal  areas  of  cross-section, 
since  the  pressure,  even  in  the  same  line  of  pipe,  increases  with 
the  area  (see  Article  205).  The  coefficient  C  should  be  deter- 
mined by  calibration,  following  essentially  the  same  method  as 
that  prescribed  for  nozzles  and  Venturi  tubes  in  Article  217. 

220.  Measurement  of  the  Flow  of  Water  in  Streams.*  — 
This  is  done  by  (i)  Floating  bodies  ;  (2)  Tachometer  ;  (3)  Pitot's 
tube  ;  (4)  Hydrometric  pendulum. 

Floating  bodies,  when  used,  should  be  small,  and  about  the 
density  of  the  water.  A  floating  body  with  a  volume  about 
one  tenth  of  a  cubic  foot  is  better  than  larger.  They  can  be 
made  of  wood  and  weighted,  or  of  hollow  metal  and  partially 
filled  with  water.  A  coat  of  paint  will  serve  to  render  them 
visible.  To  obtain  the  velocity  for  different  depths,  the  sur- 
face velocity  is  first  found,  the  float  is  then  connected  with  a 
weighted  ball  that  can  be  adjusted  to  float  at  any  depth,  and 
the  joint  velocity  observed. 

Call  the  surface  velocity  v0  ,  the  joint  velocity  vm  ;  then  will 
the  velocity  of  the  submerged  ball  be 


A  floating  staff  that  remains  vertical  in  still  wat^r  is  some- 
times used. 

In  case  floats  are  used,  the  velocity  is  obtained  by  noting 
the  time  of  passing  over  a  measured  distance.  The  measured 
distance  should  be  marked  by  sights,  so  that  the  line  of  begin- 

*  See  Weisbach's  Mechanics,  Vol.  I. 


290 


EXPERIMENTAL  ENGINEERING. 


[§  221- 


ning  and  ending  can  be  accurately  determined.     The  float  is 
put  in  above  the  initial  point,  and  the  instant  of  passing  the 


FIG.  141. — THE  TACHOMETER. 


firs;  aind  last  lines  of  the  course  is  to  be  determined  by  a  stop- 
watch. 

221.  The  Tachometer,  or  Woltman's  Mill,  consists  of  a 
small  water-wheel  connected  to  gearing  so  as  to   register  the 


§221.]        MEASUREMENT  OF  LIQUIDS  AND    GASES.  29 1 

number  of  revolutions.  The  wheel  is  anchored  at  the  required 
depth  in  the  stream,  and  at  a  given  instant,  the  time  of  which 
is  noted  on  a  stop-watch,  the  gearing  is  set  in  motion  by  pull- 
ing on  a  lever  ;  at  the  instant  of  stopping  the  experiment,  the 
gears  are  stopped  by  a  trip.  The  machine  is  removed,  and 
the  number  of  revolutions  multiplied  by  a  constant  factor  gjyes 
the  total  space  moved  by  the  water;  this  divided  by  the  time 
gives  the  velocity. 

The  shape  of  the  vanes  of  the  revolving  wheel  are  varied 
by  different  makers,  and  the  wheel  is  made  to  revolve  either  in 
a  horizontal  or  a  vertical  plane. 

Fig.  141  shows  a  form  used  extensively,  in  which  the  gearing 
for  registering  the  number  of  revolutions  is  operated  by  an 
electric  current,  and  can  be  seen  at  any  instant. 

The  electric  register  shown  in  Fig.  142  can  be  located  at 
any  distance  from  the  tachometer  convenient  to  the  observer. 

Calibration. — The  constant  factor,  which  multiplied  into 
the  dial-reading  gives  the  velocity,  is  obtained  by  calibration. 
The  calibration  is  performed  by  attaching  the  instrument  to 
a  float  or  a  boat,  and  towing  it  past  fixed  marks  at  a  known  dis- 
tance from  each  other.  The  velocity  is  obtained  as  for  floating 
bodies,  and  the  constant  is  found  by  comparing  this  with  the 
readings  of  the  instrument.  One  method  of  calibrating  the 


FIG.  143, 

instrument  is  as  follows  (see  Fig.  143)  :  The  instrument  is 
attached  to  the  bow  of  a  boat,  so  as  to  remain  in  a  vertical 
position;  the  water  being  still,  and  little  or  no  current.  The 
boat  is  propelled  by  a  cord,  which  may  be  wound  up  by  a 
windlass;  the  motion  must  be  in  a  right  line,  and  over  a  known 


292 


EXPERIMEN  TA  L   ENGINEERING. 


[§222. 


distance.  Several  trials  are  to  be  made,  and  the  average  results 
taken,  and  reduced  by  the  method  of  Least  Squares,  as  ex- 
plained in  Chapter  I. 

The  tachometer  is  the  most  convenient,  and  •  if  properly 
constructed  the  most  accurate,  method  of  measuring  the  ve- 
locity of  running  water. 

222.  Pitot's  Tube. — This  is  a  bent  glass  tube,  held  in  the 
water  in  such  a  manner  that  the  lower  part  is  horizontal  and 
opposite  the  motion  of  the  current.  By  the  impulse  of  the 
current  a  column  of  the  water  will  be  forced  into  the  tube  and 

held  above  the  level  of  the  water  in 
the  stream ;  this  rise,  DE  (see  Fig. 
144)  is  proportional  to  the  impulse 
or  to  the  velocity  of  the  water  that 
produces  it.  If  the  height  DE  above 
the  surface  of  the  water  equal  h  and 
the  velocity  of  the  water  equal  vt 
we  have 


in  which  c  equals  the  coefficient  to  be 
determined  by  experiment. 

To    determine    the  coefficient    r, 

FIG.  144-PrroT's  TUBE.  the  instrument    jg    either   to    be    hdd 

in  moving  water  whose  velocity  is  known,  or  else  moved 
through  the  water  at  a  constant  velocity.  From  the  known 
value  of  v  and  the  observed  value  of  h  the  coefficient  c  can  be 
calculated. 

Weisbach  found  that  with  fine  instruments,  when  the 
velocities  were  between  0.32  and  1.24  meters  (1.04  and  4.068 
feet)  per  second,  that 

v  —  3-545  ^  meters  per  second, 
or,  in  English  measures, 

v  =  6.43  Vh  feet  per  second. 


§  222.]        MEASUREMENT  OF  LIQUIDS  AND   GASES. 


293 


Pitofs  tube,  as  ordinarily  used,  is  shown  in  the  diagram 
Fig.  145.  It  consists  of  two  tubes,  one,  AB,  bent  as  in  Fig. 
144,  the  other,  CD,  vertical.  The  mouth-pieces  of  both  tubes 
are  slightly  convergent,  to  prevent  rapid  fluctuation  in  the 


FIG.  145.— SKETCH  OF  PITOT'S  TUBE. 

cubes.  These  tubes  are  so  arranged  that  both  can  be  closed  at 
any  instant  by  pulling  on  the  cord  ss  leading  to  the  cock  R. 
Between  the  glass  tubes  dD  and  bB  is  a  scale  which  can  be  read 
closely  by  means  of  the  sliding  verniers  m  and  n.  The  tubes 
are  connected  at  the  top,  and  a  rubber  tube  with  a  mouth-piece 
O  is  attached. 

In  using  the  instrument  it  is  fastened  to  a  stake  or  post  by 
the  thumb-screws  EF\  the  bent  tube  is  placed  to  oppose  the 
current  of  water,  the  cocks  K  and  R  opened.  The  difference 
in  height  of  the  water  in  the  tubes  will  be  that  due  to  the 
velocity  of  the  current.  The  water  in  the  column  dD  will  not 
rise  above  the  surface  of  the  surrounding  water,  and  the  instru- 
ment may  be  inconvenient  to  read.  In  that  case  some  of  the 
air  may  be  sucked  out  at  the  mouth-piece  O,  and  the  cock  K 
closed  :  this  will  have  the  effect  to  raise  the  water  in  both 


294 


EXPERIMENTAL   ENGINEERING. 


L§  223. 


columns  without  changing  the  difference  of  level,  so  that  the 
readings  can  be  taken  in  a  more  convenient  position;  or  by  clos- 
ing the  cock  K,  by  pulling  on  the  strings  ss,  the  instrument 
may  be  withdrawn,  and  the  readings  made  at  any  convenient 
place. 

223.  Pitot's  Tube  for  High  Pressures.  —  A  modified 
form,  as  shown  in  Fig.  146,  of  Pitot's  tube  is  useful  for  obtain- 
ing the  velocity  of  liquids  or  gases  flowing  under  pressure. 
The  arrangement  is  readily  understood  from  the  drawing. 


FIG.  146.  —  SKETCH  OF  PITOT'S  TUBE  FOR  HIGH  PRESSURES. 

The  difference  of  pressure  is  shown  by  the  difference  in  heights 
of  the  liquid  in  the  branches  of  the  U-shaped  tube  MM'  \  this 
difference  is  due  entirely  to  the  velocity,  since  both  branches 
are  under  equal  pressure.  Thus,  if  the  liquid  stand  at  M  on 
one  side  and  at  M'  on  the  other,  the  velocity  is  that  due  to  the 
height  of  a  column  of  liquid  equal  to  the  distance  that  M  is 
above  M'.  Call  this  distance  h\  then 


The  coefficient  c  is  to  be  determined  by  experiments  made 
on  a  tube  in  which  the  velocity  of  flow  is  known. 


§  225-]        MEASUREMENT  OF  LIQUIDS  AND    GASES.  295 

224.  Hydrometric  Pendulum. — This  instrument  consists 
of  a  ball,  two  or  three  inches  in  diameter,  attached  to  a  string. 
The  ball  is  suspended  in  the  water  and  carried  downward  by 
the  current ;  the  angle  of  deviation  with  a  vertical  may  be 
measured  by  a  graduated  arc  supported  so  that  the  initial  or 
zero-point  is  in  a  vertical  line  through  the  point  of  suspension. 
If  the  current  is  less  than  4  feet  per  second  an  ivory  ball  can 
be  used,  but  for  greater  velocities  an  iron  ball  will  be  required. 
The  instrument  cannot  give  accurate  determinations,  because 
of  the  fluctuations  of  the  ball  and  consequent  variations  in  the 
angle.  The  formulae  for  use  are  as  follows :  Let  G  equal  the 
weight  of  the  ball,  D  equal  the  weight  of  an  equal  volume  of 
water ;  then  G  —  D  is  the  resultant  vertical  force.  Let  F  equal 
area  of  cross-section  of  the  body,  v  the  velocity  of  the  current, 
c  a  coefficient  to  be  determined  by  experiment ;  then  we  have 
the  horizontal  force  P  —  cFv*.  Let  angle  of  deviation  be  d ; 
then 

cFv* 


G-D      G-D 
from  which 


'T  —  D}  tan  d 
cF 


The  best  results  with  this  instrument  will  be  only  approxi- 
mations. 

225.  Flow  of  Compressible  Fluids  through  an  Orifice.— 

General  Case. — In  this  case,  as  heat  is  neither  given  nor  taken 
up,  the  flow  is  adiabatic.  The  formulae  are  deduced  by  prin- 
ciples of  thermodynamics,  and  their  derivation  can  be  studied 
in  treatises  devoted  to  those  subjects.* 

Denote  the  velocity  by  v,  the  weight  per  cubic  foot  by  G, 
the  pressure  per  square  foot  in  the  vessel  from  which  the  flow 

*  See  Peabody's  Thermodynamics,  p.   132;  also,  art.  "  Hydromechanics," 
Encyc.  Britannica. 


296  EXPERIMENTAL   ENGINEERING.  [§  226. 

takes  place  by  /,  ,  the  pressure  against  which  the  flow  takes 
place  by/>2,  the  volume  of  one  pound  in  cubic  feet  by  C,  the 
absolute  temperature  corresponding  to  pressure  /t  by  Tlt  the 
ratio  of  specific  heats  by  y. 


M  \ 

-il\ 


also, 

-jr^  =  Zjr-      and      -gr-—-  =  Tr^f-     •     •     •     (30) 

226.  Flow  of  Air. — For  air,  p0  —  2116.8,  G0  =  0.08075, 
T0  =  492.6  at  32°  Fahr.,  y  =  1.405.  Inserting  these  numerical 
values,  we  have  the  following  equation  for  the  theoretical 
velocity  of  flow  of  air  through  an  orifice  : 

0.29 


Volume  of  Air  discharged.  —  The  volume  of  air  discharged, 
in  cubic  feet  per  second  at  pressure  of  discharge,  is  to  be  com- 
puted by  multiplying  the  area  of  the  orifice  Fl  in  square  feet,  by 
the  velocity  v^  ,  by  a  coefficient  of  discharge  c.  Then 


.    (32) 


Substituting  numerical  values  for  the  ratio  of  /„  to  pl ,  we 
have 

a  =  108.7^X0.16957; (33) 

*  See  article  "  Hydromechanics,"  Encyc.  Britannica,  Vol.  XII,  page  481. 


§  22/.]        MEASUREMENT  OF  LIQUIDS  AND    GASES. 


297 


To  express  this  in  terms  of  the  volume  discharged  from  the 
reservoir  Ql ,  in  which  /,  is  reservoir  pressure  and  />„  pressure 
of  discharge,  we  have 


Substituting  numerical  values  for  free  flow, 

i 
~5<2,  =  0.6339(2,; 


Substituting  values  of  /„  -:- 


,  =  68.8^  1/0.16957;. 


(35) 


227.  Velocity  of  Flow  of  Air  through  an  Orifice. — The 

velocity  of  flow  is  obtained  by  substituting  numerical  values  in 
the  preceding  equations.  We*  have,  denoting  by  7",  the  abso- 
lute temperature  in  the  reservoir  as  the  greatest  velocity  of 
flow  of  air, 


^=183.6^(1-0.8305). 


(36) 


Solving   equation  (36),  we  have  the  following  theoretical 
results : 


Temperature  of  Air  in  Reservoir. 

i      Velocity  of 

Flow  in  Feet 

Degrees  Fahr. 

Absolute. 

per  Sec. 

32 

4Q2.6 

991 

70 

530.6 

1030 

100 

560.6 

1058 

150 

610.6 

1105 

200 

660.6 

1148 

300 

760.6 

1233 

400 

860.6 

1312 

500 

960.6 

1386 

298  EXPERIMENTAL   ENGINEERING.    .  [§228. 

228.  The  Weight  of  Air  discharged.— This  is  to  be  com- 
puted  by  multiplying  the  volume  of  discharge  by  the  specific 
weight. 

Thus  the  weight  of  air  is 


Gl  =  „     *y  pounds  per  cubic  foot, 

3  O*         i 


when  /,  and  7^  are,  respectively,  pressure  and  absolute  tem- 
perature in  the  reservoir.  Hence  the  weight  of  air  dis- 
charged is 


.    .     (37) 


Weisbach  has  found  the  following  values  of  cy  the  coefficient 
of  discharge  : 

Conoidal  mouth-piece  of  the  form  of  the  con- 
tracted vein,  with    effective  pressures    of 

0.23  to  i.i  atmospheres  ................   0.97  to  0.99 

Circular  sharp-edged  orifices  ................   0.563  to  0.788 

Short  cylindrical  mouth-pieces  ..............   0.81  to  0.84 

The  same  rounded  at  the  inner  end  ........  .  .   0.92  to  0.93 

Conical  converging  mouth-pieces  ......  .',  ....    0.90  to  0.99 

In  the  general  formula  for  the  flow  of  air,  the  weight  de- 
livered becomes  a  maximum  when 


A 


This  equals  0.527  for  air  and  0.58  for  dry  steam.  This  has 
been  verified  by  experiment,  and  tends  to  prove  that  the  press- 
ure of  the  orifice  of  discharge  is  independent  of  the  back- 
pressure. In  the  flow  of  air  from  a  higher  to  a  lower  pressure 


§  229.]        MEASUREMENT  OF  LIQUIDS  AND   GASES.  299 

through  a  small  tube  or  orifice,  the  pressure  in  the  orifice  may 
be  less  than  the  back-pressure. 

229.  Flow  of  Air  in  Pipes.  —  When  air  flows  through  a  long 
pipe,  a  great  part  of  the  work  is  expended  in  overcoming  fric- 
tional  resistances.  This  friction  generates  heat,  which  is  largely 
used  in  increasing  the  pressure  in  the  pipes,  the  only  loss  being 
from  radiation,  which  is  small. 

The  expansion  then  is  isothermal,  the  heat  generated  by 
friction  exactly  neutralizing  the  heat  due  to  work. 

For  pipes  of  circular  section,  when  d  is  the  diameter,  /  the 
length,  p0  the  greater  and  /,  the  less  pressure,  T  the  absolute 
temperature,  C  the  coefficient  of  discharge,  cp(=  53.15  foot-lbs.) 
the  specific  heat,  we  have  the  initial  velocity 


_ 

~       &      p:   )  ......  (3  } 

This  may  be  reduced  to 


It  has  been  found  from  recent  experiments  that  fair  values 
of  the  coefficient  are  as  follows:  * 


C,  =  O.OO51  I  4-  -z- 
D\  I0d 

in  ordinary  pipes  for  velocities  of  100  feet  per  second  ; 

C  =  0.0028(1  +  -~] 
\         loo/ 

for  pipes  as  smooth  as  those  at  the  St.  Gothard  Tunnel. 

*  See  "  Hydromechanics,"  Encyc.  Britannica,  Vol.  XII,  p.  491. 


3OO  EXPERIMENTAL   ENGINEERING.  [§  230. 

Weight  of  air  flowing  per  second  in  circular  pipes  in  pounds 
is  given  by  the  equation 


Approximately, 

*.     •    •    •    (39) 


230.  Flow  of  Steam  through  an  Orifice.  —  Velocity.  —  In 
this  case,  as  in  Article  226,  the  expansion  is  supposed  to  be 
adiabatic. 

Denote  by  A  the  reciprocal  of  the  mechanical  equivalent 
of  one  B.  T.  U.  corresponding  to  the  quantity  778  ;  by  xl  the 
quality  or  percentage  of  dry  vapor  in  the  reservoir,  corre- 
sponding to  the  pressure  per  sq.  foot/j  ,  and  by  xz  the  quality 
in  the  tube,  corresponding  to  pressure  p^  ;  by  rl  the  latent  heat 
per  pound  in  reservoir,  r2  the  same  in  the  tube  ;  Tl  and  Zi,  the 
respective  absolute  temperatures,  0,  and  6^  the  respective 
entropies  of  the  liquids,  c  the  specific  heat  of  the  liquid,  q^  and 
q^  the  sensible  heat  of  the  liquid  in  reservoir  and  tube  ;  the 
reciprocal  of  the  weight  of  a  cubic  foot  of  the  liquid  by  <r. 
Then 

Av* 

—  =  *fi  -  *S,  -\-qi-q^JrA  <r(pl  -  /a).      .     (40) 

x,  can    be    determined    from    the   relation    expressed   in   the 
equation 


(4I) 


£  230.]        MEASUREMENT  OF  LIQUIDS  AND   GASES.  301 

If  no  tables  are  at  hand  for  Bl ,  its  approximate  value  can  be 
deduced,  since 


9,  -  6,  =  c  log. 


(42) 


So  that 


*s*    x^  T; 

-r-  =  -^-  +  c  log*     ^-- 


Eliminating  ^r3  in  equations  (40)  and  (41), 


A  fjfi 


»  -A)-  (43) 


The   following    table,    condensed    from    Peabody's   steam 
tables,  gives  the  value  of  the  entropy  of  the  liquid  : 

TABLE   OF   ENTROPY  OF  THE  LIQUID. 


Absolute 
Steam- 

Entropy 
of  the 

Absolute 
Steam- 

Entropy 
of  the 

pressure^ 

Liquid, 

pressure, 

Liquid, 

P 

e 

/ 

0 

I 

0.1329 

65 

0-4337 

10 

0.2842 

70 

0.4402 

15 

0.3143 

75 

0.4464 

20 

0.3363 

80 

0.4522 

25 

0.3539 

85 

0.4579 

30 

0.3685 

90 

0.4633 

35 

0.3811 

95 

0.4686 

40 

0.3921 

100 

0.4733 

45 

0.4020 

105 

0.4780 

50 

0.4109 

no 

0.4826 

55 

0.4191 

115 

0.4869 

60 

0.4267 

120 

0.4911 

In  the  above  equations^  has  a  numerical  value  of  I  -f-  778, 
<r  is  nearly  equal  to  0.016,^-  to  32.16. 


See  Thermodynamics,  by  Peabody,  page  138. 


3O2  EXPERIMENTAL   ENGINEERING.  [§  232. 

It  has  been  shown  that  in  the  flow  of  saturated  steam/, 
will  not  fall  below  0.58  of/^  because  at  that  point  there  is  the 
maximum  weight  of  discharge.  In  the  actual  trials  this  seems 
to  be  nearer  0.61  than  0*58.  If  we  assume  /a  equal  to  Q.6pl  , 
the  velocity  will  be  found  to  be  nearly  constant,  and  to  vary 
but  little  from  1400  feet  per  second. 

231.  Weight  of  Steam  discharged  through  an  Orifice. 
—  This  was  determined  experimentally  by  R.  D.  Napier,  and 
expressed  by  the  formula 


in  which  W=  weight  discharged  in  pounds  per  second,  F  =^ 
area  of  orifice  in  square  inches,  and/t  is  the  absolute  pressure 
of  the  steam,  pounds  per  square  inch,  which  is  equal  to  or 
greater  than  if  that  of  the  atmosphere. 

This  formula  has  been  verified  by  experiments  made  in  the 
Laboratories  of  Sibley  College  and  also  at  the  Massachusetts 
Institute  of  Technology,  and  is  found  to  vary  but  little  from 
the  actual  results. 

232.  Measurement  of  the  Flow  of  Gas.  —  Gas-meters.— 
In  the  measurement  of  gas  the  product  of  absolute  pressure, 
/>,  by  volume,  v,  divided  by  absolute  temperature,  T,  is  a  con- 
stant quantity.  Thus 

P^_  _Ayi 
T        T,' 

If  p  and  T  can  be  kept  constant,  the  quantity  discharged 
will  vary  as  the  volume  ;  if  p  and  T  are  known,  the  quantity  dis- 
charged can  be  computed. 

Gas-meters  are  instruments  for  measuring  the  volume  of 
gas  passing  them.  They  are  constructed  on  various  plans  and 
are  known  as  Wet  or  Dry,  depending  on  whether  water  is  used. 
The  volume  is  usually  measured  in  cubic  feet. 

Meter-prover.  —  This  is  the  name  given  to  a  sort  of  gasometer 
arranged  as  shown  in  Fig.  147.  It  consists  of  an  open  vessel. 


§  232.J        MEASUREMENT  OF  LIQUIDS  AND   GASES. 


303 


DE,  partly  filled  with  water,  into  which  a  vessel,  AF,  of  some, 
what  smaller  diameter  is  inverted.  The  weight  of  the  vessel  AF 
is  counterbalanced  by  a  weight  W  which  descends  into  a  vessel 
of  water  CK  at  such  a  rate  as  to  keep  the  sum  of  the  displace- 
ments of  the  two  vessels  constant,  in  which  case  the  pressure 


w 


FIG. 


on  the  confined  gas  in  the  vessel  AF  will  remain  constant. 
The  gas  flows  out  through  the  pipe  7",  its  pressure  being  taken 
by  a  manometer  at  m,  its  temperature  by  a  thermometer  at  /. 

Fig.  148  shows  a  form  of  meter-prover  made  by  the  Ameri- 
can Meter  Co.,  in  which  the  counterweight  lifts  an  additional 
weight  moving  over  an  involute  wheel,  so  calculated  that  the 
pressure  on  the  outflowing  gas  remains  constant.  These  instru- 
ments are  used  principally  to  calibrate  meters ;  they  give  very 
accurate  results,  but  are  not  suited  for  continuous  measure- 
ments. 

Wet-meter. — The  wet-meter  works  on  the  same  principle  as 
the  meter-prover,  but  is  arranged  with  a  series  of  chambers 


304 


EXPERIMENTAL   ENGINEERING. 


[ 


which  are  alternately  filled  and  emptied  with  gas.  These 
chambers  are  usually  arranged  like  an  Archimedean  screw,  as 
shown  in  section  in  Fig.  149. 


FIG.  148.— METER-PROVER. 

Gas  is  admitted  just  above  the  surface  of  the  water,  and 
raises  the  partition  of  the  chamber,  bringing  it  above  the  water 
and  filling  it.  The  outlet-pipe  is  submerged  until  the  chamber 
is  filled.  It  is  connected  with  the  case  of  the  meter,  as  shown 
in  the  figure.  The  gas  is  completely  expelled  as  the  cylinder 
revolves. 


g  232.J        MEASUREMENT  OF  LIQUIDS  AND   GASES.  305 

The  wet-meter  is  a  very  accurate  measure  of  the  gas  pass- 
ing, provided  the  water-level  be  maintained  at  the  constant 
standard  height.  Any  change  of  the  water-level  changes  the 
size  of  the  chambers  accordingly.  The  motion  of  the  cylinder 
actuates  the  recording  mechanism. 


FIG    149.— THE  WET-METER. 

The  Dry  Gas-meter. — The  dry  gas-meter  possesses  the  ad- 
vantage of  not  .being  affected  by  frost,  nor  of  increasing  the 
amount  of  moisture  in  the  gas.  The  dry-meter  is  made  in  vari- 
ous forms,  and  generally  consists  of  two  chambers  separated 
from  each  other  by  partitions.  Each  chamber  is  divided  into 
two  parts  by  a  flexible  partition  which  moves  backwards  and 
forwards,  and  actuates  the  recording  mechanism  as  the  gas 
flows  in  or  out.  This  motion  is  regulated  by  valves  somewhat 
similar  to  those  of  a  steam-engine.  The  gas-meter  is  calibrated 
by  comparing  with  a  meter-prover  as  already  described. 
These  meters  are  not  supposed  to  be  instruments  of  great 
accuracy. 


306  EXPERIMENTAL   ENGINEERING.  [§  233. 

233«  Anemometers. — Instruments  that  are  used  to  measure 
the  velocity  of  gases  directly  are  termed  anemometers.  They 
consist  of  flat  or  hemispherical  vanes  mounted  like  arms  of  a 
light  wheel  so  as  to  revolve  easily.  The  motion  of  the  wheel 
actuates  a  recording  mechanism.  Robinson's  Anemometer, 
which  consists  of  hemispherical  cups  revolving  around  a  vertical 
axis,  is  much  used  for  meteorological  observations. 

A  form  shown  in  Fig.   150  with  flat  vanes,  and  with  the 


FIG.  150. — BIRAM'S  PORTABLE  ANEMOMETER. 

dial  arranged  in  the  centre  as  shown,  or  on  top  of  the  case  in 
various  positions,  is  much  used  as  a  portable  instrument. 

The  dial  mechanism  of  the  anemometer  can  be  started  or 
stopped  by  a  trip  arranged  convenient  to  the  operator  ;  in  some 
instances  the  dial  mechanism  is  operated  by  an  electric  current 
similar  to  that  described  in  connection  with  the  tachometer, 
Article  221,  page  262.  It  is  also  made  self-recording,  by  attach- 
ing clock-work  carrying  an  endless  paper  strip  which  is  moved 
under  a  pencil  operated  by  the  anemometer  mechanism. 


§  234-J        MEASUREMENT  OF  LIQUIDS  AND   GASES.  307 

234.  Calibration  of  Anemometers. — Anemometers  are 
calibrated  by  moving  them  at  a  constant  velocity  through  still  air 
and  noting  the  readings  on  the  dials  for  various  positions.  This 
is  usually  done  by  mounting  the  anemometer  rigidly  on  a  long 
horizontal  arm  which  can  be  rotated  about  a  vertical  axis  at  a 
constant  speed.  The  distance  moved  by  the  anemometer  in 
a  given  time  is  computed  from  the  known  distance  to  the  axis 
and  the  number  of  revolutions  per  minute ;  from  these  data 
the  velocity  is  computed. 

In  performing  this  experiment  care  must  be  taken  that  the 
axis  of  the  anemometer  is  at  right  angles  to  the  rotating  arm. 
Readings  should  be  taken  at  various  speeds,  since  the  correc- 
tion is  seldom  either  a  constant  quantity  or  one  directly  de- 
pendent on  the  velocity. 

The  Anemometer  can  also  be  calibrated  by  computing  the 
heating  effect  due  to  the  condensation  of  a  given  amount  of 
steam.  The  method  of  calibration  would  be  as  follows:  pass 
the  air  through  a  tube  or  box  containing  a  coil  of  steam-pipe 
sufficient  to  warm  the  air  sensibly,  say  20  or  30  degrees. 
Measure  the  quality  of  the  entering  steam  and  the  amount  of 
condensation,  and  from  that  compute  number  of  heat-units 
taken  up  by  the  air.  Guard  against  all  loss  of  heat  by  the 
air;  then  th's  last  quantity  becomes  evidently  equal  to  the 
increase  in  temperature  of  the  air  multiplied  by  its  specific 
heat,  multiplied  by  its  weight.  From  this  computation  the 
weight  of  the  air  can  be  computed.  Knowing  the  weight  of 
air  and  its  temperature,  compute  the  volume  flowing  in  a  given 
time,  divide  this  result  by  the  area  of  the  cross-section,  and 
obtain  the  velocity.  This  method  is  likely  to  give  more 
satisfactory  results  than  that  of  swinging  the  dynamometer  in 
the  air.  Also  see  Chapter  XXIV,  Art.  490. 


CHAPTER   IX. 
HYDRAULIC    MACHINERY. 

235.  General   Classification. — Hydraulic   machinery  may 
be  divided  into  the  two  clashes,  hydraulic  motors  and  pumps. 
In  the  first  class  a  quantity  of  water  descending  from  a  higher 
to  a  lower  level,  or  from  a  higher  to  a  lower  pressure,  drives  a 
machine  which  receives  energy  from  the  water.     In  the  latter 
class  a  machine  driven  by  some  external  source  of  energy  is 
employed  in  lifting  water  from  a  lower  to  a  higher  level. 

The  student  is  advised  to  consult  the  following  authorities 
on  the  subject : 

Rankine's  Steam-engine ;  article  "  Hydromechanics,"  En- 
cyc.  Britannica;  Weisbach's  Mechanics,  Vol.  II.  (Hydraulics); 
<;  Systematic  Turbine-testing,"  by  Prof.  Thurston,  Vol.  VIII. 
Transactions  Mechanical  Engineers ;  "  Notes  on  Hydraulic 
Motors,"  by  Prof.  I.  P.  Church. 

236.  Hydraulic   Motors — Classification. — The    following 
classes  of  hydraulic  motors  are  usually  recognized : 

I.  Water-bucket  Engines,  in  which  water  poured  into  sus- 
pended buckets  causes  them  to  descend  vertically,  so  as  to  lift 
loads  and  overcome  resistances. 

II.  Water-pressure  Engines,  in  which  water  by  its  pressure 
drives  a  piston  backward  and  forward. 

III.  Vertical  Water-wheels,    in  which    the   water  acts   by 
weight  and  impulse  to  rotate  them  on  a  horizontal  axis. 

IV.  Turbines,  in  which  the  water  acts  by  pressure  and  im- 
pulse to  rotate  them  around  a  vertical  axis. 

V.  Rams  and  Jet-pumps,  in  which  the  impulse  of  one  mass 
of  fluid  is  used  to  drive  another. 

308 


§239.]  HYDRAULIC  MACHINERY.  309 

237.  Energy  of  Falling  Water.  —  Hydraulic  motors  are 
driven  either  by  the  weight,  pressure,  or  impulse  of  moving 
water.  Neglecting  the  losses  due  to  friction  or  other  causes, 
the  energy  of  falling  water  is  the  same  whether  it  act  by  (I.) 
weight,  (II.)  by  pressure,  or  (III.)  by  impulse.  This  is  proved 
as  follows  : 

Let  h  equal  the  head  or  total  height  of  fall,  gthe  discharge  in 
cubic  feet  per  second,  G  the  weight  per  cubic  foot,/  the  pressure 
in  pounds  per  square  foot,  v  the  velocity  in  feet  per  second,  P 
the  pressure  in  pounds  per  square  inch.  Since  the  work  done 
is  equal  to  the  product  of  the  force  acting  into  the  space  moved 
through,  we  have  for  the  work  done  per  second  in  the  several 

cases  (I.)  GQh,  (II.)  (pQ\  (III.)  GQ^-  ;  but  since  p  =  Gh  and 

V* 

h  =  —  ,  we  have  by  substitution 


(I.) 


238.  Parts  of  an  Hydraulic  Power-system.  —  The  hydrau- 
lic power-system  in  general  requires  — 

1.  A  supply-channel  or  tube  leading  the  water   from  the 
highest  accessible  level. 

2.  A  discharge-pipe  or  tail-race  conveying  the  water  away 
from  the  motor. 

3.  Gates  or  valves  in  the  supply-channel,  and  a  waste-chan- 
nel or  weir  to  convey  surplus  water  away  from  the  motor. 

4.  The  motor,  which  may  belong  to  any  of  the  classes  de- 
scribed in  Article  236,  and  suitable  machinery  for  transmitting 
the  energy  received  from  the  motor  to  a  place  where  it  can  be 
usefully  applied. 

239.  Water-pressure  Engines.*—  Water-pressure  engines 
are  well  adapted  for  use  where  a  slow  motion  is  required  and  a 
great  pressure  is  accessible. 

*  See  Weisbach's  Hydraulics,  Vol.  II,  p.  558. 


3io 


EXPERIMENTAL   ENGINEERING. 


[§  240, 


These  engines  resemble  in  many  respects  a  steam-engine, 
water  being  the  motive  force  instead  of  steam.  They  consist 
of  a  cylinder  (Fig.  151)  in  which  a  piston  T  is  worked  alter* 


FIG.  151. — WATER-PRESSURE  ENGINE. 


nately  forward  and  backward,  water  being  admitted  alternately 
at  the  two  ends  of  the  cylinder  by  the  moving  slide-valve  S. 
While  water  is  passing  into  one  end  of  the  cylinder  through 
the  passages  D,  E,  C,  it  is  being  discharged  through  the  pipe 
E,  G,  H,  which  is  proportioned  so  as  to  afford  a  free  exit  to 
the  water.  Near  the  end  of  the  stroke  of  the  piston  the  slide* 
valve  5  closes  both  admission-ports,  and  the  pressure  in  the 
cylinder  Cl  is  increased  by  the  diminution  of  volume  caused 
by  the  motion  of  the  piston.  When  the  pressure  in  the  cham- 
ber £7,  exceeds  that  in  the  supply-pipe  the  valve  Wt  opens, 
and  the  water  passes  into  the  supply.  Simultaneously  the 
valve  Fis  opened  by  suction,  and  water  passes  into  the  cham- 
ber C  from  the  discharge-pipe.  The  effect  of  this  action  is  to 
gradually  arrest  the  motion  of  the  piston  at  the  end  of  the 
stroke  by  reducing  the  pressure  on  one  side  and  increasing  the 
resistance  on  the  other.  When  the  piston  reaches  the  end  of 
the  stroke  the  slide-valve  is  reversed  in  position  and  a  new 
stroke  is  commenced. 

240.  Vertical  Water-wheels. — There  are  four  classes  of 
vertical  water-wheels  : 

I.   Overshot,  in  which  the  water  is  received  on  the  top  of 


§  24i.] 


HYDRA  ULIC  MA  CHINER  Y. 


the  wheel  and  discharged  at  the  bottom,  the  water  acting  prin- 
cipally by  weight. 

2.  Breast,  in  which  the  water  is  received  on  the  side  of  the 
wheel  and  held  in  place  by  a  guide  or  breast,  the  water  acting 
both  by  impact  and  weight. 

3.  Undershot,  in  which  the  water  acts  only  on  the  under 
side  of  the  wheel,  the  water  acting  principally  by  impact. 

4.  Impact,   in  which   the  water  is  delivered  to   the  wheel 
by  a  nozzle,  acting  generally  on  the  top  or  bottom,  and  by  im- 
pulse only. 

241.  Overshot  Water-wheels. — The  overshot  water-wheel 
shown  in  section  in  Fig.  152  is  well  adapted  to  falls  between  10 
and  70  feet  and  to  a  water- 
supply  of  from  3  to  25  cubic 
feet  per  minute.  On  the 
outside  of  the  wheel  is  built 
a  series  of  buckets,  which 
should  be  of  such  a  form  as 
to  receive  the  water  near  the 
top  at  D  without  spilling  or 
splashing,  to  retain  the  water 
until  near  the  bottom,  and  to 
empty  completely  at  the  bot- 
tom. The  number  of  buckets 
must  be  such  that  there  shall 
be  no  spilling  by  overflow  at 
the  top.  The  head  of  water 
above  the  wheel  must  be  sufficient  to  give  the  falling  water 
greater  velocity  than  the  periphery.  The  peripheral  velocity 
in  practice  is  from  5  to  10  feet  per  second,  that  of  the  falling 
water  from  9  to  12  feet  per  second,  corresponding  to  a  height 
of  from  16  to  27  inches  above  the  wheel. 

These  wheels  are  not  adapted  to  run  in  back  water,  and 
have  the  greatest  efficiency  for  a  given  head  when  revolving 
just  free  from  the  discharged  water. 

The  principal  formulae  relating  to  the  overshot-wheel  are  as 
follows  : 


FIG.  152. — SECTION  OF  OVERSHOT  WATER- 
WHEEL. 


3I2 


EXPERIMENTAL   ENGINEERING. 


[§  241. 


Let  d  equal  the  depth  of  the  buckets,  b  the  width  of  the 
wheel,  r  the  radius  of  the  wheel,  n  the  number  of  revolutions 
per  second,  v  the  peripheral  velocity  in  feet  per  second,  Q  the 
water-supply  in  cubic  feet  per  second,  Ql  the  capacity  of  that 
part  of  the  wheel  that  passes  in  one  second,  m  the  ratio  of  the 
water  actually  carried  to  the  capacity  of  the  buckets — m  being 
usually  about  one  fourth — N  the  number  of  buckets. 


-infill 


FIG.  153.— SECTION  OF  BREAST-WHEEL. 

Then,  supposing  the  wheel  to  be  set  just  free  of  the  back 
water, 

h  =  2r  -f-  (i-J  to  2)  all  in  feet ; 


N  =  —r  =  ,  usually,  6r  ; 


bv 
Ql  =  —(2rd—  d*}  =  bdv,  nearly; 


Q  =  mQ,  =mbdv  ; 
v  =  27tnr. 


§  243»]  H  YDRA  ULIC  MA  CHINER  Y.  313 

The  efficiency  is  the  ratio  of  the  work  delivered  to  the  en- 
ergy received  from  the  falling  water. 

The  efficiency  of  the  best  wheels  of  this  class  reaches  75 
per  cent. 

242.  Breast-wheels. — The  form  of  breast-wheel  is  shown 
in  Fig.  153.     The  water  is  received  at  a  height  slightly  above  or 
below  the  centre  C  of  the  wheel,  and  is  prevented  from  falling 
away  from  the  wheel  by  the  curved  breast  ABR\  the  water 
acts  on  the  radial  or  slightly  curved  buckets,  thus  tending  to 
revolve  the  wheel  partly  by  weight  and  partly  by  impulse. 

The  flow  of  water  is  regulated  by  a  gate  at  5. 

The  formulae  applying  to  breast-wheels  are  essentially  the 
same  as  those  for  overshot-wheels.  The  efficiency  of  the  best 
wheels  of  this  class  varies  from  58  to  62  per  cent. 

243.  Undershot-wheels. — The    undershot-wheel    differs 
from  the  breast-wheel  in  receiving  the  water  at  or  near  the 
bottom  ;  the  water  flows  in  a  guide  under  the  wheel,  which  guide 
in  some   cases    extends  some  dis- 
tance up  the  sides.  The  usual  form 

of  such  wheels  is  shown  in  Fig. 
154;  the  buckets  or  floats  are  often 
radial,  sometimes,  however,  of  con- 
cave or  bent  form. 

If  we  let  c  equal  the  velocity  of 
water  as  it  strikes  the  wheel,  v  the 
peripheral  velocity  of  the  wheel,  Q 

the  quantity  Of  Water  in  Cubic  feet  FlG-   J54.— UNDERSHOT-WHEEL. 

per  second,  G  the  weight  per  cubic  foot,  //3  the  portion  of  the 
head  corresponding  to  the  elevation  of  the  entering  water  as  it 
strikes  the  wheel  over  that  of  the  discharge,  P  the  force  de- 
livered at  the  circumference  of  the  wheel ;  then  will  the  effi- 
ciency rj  be  obtained  by  the  following  formulae  :* 

Pv 

Tf  =  — 


*  See  Weisbach's  Hydraulics,  page  291. 


314  EXPERIMENTAL  ENGINEERING.  [§244 

From  experiments  of  Morin  it  was  found  that  when  v  -~  c 
was  less  than  0.63,  the  efficiency  17  was  0.41.  When  v  -f-  c  was 
between  0.63  and  0.8,  rj  was  0.33.  The  efficiency  obtained 
from  the  best  form  of  these  wheels  is  0.55. 

Poncelefs  Wheel.  —  When  the  floats  of  the  undershot  wheel 
are  curved  in  such  a  manner  that  the  entering  jet  of  water  is 
allowed  to  flow  along  the  concave  sides  and  press  against  them 
without  causing  shock,  a  greater  effect  is  obtained  than  when 
the  water  strikes  more  or  less  perpendicularly  against  plane 
floats.  Such  wheels  are  called,  after  their  inventor,  Poncelet 
wheels.  The  efficiency  of  such  wheels  in  some  instances  has 
reached  68  per  cent. 

244.  Impulse-wheels.  —  In  this  class  of  wheels  several  jets 
of  water  impinge  on  the  buckets  of  the  wheel  as  they  are 
successively  brought  into  position  by  the  rotation.  This  class 
is  very  efficient  for  high  heads  and  a  small  supply  of  water. 
The  efficiency  to  be  obtained  by  the  action  of  a  jet  of  water 
on  a  moving  bucket  is  fully  discussed  in  Vol.  II.,  Church's 
"  Mechanics  of  Engineering,"  page  808. 

Denote  by  c  velocity  of  the  jet,  v  the  peripheral  velocity  of 
the  vane,  a  the  angle  of  total  deviation  relatively  to  the  vane 
of  the  stream  leaving  the  vane  from  its  original  direction,  G 
the  weight  per  cubic  foot  of  water,  F  the  area  of  the  stream, 
Q  the  volume  of  flow  per  unit  of  time  over  the  vane.  The 
work  done  per  unit  of  time, 

L  =  Pv  ==  —-(c  —  v)v[i  —  cos  a], 

o 

This  is  maximum  when  v  =  \c. 

In  case  a  hemispherical  vane  is  used,  a  will  equal  180°,  and 
I  —  cos  a  =  2.  For  that  case,  a  =  180°  and  v  =  fc,  we  have 


In  case  the  absolute  velocity  of  the  particles  leaving  the 
vane  equal  zero,  an  efficiency  equal  to  unity  would  be  possible. 


§  245-] 


HYDRAULIC  MACHINERY 


315 


Qne  or  more  jets  of  water  are  used  as  necessary  to  produce 
the  maximum  power.  Fig.  155  shows  the  Pelton  wheel,  provided 
with  four  jets.  The  bucket  of  this  wheel  shown  at  B  is  of  double 
hemispherical  form  with  a  sharp  midriff,  separating  the  two  parts, 
which  splits  the  jet  and  turns  each  part  through  an  angle  of 
1 80°.  The  efficiency  of  is  wheel  has  in  some  instances  ex- 
ceeded 80  per  cent. 


FIG.  155. — THE  PELTON  IMPULSE-WHEEL  WITH  FOUR  JETS. 

There  is  a  large  number  of  motors  in  this  class,  some  of 
which  are  adapted  for  high  heads  and  large  powers.  The  Doble 
wheel  is  provided  with  a  needle  regulating- valve  controlled  by 
the  governor.  The  Cascade  has  buckets  arranged  on  each  side  of 
the  wheel,  the  edge  of  the  wheel  serving  to  divide  the  jet.  Most 
of  the  small  hydraulic  motors  are  of  impulse  type. 

245.  Turbines. -- The  turbine- wheels  receive  water  con- 
stantly and  uniformly,  and  usually  in  each  bucket  simultane- 
ously. The  buckets  are  usually  curved,  and  the  water  is  guided 
into  the  buckets  by  fixed  plates.  The  name  was  originally 
applied  in  France  to  any  wheel  rotating  in  a  horizontal  plane, 
but  the  wheels  are  now  frequently  erected  so  as  to  revolve  in 
vertical  planes.  The  turbine  was  invented  by  Fourneyron  in 
1823,  the  original  wheel  being  constructed  to  receive  water  near 


EXPERIMENTAL   ENGINEERING.  [§246. 

the  axis,  and  to  deliver  it  by  flow  outward  at  the  circumfer- 
ence. Turbines  are  now  built  for  water  flowing  parallel  to  the 
axis,  and  also  inward  from  the  circumference  toward  the 
centre  ;  they  are  also  constructed  double  and  compound.  In 
some  of  the  turbines  the  wheel-passages  or  buckets  are  com 
pletely  filled  with  water,  in  others  the  passages  are  only  partly 
filled. 

The  following  classes  are  usually  recognized  : 

I.  Impulse  Turbines. 

II.  Reaction  Turbines. 

In  both  these  classes  the  flow  may  be  axial  outward,  in- 
ward, or  mixed,  and  the  turbine  may  be  in  each  case  simple, 
double,  or  compound. 

In  the  Impulse  turbines  the  whole  available  energy  of  the 
water  is  converted  into  kinetic  energy  before  it  acts  on  the  mov- 
ing part  of  the  turbine.  In  these  wheels  the  passages  are  never 
•entirely  filled  with  water.  To  insure  this  condition  they  must  be 
placed  a  little  above  the  tail-water  and  discharge  into  free  air. 

In  the  Reaction  turbines  a  part  only  of  the  available  energy 
of  the  water  is  converted  into  kinetic  energy  before  it  acts  on 
-the  turbine.  In  this  class  of  wheels  the  pressure  is  greater  at 
the  inlet  than  at  the  outlet  end  of  the  wheel-passages.  The 
wheel-passages  are  entirely  filled  with  water,  and  the  wheel  may 
be,  and  is  generally,  placed  below  the  water-level  in  the  tail-race. 

246.  Theory  of  the  Turbine.  *  —  The  water  flowing  through 
a  turbine  enters  at  the  admission-surface  and  leaves  at  the  dis- 
charge-surface of  the  wheel,  with  its  angular  momentum  rela- 
tive to  the  wheel  changed.  It  must  exert  a  couple  —M,  tend- 
ing to  rotate  the  wheel,  and  equal  and  opposite  to  the  couple 
M  which  the  wheel  exerts  on  the  water.  Let  Q  cubic  feet  enter 
.and  leave  the  wheel  per  second,  cl  ,  c^  be  the  tangential  com- 
ponents of  the  velocity  of  the  water  at  the  receiving  and  dis- 
charging surfaces  of  the  wheel,  rl  ,  r^  the  radii  of  these  surfaces. 
Then 


(I) 


*  See  "  Hydromechanics,  "  Encyc.  Britannica. 


§  246.]  H  YD  It  A  ULIC  MA  CHINER  Y.  317 

If  a  is  the  angular  velocity  of  the  wheel,  the  work  done  on 

the  wheel  is 

T  —  Ma  =  — —  (clrl  —  cj-^a  foot-pounds  per  second.      (2) 

o 

The  total  head  of  the  water  ht  is  reduced  by  friction  and 
resistances  hp  in  the  channels  leading  to  the  wheel,  so  that 
the  effective  head  h  which  should  be  used  in  calculating  the 
efficiency  is 

h  =  ht-hp (3) 

In  case  the  construction  of  the  turbine  requires  that  it  set 
above  tail-race  d  feet,  the  velocity  of  water  in  the  turbine 
should  be  calculated  for  a  head  of  k—d,  but  the  efficiency  for 
a  head  of  h  feet.  The  work  of  the  turbine  is  partially  absorbed 
in  friction. 

Let  T  equal  the  total  work,  Td  the  useful  work,  and  Tt  the.- 
work  used  in  friction.  Then 

T=Td+Tt (4) 

The  gross  efficiency 


The  hydraulic  efficiency 

T 


The  hydraulic  efficiency  is  of  principal  importance  in  the 
theory  of  turbines.    Substituting  this  value  of  T  in  equation  (2), 


(7) 


which  is  the  fundamental  equation  in  the  theory  of  turbines. 


318  EXPERIMENTAL   ENGINEERING.  [§  247- 

For  greatest  efficiency  the  velocity  of  the  water  leaving 
should  be  o,  in  which  case  ct  =  o  and 


(8) 


But  r,a  is  the  lineal  velocity  of  the  wheel  at  the  inlet  surface  ; 
if  we  call  this  Vl  , 


(9) 


The  efficiency  of  the  best  turbines  is  0.80  to  0.90. 

Speed  of  the  Wheel.— The  best  speed  of  the  wheel  depends 
on  frictional  losses  which  have  been  neglected  in  the  preced- 
ing formulae.  The  best  values  are  the  ones  obtained  by  ex- 
periment. Let  F0  equal  the  peripheral  velocity  at  outlet,  Vt 
at  inlet,  r0  and  rt  the  corresponding  radii  of  outlet  and  inlet 
surfaces.  Then  we  shall  have  as  best  speeds*  for 


axial-flow  turbine          F0  —  V{  =  0.6  V2gh  to  0.66  V2gk ; 


radial  outward-flow  turbine  Vt  =  0.56  Vlgh ;      F0  =  PJ  -  ; 


radial  inward-flow  turbine    Vt  =  O.66  V2gh  ;     F0  =  Vt  -  . 

247.  Forms  of  Turbines. — Fourneyroris  Turbine. — This  is 
an  outward-flow  turbine,  with  a  horizontal  section  as  shown  in 
Fig.  156.  C  is  the  axis  of  the  wheel,  which  is  protected 
trom  the  water  by  vertical  concentric  tubes  shown  in  section. 
On  the  same  level  with  the  wheel  and  supported  by  these 
tubes  is  a  fixed  cylinder,  with  a  bottom  but  no  top.  contain- 
ing the  curved  guides  F  F.  The  wheel  AA  is  supplied  with 
curved  buckets  bd>  b^d, ,  so  arranged  as  to  absorb  most  of  the 
energy  of  the  water ;  the  water  enters  the  wheel  at  the  inner 
edges  of  the  buckets  and  is  discharged  at  the  outer  circum- 

*  "  Hydromechanics  "  Encyc.  Britannica. 


§  248.]  HYDRA  ULIC  MA  CHINE R  Y.  319 

ference.    Gates  for  regulating  the  supply  of  water  are  shown  in 
section  between  the  ends  of  the  guides  and  the  wheel. 


-3—37 

FIG.  156. — OUTWARD-FLOW  TURBINE. 

248.  Reaction -wheels. — The  simple  reaction-wheel  is 
shown  in  Fig.  157,  from  which  it  is  seen  to  consist  of  a  vertical 
cylinder,  CB,  which  receives  the  water,  and  two  cylindric  arms, 
G  and  F\  on  opposite  sides  of  each 
arm  is  a  circular  orifice  through  which 
the  water  is  discharged.  The  effect 
of  this  arrangement  is  to  reduce  the 
pressure  on  the  sides  toward  the  ori- 
fices, thus  producing  an  unbalanced 
pressure  which  tends  to  make  the 
wheel  revolve.  If  we  denote  by  //  the 
available  fall  measured  from  the  level 
of  the  water  in  the  vertical  pipe  to  the 
centre  of  the  orifices,  r  the  radius  of 
rotation  measured  from  the  axis  to  the  FlG-  IS^-THE  REACTION-WHEEL. 
centre  of  each  orifice,  v  the  velocity  of  discharge,  a  the  angular 
velocity  of  the  machine,  F  the  area  of  the  orifices, — when  at 
rest  the  velocity  would  equal  V2gk,  but  when  in  motion  the 
water  in  the  arms  moves  with  a  velocity  ar,  which  corresponds 
to  an  increased  head  due  to  centrifugal  force  of  arV  -f-  2g. 


320  EXPERIMENTAL   ENGINEERING.  [§  24$, 

Hence  the  velocity  of  discharge  through  the  orifices  is 


v  =  V2gh  +  « V  ; 
/he  quantity  discharged 


Since  the  orifices  move  with  a  velocity  ar,  the  velocity  with 
reference  to  a  fixed  point  is  v  —  ar. 

If  G  be  the  weight  per  cubic  foot,  the  momentum  or  mass 
times  the  velocity  is 


This  mass  moves  with  an  angular  velocity  a  and  arm  r,  hence 
the  work  done  per  second  in  rotating  the  wheel  is 

—  (v  —  ar}ar  foot-pounds. 

o 

The  work  expended  by  the  water-fall  is  GQk. 
Hence  the  efficiency 

(v  —  ar\ar 

=  —- 


This  increases  as  ar  increases,  or  the  maximum  efficiency  is 
reached  when  the  velocity  is  infinite.  The  friction  considera- 
bly reduces  these  results,  and  experiment  indicates  the  greatest 
efficiency  when  ar  =  V2gh.  In  which 
case,  by  substitution,  we  should  have 
/;  =  0.828. 

The  best  efficiency  realized  in  prac- 
tice with  these  wheels  is  about  0.60. 

The  Scottish  turbine,  shown  in  Fig. 
1  16  in  section,  is  a  reaction-wheel   with 
FIG,  158.—  SCOTTISH  TURBINE,    three    discharge-jets,    the    water    being 
supplied  from  a  tube  filled  with  water  under  pressure  beneath 
the  wheel. 


g  249-] 


HYDRAULIC  MACHINERY. 


321 


249.  The  Hydraulic  Ram. — The  hydraulic  ram  is  a  ma- 
chine  so  arranged  that  a  quantity  of  water  falling  a  height  h 
forces  a  smaller  quantity  through  a  greater  height  kf. 


FIG.  159.— HYDRAULIC  RAM. 


The  essential  parts  of  the  hydraulic  ram  are :  I.  The  air- 
chamber  C,  connected  with  the  discharge-pipe  eD,  and  pro- 
vided with  a  clack  or  check-valve  o,  opening  into  the  chamber 
C  from  the  pipe  ss. 

2.  The    waste-valve,   Bd>  is   a  weighted    clack   or   check- 
valve,  opening  inward  and  connected  to  a  stem  df\   on  the 
stem  is  a  nut  or  cotter  at  f  to  regulate  the  length  of  stroke,  i.e., 
amount  of  opening  of  the  waste-valve. 

3.  The  supply-pipe  ss,  that  leads  to  a  reservoir  from  which 
the  supply  is  derived,  should  be  of  considerable  length.    If  it  is 
very  short  when  laid  in  a  straight  line,  bends  must  be  made  to 
secure  additional  length,  and  also  to  present  some  resistance  to 
the  backward  wave-motion  ;  its  length  must  not  be  less  than 
five  times  the  supply-head.     The  working  parts  of  the  ram  are 
the  check-valve  o  and  the  waste-valve  dB ;  these  parts  move 
in  opposite  directions,  and  alternately. 

The  action  of  the  ram  is  explained  as  follows : 


322  EXPERIMENTAL   ENGINEERING.  [§  250. 

Water  is  supplied  the  ram  by  the  pipe  ss ;  the  waste-valve 
dB  being  open,  the  water  escapes  with  a  velocity  due  to  the 
height  h.  The  water  escaping  at  ^/ suddenly  closes  the  waste- 
valve.  The  'acquired  momentum  of  the  moving  column  of 
water  in  the  pipe  ss  is  sufficient  to  raise  the  valve  o  and  dis- 
charge a  portion  of  its  weight  to  a  height  h'.  As  soon  as  the 
pressure  is  reduced  the  valve  o  closes,  the  waste-valve  dB  opens 
and  the  water  again  flows  down  the  pipe  ss.  These  motions 
are  produced  with  regularity,  and  the  water  acquires  a  backward 
and  forward  wave-motion  in  the  pipe  ss.  A  small  air-chamber 
at/,  with  a  small  check-valve  opening  inward  at  c  to  supply  the 
chamber  with  air,  are  found  to  add  to  its  efficiency. 

The  wave-motion  has  been  utilized  to  operate  a  piston  back- 
ward and  forward  beyond  the  waste-valve,  the  piston  being 
utilized  as  a  pump  in  raising  water  from  a  different  supply. 

Formula. — Let  h  equal  the  height  of  the  reservoir  above 
the  discharge-valve  of  the  ram,  h'  the  height  to  which  the 
water  is  raised  above  reservoir,  Q  the  total  water  supplied  to 
the  ram  per  second,  q  the  amount  raised  to  the  height  //,  G  the 
weight  per  cubic  foot.  Then  the  useful  work  equals  Gqh' ;  the 
work  which  the  water  is  capable  of  doing  equals  Gh(Q  —  q). 

The  efficiency 

«*_ 

n~(Q-W 

Rankine  (see  Steam-engine,  page  212)  gives  the  following 
formulae  for  obtaining  the  dimensions  of  a  ram  : 

Let  L  equal  length  of  supply-pipe,  D  the  diameter  of 
supply-pipe  in  feet ;  other  symbols  as  above.  Then 

2hf 


Volume  of  air-chamber  C  equals  volume  of  feed-pipe. 
250.  Methods  o£ Testing  Water-motors. — The  methods 
of  testing  hydraulic  motors  require  in  all  cases  the  measure- 


§25O.]  H  YDRA  ULIC  MA  CHINER  Y.  323 

ment  (l)  of  volume  or  weight  of  the  water  discharged,  (2)  of 
the  net  head,  or  pressure  acting  on  the  motor,  or  (3)  the 
velocity  of  .discharge.  From  these  measurements  may  be  com- 
puted the  energy  received  by  the  motor,  by  the  formulas 
already  given. 

1.  Measurement  of  the  Water  may  be  made  in  the  case  of 
small  motors  by  receiving  the  discharge  in  tanks  standing  on 
scales ;  two  tanks  will  be  required,  one  of  which  is  filling  while 
the  other  is  emptying.     Temperature   observations  must  be 
taken,  and  from  the  known  weight  and  temperature  the  volume 
(Q)  may  be  computed,  if  required.     The  tanks  may  be  previ- 
ously calibrated  by  filling  to  a  known  point,  and    be  so  con- 
nected that  any  excess  will  pass  into  the  tank  recently  emptied, 
in  which  case  a  method  similar  to  the  above  may  be  used  with- 
out scales. 

The  measurement  will  usually  have  to  be  made  by  discharg- 
ing over  weirs  (see  page  2  74)  or  through  nozzles  or  Venturi  tubes; 
this  will  be  especially  true  for  large  motors. 

With  water-pressure  engines  an  approximate  measurement 
may  be  made  by  the  piston-displacement,  corrected  for  slip. 
A  discussion  of  the  effect  of  slip  is  to  be  found  on  page  302. 

2.  Measurement  of  the  Head  (h]  may  be  made,  in  the  first 
place,  by  taking  a  series  of  levels  from  standing  water  in  the 
tank  or  dam  above,  to  the  level  of  the  water  in  the  tail-race. 
This  measurement  must  be  corrected  for  loss  of  head  by  fric- 
tion in  the  .pipes,  or  by  flowing  over  obstructions,  etc.,  this  at 
best  can  be  made  only  in  an  approximate  manner.     To  secure 
the  full  effects  of  the  head,  some  turbine-wheels  are  set  with 
draught  or  suction  tubes  leading  from  the  wheel  to  the  water- 
level  in  the  tail-race  ;  this  will  not  affect  the  method  of  measur- 
ing the  head.    The  head  acting  on  the  wheel  is  measured  most 
accurately  by  a  calibrated  pressure-gauge,  placed  in  the  supply- 
pipe  near  the  motor.     The  reading  of  this  gauge  if  merely  at- 
tached to  the  supply-pipe  in  the  usual  manner,  would  be  that 
due  to  the  pressure-head  only,  and  would  be  less  than  the  true 
head  acting  on  the  pipe.     By  inserting  a  tube  well  into  the 
current,  and  bent  so  as  to  face  the  current,  thus  forming  a  Pitot 


324  EXPERIMENTAL   ENGINEERING.  [§25l- 

tube  (Article  222,  page  292),  the  pressure  will  be  increased  the' 
amount  due  to  the  velocity- head,  and  the  gauge  if  attached  to 
this  tube  will  give  the  pressure  corresponding  to  the  actual  head. 
To  the  head  so  obtained  must  be  added  tke  distance  from  the 
centre  of  the  gauge  to  the  level  of  the  water  in  the  tail-race. 
In  case  the  draught-tube  is  used,  a  vacuum  gauge  or  mercury 
manometer  can  be  attached,  and  the  suction-head  calculated 
from  the  gauge-reading  may  be  compared  with  the  measured 
distance.  In  case  two  gauges  are  used,  the  vertical  distance 
between  them  must  be  measured,  and  considered  a  portion  of 
the  head. 

To  obtain  the  head  corresponding  to  a  given  pressure,  in 
pounds  per  square  inch,  multiply  the  gauge-reading  by  the 
height,  in  feet,  of  water  corresponding  to  one  pound  of  pressure. 

One  pound  of  pressure  per  square  inch  corresponds  to 
2.308,  2.309,  2.31,  2.312,  2.315,2.319,  and  2.32  feet  of  head  of 
water  at  the  temperatures  of  40°,  50°,  60°,  70°,  80°,  90°,  and 
100°  F.,  respectively. 

The  head  of  one  inch  of  mercury  corresponds  to  1.13  feet 
of  water  a.  70°  F. 

Knowing  che  quantity  or  weight  of  discharge  and  the  head, 
the  energy  received  may  be  computed  by  any  one  of  the  four 
forms  in  equation  (i),  Article  237,  p.  309. 

3.  The  velocity  of  discharge  can  seldom  be  measured  directly; 
it  can  be  computed  from  measures  of  the  pressure  or  net  head, 
since  the  velocity  V  =  V2gh.  It  is  rarely  of  importance. 

In  case  the  motor  is  supplied  with  water  through  a  nozzle, 
its  least  area  may  be  determined  by  measurement ;  then  the 
quantity  discharged  may  be  computed  as  the  product  of  ve- 
locity, least  area,  and  coefficient.  (See  Article  204,  p.  275.) 

251.  Special  Tests. — Backus  or  Pelton  Motors. — Apparatus 
needed. — Pressure-gauges,  two  receiving  tanks  on  scales  or  small 
weirs,  Prony  brake,  pipes  to  remove  water,  thermometer. 

Testing  Directions. — Measure  nozzle  ;  note  its  position  and 
the  angle  at  which  jet  will  strike  buckets ;  attach  pressure- 
gauge,  and  arrange  to  measure  discharged  water  ;  attach  Prony 
brake.  Vary  the  head  of  water  by  throttling  the  supply ;  if 


§251.]  H  YDRA  ULIC  MA  CHINE R  Y.  325 

heads  are  required  greater  than  will  be  given  by  the  water-works 
pressure,  they  must  be  supplied  by  pumping  with  a  steam- 
pump.  Take  four  runs  of  one  half-hour  each,  with  heads 
varying  by  one  fourth,  the  greatest  to  be  attained.  Obtain 
corrections  to  head  for  position  of  gauge.  Make  running 
start.  Take  observations  once  in  five  minutes  of  water  dis° 
charged,  temperature,  gauge-readings,  weight  on  Prony  brake- 
arm,  and  number  of  revolutions. 

In  report,  describe  motor,  with  dimensions,  method  of  test- 
ing ;  compute  energy  received  in  foot-pounds  per  minute  and 
in  horse-power  ;  compute  work  done  in  the  same  units  ;  compute 
efficiency  of  each  run,  also  for  varying  velocity  of  perimeter. 
•  Make  a  plot  on  cross-section  paper,  with  work  delivered  in 
foot-pounds  per  minute  as  abscissae,  and  heads  as  ordinates. 
Compare  theoretical  with  actual  efficiency. 

Turbine  Water-wheels. — Large  weirs  must  be  arranged 
with  which  the  discharged  water  can  be  measured.  A  Prony 
brake  is  to  be  arranged  to  absorb  the  power  from  the  wheel, 
or  a  large  transmitting  dynamometer  may  be  provided  to 
receive  the  power  developed  by  the  wheel.  Measurements  to 
:be  made  as  explained  in  Article  250. 

Water-pressure  Engines  are  to  be  tested  essentially  as 
described  for  the  hydraulic  ram.  When  used  to  operate  a 
pump,  indicator-diagrams  are  to  be  taken  from  both  engine  and 
pump  ends,  as  explained  in  the  chapter  on  steam-engine  testing. 
From  these  can  be  computed  the  energy  received  by  the  pistons 
of  the  water-engine  and  that  delivered  from  the  piston  of  the 
pump.  The  quantity  of  water  received  will  have  to  be  meas- 
ured independently. 

Hydraulic  Ram. — Apparatus  as  before,  with  additional 
pressure-gauge  for  discharge-pipe,  means  of  measuring  the 
water  delivered  and  the  water  wasted. 

Testing. — Measure  head  of  water  acting  on  the  ram  and  of 
that  delivered  as  explained.  Make  runs  of  one  half-hour 
each,  with  varying  heads  of  supply  and  delivery.  Take  ob- 
servations once  in  five  minutes  of  gauge  on  supply-pipe,  on 


326 


EXPERIMEN  TA  L   ENGINEERING. 


[§  252. 


delivery-pipe,  of  weir-readings  or  weights  of  water  wasted,  and 
of  water  delivered.  Compute  the  energy  received  and  work 
done  expressed  in  foot-pounds  per  minute,  and  also  the  effi- 
ciency for  each  run. 

In  Report. — Describe  the  ram,  method  of  testing,  and  draw 
a  curve,  with  heads  as  ordinates  and  foot-pounds  of  work  as 
abscissae. 

252.  Forms  for  Tests  of  Hydraulic  Motors. — The  fol- 
lowing form  for  log  and  results  has  been  used  by  the  author : 


Efficiency  test  of Water-wheel. 

Type Capacity Diam «. 

At...  \ 

Date Bn 

Length  of  Brake-arm. ft. ;    Weir  zero ;    Temp.  Water °  F. 


Q  = 


DATA. 


4 

h 

d 

Q 

IV 

P 

D 

D.H.P. 

Efficiency, 
per  cent. 

Ratio  of  velocity 
of  periphery  of 
wheel  to  veloc- 
ity due  to  head. 

g 

a 

H 

Gate 
Opening. 

Head  on 
Wheel. 

%  . 

H 

0 

Water 

used. 

Brake-load 
(net). 

Revolutions 
per  minute. 

H.  P.  de- 
veloped by 
Wheel. 

Lbs. 

Ft. 

Cu.  ft. 
per  sec. 

Lbs.  per 
min. 

Form  and  dimensions  of  Buckets 

Number  of  Buckets Form  of  Delivery-tube. 

Diameter. .  


The  following  form  for  test  of  the  Swain  turbine  is  used  at 
the  Massachusetts  Institute  of  Technology : 


253J 


HYDRAULIC  MACHINERY. 


327 


No. 


TEST   ON   SWAIN   TURBINE. 

Date ..188, 


Time. 

Read- 
ing of 
Coun- 
ter. 

Revolu- 
tions 
per  

Minutes. 

Load 
on 
Brake. 

Height 

Water 
in 
Tank. 

Height 
of 
Water 
in 
Wheel- 
pit. 

Read- 
ing of 
Hook- 
gauge. 

fHook-H 
I  gauge  I 
1   Read-f 
I    ing.    J 

Tem- 
pera, 
lure  in 
Wheel- 
pit. 

Total 

Corrected 

Diameter  of  wheel ft.         Radius  of  brake ft. 

Crest  of  weir  above  floor  of  pit ft. 

Width  of  weir  and  pit ft. 

Correction  for  hook-gauge ft. 


Observed  depth  on  weir  (corrected) .....ft. 

Total  head  acting  on  wheel ft. 

Weight  of  i  cubic  foot  water  at °  Fahr Ibs. 

Revolutions  of  wheel  per  minute 

Quantity  of  water  passing  weir  (uncorrected) cu.  ft. 

"  "  "          "     (corrected) cu.  ft. 

Available  work ft. -Ibs.  per  sec. 

Work  at  brake ft.-lbs.  per  sec. 

Efficiency.... percent. 

Horse-power  of  wheel , 

Velocity  due  to  head  acting  on  wheel ft.  per  sec 

Velocity  of  outside  of  wheel ft.  per  sec 

Signed 

253.  Classification  of  Pumps. — The  different  classes  of 
pumps  correspond  almost  exactly  to  the  different  classes  of 
water-motors,  with  the  mechanical  principles  of  operation 
reversed. 


328  EXPERIMENl^AL   ENGINEERING,  [§  2.34. 

Ordinary  reciprocating  pumps  correspond  to  water-engines; 
chain-  and  bucket-pumps,  to  water-wheels  in  which  the  water 
acts  principally  by  weight.  Scoop-wheels  are  similar  to  under- 
shot water-wheels,  and  centrifugal  pumps  to  turbines.  The 
various  classes  of  pumps  are  as  follows : 

A.  Reciprocating,  divided  according  to  the  method  of  con- 
struction into  lift,  force,  combined  lift  and  force,  double-acting, 
and  diaphragm. 

B.  Rotary,  divided  into:  (i)  inferential,  in  which  the  water 
is  urged  forward  by  the  velocity  of  the  working  parts  of  the 
pump,  as  in  the  centrifugal  pump  ;    (2)  positive,  in  which  all 
the  water  that  passes  the  pump  is  lifted  or  forced  by  the  work- 
ing parts  of  the  pump  to  a  higher  level ;  the  working  parts  of 
these   pumps   are   usually  gears    or    cams    meshing  together. 
These  pumps  are  often  spoken  of  as  rotary,  in  distinction  from 
centrifugal. 

Pumps  are  also  classified  by  the  power  used  to  drive  them. 
Thus,  pumps  driven  directly  by  attached  engines  are  termed 
steam  pumping-engines  or  steam-pumps;  those  driven  from  run- 
ning machinery  by  belts  or  gears  are  termed  power-pumps;  those 
operated  by  hand,  hand-pumps. 

254.  Duty  and  Capacity. — The  term  duty  is  applied  to  the 
work  done  by  steam-pumps.  This  term  originally  signified  the 
number  of  pounds  of  water  lifted  one  foot  by  the  consumption 
of  one  bushel  (94  pounds)  of  coal ;  more  recently  it  has  been 
the  water  lifted  one  foot  by  the  consumption  of  100  pounds  of 
•coal.  It  has,  in  recent  tests,  been  customary  to  assume  that 
each  pound  of  coal  evaporates  ten  pounds  of  water,  from  and 
at  212°,  under  atmospheric  pressure.  As  each  pound  of  water 
evaporated  under  such  conditions  requires  965.7  British  thermal 
units,*  and  each  B.  T.  U.  is  equivalent  to  778  foot-pounds  of 
work,  a  definite  amount  of  work  is  done  by  100  pounds  of  coal, 
equivalent  to  965,700  B.  T.  U.,  or  to  751,314,600  foot-pounds. 

The  duty  of  a  power-pump,  expressed  in  the  same  manner, 


*  A  British  thermal  unit,  symbol  B.  T.  U.,  is  the  heat  absorbed  in  raising 
one  pound  of  water  one  degree  Fahr.  in  temperature. 


§255-]  H  YDRA  ULIC  MA  CHINE R  Y.  329 

k  the  number  of  foot-pounds  of  water  raised  by  751,314,600 
foot-pounds  of  energy  expended  on  the  pump  and  accessories. 

A  committee  appointed  by  the  American  Society  of  Me* 
chanical  Engineers  (see  Vol.  XL  of  Transactions  American 
Society  Mechanical  Engineers,  p.  668)  recommend  that  in  a 
standard  method  of  conducting  duty  trials,  1,000,000  thermal 
units,  or  778,000,000  foot-pounds,  be  taken  as  the  basis  from 
which  the  duty  is  computed.  This  is  equivalent  to  the  evapo- 
ration of  10.35  pounds  of  water  per  pound  of  coal,  from  and 
at  212°,  and  is  likely  to  be  adopted  in  future  trials,  in  which 
case  the  duty  becomes  the  number  of  foot-pounds  of  water 
delivered  for  1,000,000  British  thermal  units  of  energy  supplied 
the  plant. 

The  capacity  of  a  pump  is  usually  expressed  as  the  number 
of  gallons  of  water  that  can  be  raised  against  a  specified  head 
in  24  hours  of  time ;  a  gallon  being  considered  as  equivalent  to 
8.3389  pounds  at  a  temperature  of  39.2°. 

255.  Measurement  of  Useful  Work. — The  useful  work 
done  by  a  pump  is  the  product  of  the  number  of  pounds  of 
water  delivered  into  the  head  through  which  it  is  raised. 

The  head  is  the  total  vertical  distance  in  feet  from  the  sur- 
face of  the  water-supply  to  the  discharge,  increased  by  friction. 
It  is  measured  most  accurately  by  pressure-gauge  connected  to 
a  Pitot's  tube  (p.  292)  with  its  nozzle  facing  the  current  inserted 
in  the  discharge  pipe,  near  the  pump,  and  by  a  vacuum  gauge 
or  manometer  connected  to  the  suction  pipe.  The  head  in 
feet  is  equal  to  the  distance  between  these  gauges  plus  the 
total  readings  of  the  gauges,  reduced  to  equivalent  heads  of 
water  (see  p.  324). 

The  water  delivered  may  be  measured  by  discharging  over 
a  weir,  or  through  a  nozzle  or  tapering  pipe  called  a  Venturi 
tube.  (See  Article  204,  p.  275.) 

The  discharge  through  a  Venturi  tube  may  be  taken  as  98 
per  cent  of  the  theoretical  discharge,  that  through  a  straight 
conical  nozzle  as  97.7  per  cent.* 

*  See  papers  before  Am.  Soc.  Civil  Engineers,  by  Clemens  Herschel,  Nor. 
1887  and  Jan.  1888,  and  by  J.  R.  Freeman,  Nov.  1889. 


330  EXPERIMENTAL   ENGINEERING.  [§256, 

Delivery  measured  from  Piston-displacement. — Slip. — The 
water  delivered  in  the  case  of  piston-pumps  is  often  computed 
by  multiplying  the  total  piston-displacement  during  the  test 
by  I,  minus  the  slip.  The  total  piston-displacement  is  equal  to 
the  product  of  area  of  piston  by  length  of  strokes,  by  total 
number  of  single  strokes.  In  piston-pumps  the  length  of 
stroke  is  often  variable,  in  which  case  especial  means  must  be 
adopted  to  find  the  average  length.  The  slip  is  the  percentage 
that  the  actual  delivery  is  less  than  the  total  piston-displace- 
ment ;  it  can  only  be  determined  accurately  by  comparing  the 
volume  actually  discharged  with  the  total  displacement.  The 
slip  is  caused  by  air  in  suction-pipe,  leakage  past  piston,  leak- 
age past  valves  in  either  suction-  or  discharge-pipe,  and  imper- 
fect port-openings.  The  principal  cause  probably  comes  from 
leakage  past  the  piston,  and  this  leakage  can  often  be  deter- 
mined by  removing  the  cylinder-head,  blocking  the  piston, 
subjecting  it  to  the  water-pressure  for  at  least  one  hour,  and 
measuring  all  the  water  that  leaks  past  it.  This  test  should  be 
repeated  for  various  positions  in  the  stroke.  The  valve  leakage 
can  often  be  determined  by  a  similar  test.  No  air  should  be 
admitted  to  the  suction-pipe. 

A  table  of  percentage  of  slip  is  given  in  Hill's  Manual, 
published  by  the  Harris-Corliss  Engine  Co.,  from  which  it  is 
seen  that  the  slip  for  large  pumps  is  about  two  per  cent,  and 
that  it  varies  from  one  to  five  per  cent. 

256.  Efficiency-tests  of  Pumps. — An  -efficiency-test  will 
require  in  each  case  measurements  of,  firstly,  the  energy  or 
work  supplied  the  pump;  secondly,  the  useful  work  ;  thirdly 
the  lost  work. 

The  difference  in  methods  of  testing  the  various  classes  of 
pumps,  as  described  in  Article  253,  simply  extends  to  the  meas- 
urement of  the  power  supplied  the  pump. 

The  steam-piimp,  or  steam  pumping-engine,\s  to  be  con 
sidered  as  a  combination  of  the  steam-engine  with  a  pump. 
The  power  received  by  the  pump  is  that  delivered  by  the 
engine,  and  is  determined  by  a  steam-engine  test.  The 
method  of  testing  steam  pumping-engines,  and  standard  method 


§257]  H  YDXA  UL1 C  MA  CHINER  Y.  331 

of  making  duty-trials,  as  adopted  by  the  American  Society  of 
Mechanical  Engineers,  will  be  given  under  special  applications 
of  the  method  of  testing  engines. 

The  power-pump  receives  its  energy  from  machinery  in 
operation  ;  the  energy  received  may  be  measured  by  a  stand- 
ardized transmitting-dynamometer  (see  Chapter  VII.),  or,  in 
the  case  of  a  rotary  or  centrifugal  pump,  by  mounting  in  a 
frame  having  a  free  angular  motion,  which  is  unaffected  by  the 
tension  on  the  driving-belt.  The  resistance  to  rotation  is  ob- 
tained by  a  known  weight  on  a  known  arm,  and  the  power 
supplied  in  foot-pounds  is  the  product  of  the  circumference 
that  might  be  described  by  the  arm  as  radius,  number  of 
revolutions,  and  the  weight.  Such  a  framework  is  termed  a 
cradle-dy  narnometer. 

257.  Special  Efficiency-tests — Power-pumps. — Efficiency- 
test  of  Centrifugal  Pumps — Directions. 

Apparatus  needed. — Pressure-gauge  for  delivery,  manometer 
for  suction,  transmission-dynamometer,  thermometer,  weir  for 
discharge. 

Directions. — Connect  suction-pipe  to  supply-tank,  and  ar- 
range discharge  with  throttle-valve  to  deliver  water  over  a 
weir.  Connect  delivery-gauge  to  an  elongated  air-chamber, 
which  in  turn  is  connected  with  the  delivery-pipe,  provided 
with  a  water  gauge-glass  opposite  the  pressure-gauge,  and 
means  of  changing  water-level  and  air-level.*  Connect  manom- 
eter or  vacuum-gauge  to  suction-pipe ;  obtain  vertical  distance 
between  these  gauges.  Arrange  a  standardized  transmission- 
dynamometer  to  receive  the  power,  and  drive  the  pump. 

During  the  test  maintain  the  water  in  the  air-chamber  at 
height  of  centre  of  the  gauge. 

Testing. — Set  the  machinery  in  operation ;  arrange  the 
throttie-valve  to  give  an  approximate  head  of  50  feet.  After 
uniform  conditions  are  assumed,  start  the  run  ;  take  readings 
once  in  five  minutes  of  hook-gauge  at  weir,  of  temperature  of 
water,  of  discharge-gauge,  of  sucticn-guage,  of  dynamometer- 

*See  Test  of  Steam  Pumping-engines. 


332 


EXPERIMEN  TA  L   ENGINEERING. 


[§253. 


or  power-scale.  Continue  the  run  for  one  hour  with  uniform 
pressure  on  discharge-gauge. 

Make  a  second  run  with  an  approximate  head  of  75  feet, 
and  a  third  run  with  an  approximate  head  of  100  feet. 

Report. — In  report,  calculate  efficiency,  duty,  and  capacity 
for  each  head  ;  draw  a  curve  of  each  test,  using  power  in  foot- 
pounds as  ordinates,  and  total  water  delivered  as  abscissae. 
Describe  the  pump  and  method  of  testing. 

Efficiency-test — Rotary  Pump — Directions. — Apparatus  and 
connections  as  for  centrifugal  pump,  the  power  transmitted 
being  measured  either  by  a  transmission-dynamometer,  or  by 
a  balanced  cradle-dynamometer ;  the  water  may  be  measured 
by  a  weir,  or  it  may  be  delivered  into  two  weighing  tanks,  one 
of  which  is  rilling,  the  other  emptying,  and  the  water  weighed. 
Directions  for  the  test  are  as  in  the  preceding. 

258.  Form  for  Log  and  Report  of  Pump-tests. — The 
following  form  for  data  and  report  is  used  at  the  Massachusetts 
Institute  of  Technology  for  log  and  data  of  test  on  Webber 
centrifugal  pump  and  on  rotary  power-pump  : 

TEST   ON   WEBBER   CENTRIFUGAL   PUMP. 


Date. 


"o 

0 

£ 

a' 

H 

Water. 

Heads. 

Emerson  Power-scale. 

Hook-gauge  Read- 
ing. 

§ 

V4 

V     . 

rt  «J 

fb  u 

<*-  c 
o--1 

i| 

«j> 

Q 

Temperature  at 
Weir. 

Suction-gauge,  ins. 
of  mercury. 

Discharge-gauge, 
Ibs.  per  sq.  in. 

Actual  Suction  in 
feet. 

c 

3 

V 

PC 

Is 

o"-< 

< 

Pumping. 

Tare. 

Scale-reading. 

Revolutions 
per  minute. 

Scale-reading. 

Revolutions 
per  minute. 

Total  .  . 

Av  

, 

Cor 

Diameter  discharge-pipe ins. 

Transverse  area  discharge-pipe , sq.  ft. 

Distance  between  gauges. ... . ft 


258.] 


HYDRAULIC  MACHINERY. 


333 


Crest  of  weir  above  bottom  of  channel f: 

Width  of  *veir ft. 

Revolutions  of  pump  per  minute 

Water  pumped  in Ibs. 

Duration  of  test mins 

o   (  Depth  of  water  on  weir ft. 

jg|   (  Temperature  at  weir  (corrected) °  C °  F. 

'Suction-gauge  (corrected) ins.          ft. 

•8       Discharge-gauge  (corrected) Ibs ft. 

Oj     . 

£      Actual  suction ft. 

Actual  head . ft. 

£    (  o,  .   (  Scale-reading „ , Ibs. 

o       6  ^  1 

w    I   s  .5   (  Revolutions  per  minute 

j!    I     o>     (Scale-reading Ibs. 

£    t  H     (  Revolutions  per  minute 

Water  pumped  in minutes Ibs. 

Capacity  in  gallons  per  minute 

Total  work  by  power-scale  (pumping) H.  P. 

Tare H.  P. 

Work  given  to  pump H.  P. 

Work  delivered  by  pump H.  P. 

Efficiency percent. 

Duly  (ft. -Ibs.  per  1,000,000  B.  T.  U.) 

Signed. 

LOG  OF  TEST  ON  ROTARY   PUMP. 
No. .  Date. . 


No.  of 
Gong. 


Total... 
Av.  ... 
Cor.... 


Time. 


Power-scale. 


Pumping. 


Counter 


Revolu- 
tions. 


Weight, 


Tare. 


C.    R.    W. 


Gauges. 


Suction, 

inches 

mercury 


Deliv- 
ery, Ibs. 

per 
sq.  in. 


Orifices. 


Head, 
in  feet. 


Temper- 


334  EXPERIMENTAL   ENGINEERING.  [§  258 

RESULTS   OF  TEST   ON   ROTARY   PUMP. 

* 

No Date 

Duration  of  test , min. 

Power-scale,  pumping,  revolutions  per  minute 

weight... ,...lbs. 

"•          tare,  revolutions  per  minute e.,  .„ 

"  "      weight r Ibs. 

Suction-head  by  gauge inches  mercury ft.  H2O 

Discharge-head  by  gauge Ibs.  per  sq.  in   '" 

Head  on  orifices " 

Temperature °C '  F. 

Revolutions  of  pump  per  minute 

A  rea  of  discharge  at  gauge sq.  f t. 

Vertical  distance  between  gauges ft. 

Diameter  of  orifices,  a.. . .,  b. . . .,  c d. . . .,  e. ...,/....,  £....,  h. . . .,  ?'.... 

Coefficients,  a. . . .,  b. . . .,  c. . . .,  d. . . .,  e. . . . ,  f. .  . .,  g. . . .,  h. . . .,  i. . . . 

Constant  for  power-scale ft. 

Power-pumping,  by  scale H.  P. 

Tare ,....H.  P. 

Power  given  to  pump H.  P. 

Velocity-head  of  discharge ,. ft. 

Total  head  =  press,  heads  -f-  vel.  head  4-  vert.  dist.  bet.  gauges ft. 

Water  pumped Ibs.  per  sec. 

Work  done  by  pump H.  P 

Efficiency  of  pump per  cent. 

Capacity  of  pump  in  gallons  per  minute 

Duty  of  pump  (ft.-lbs.  per  1,000,000  B.  T.  U.) , 

Signed * o  o . « •  • 


II. 

METHODS  OF  TESTING  THE  STEAM-ENGINE. 


CHAPTER   X. 
DEFINITIONS  OF  THERMODYNAMIC  TERMS. 

259.  General  Remarks. — The  methods  of  testing  the 
steam-engine  which  are  given  here  presume  an  accurate 
knowledge  of  the-  principles  of  action  of  the  engine,  an  ac- 
quaintance with  the  details  of  its  mechanism,  and  a  knowledge 
of  the  thermodynamic  principles  which  relate  to  the  transfer' 
mation  of  heat-energy  into  work.  In  connection  with  the 
methods  of  testing,  the  student  is  advised  to  read  one  or  more 
of  the  following  books : 

Manual    of   the    Steam-engine,  by  R.  H.  Thurston.     2  vols. 

N.  Y.,  J.  Wiley  &  Sons. 
Manual  of  Steam-boilers.     Ibid. 
Engine  and  Boiler  Trials.     Ibid. 
Etude  Experimental  Calorimetrique  de  la  Machine  a  Vapeur, 

par  V.  Dwelshauvers-Dery.  Paris,  Gauthier-Villars  et  Fils, 
Steam-engine,  by  D.  K.  Clark.  2  vols.  N.  Y.,  Blackie  &  Co. 
Steam-engine,  by  C.  V.  Holmes,  i  vol.  London,  Longman^ 

Green  &  Co. 
Steam-engine,  by   J.    M.    Rankine.      i    vol.      London,   Chas, 

Griffin  &  Co. 
Steam-making,  by  C.  A.  Smith,     i   vol.     Chicago,  American. 

Engineer. 
Steam-using.     Ibid. 

335 


336 


EXPERIMENTAL   ENGINEERING. 


[§260. 


Steam-engine,  by  James  H.  Cotterill.  London,  E.  &  F.  N.  Spon. 
Thermodynamics,  by  C.  H.  Peabody.  N.  Y.,  J.  Wiley  &  Sons. 
Thermodynamics,  by  De  Volson  Wood.  N.  Y.,  J.  Wiley  & 

Sons. 

Thermodynamics,  by  R.  Clausius.     N.  Y.,  Macmillan. 
Steam-tables,  by  C.  H.  Peabody.     N.  Y.,  J.  Wiley  &  Sons. 
Handy  Tables,  by  R.  H.  Thurston.     N.  Y.,  J.  Wiley  &  Sons. 

260.  Relations  of  Units  of  Pressure. — The  term  pressure, 
as  employed  in  engineering,  refers  to  the  force  tending  to  com- 
press a  body,  and  is  expressed  as*  follows :  (i)  In  pounds  per 
square  inch ;  (2)  In  pounds  per  square  foot ;  (3)  In  inches  of 
mercury ;  (4)  In  feet  or  inches  of  water. 

The  value  of  these  different  units  of  pressure  are  as  follows : 

TABLE  SHOWING  RELATION   BETWEEN   PRESSURE   EXPRESSED 

IN  POUNDS,  AND  THAT  EXPRESSED  IN  INCHES  OF 

MERCURY,  OR  FEET  OF  WATER. 


70°  Fah. 

Pressure  in 

Pressure  in 

pounds  per  sq. 
inch. 

pounds  per  sq. 
foot. 

Inches  of  mer- 
cury. 

Feet  of  water. 

Inches  of  water. 

I 

144 

2.0378 

2.307 

27.68 

2 

288 

4.0756 

4.614 

55.36 

3 

432 

6.1134 

6.921 

83.04 

4 

576 

8.0512 

9-23 

110.72 

5 

720 

10.1890 

IT-  54 

138-40 

6 

864 

12.2268 

13-85 

166.08 

7 

1008 

14.2646 

16.15 

193.76 

8 

1152 

16.3024 

18.46 

221.44 

9 

1296 

18.3402 

20.76 

249.12 

10 

1440 

20.3781 

23.07 

276.80 

The  barometer  pressure  is  that  of  the  atmosphere  in  inches 
of  mercury  reckoned  from  a  vacuum.  At  the  sea-level,  latitude 
of  Paris,  the  normal  reading  of  the  barometer  is  29.92  inches, 
corresponding  to  a  pressure  of  14.7  pounds  per  square  inch. 

Gauge  or  Manometer  pressure  is  reckoned  from  the  atmos- 
pheric pressure. 

Absolute  pressure  is  measured  from  a  vacuum,  and  is  equal 
to  the  sum  of  gauge-pressure  and  barometer  readings  expressed 


§26 1.]     DEFINITIONS  OF   THERMODYNAMIC   TERMS.  33/ 

in  the  same  units.  Absolute  pressure  is  always  meant  unless 
otherwise  specified. 

Pressure  below  the  atmosphere  is  usually  reckoned  in  inches 
of  mercury  from  the  atmospheric  pressure,  so  that  29.92  inches 
would  correspond  to  a  perfect  vacuum  at  sea-level,  latitude  49°. 

261.  Heat  and  Temperature. — The  term  heat  is  used 
sometimes  as  referring  to  a  familiar  sensation,  and  again  as 
applying  to  a  certain  form  of  energy  which  is  capable  of  pro- 
ducing the  sensation.  In  this  treatise  it  is  used  in  the  latter 
sense  only. 

Temperature  is  essentially  different  from  heat,  and  is  merely 
one  of  its  qualities  ;  it  is*"difficult  to  define,  but  two  bodies  are 
of  equal  temperature  when  there  is  no  tendency  to  the  trans- 
fer of  heat  from  one  to  the  other.  Temperature  is  measured 
by  the  expansion  of  some  substance  in  an  instrument  termed 
a  thermometer.  Two  points,  that  of  melting  ice  and  of  steam 
from  water  boiling  at  atmospheric  pressure,  are  fixed  tempera- 
tures on  all  scales  of  thermometry.  The  expansion  between 
these  points  is  divided  into  various  parts  according  to  the 
scale  adopted,  and  each  part  is  termed  a  degree. 

The  following  thermometric  scales  are  in  use  in  different 
portions  of  the  world  : 


Fixed  Points,  Temperature  of  Water. 

Fahrenheit. 

Centigrade. 

Reaumur. 

Degrees  between  freezing  and  boil-  \ 

180 

100 

80 

Temperature  at  freezing  point    

32 

O 

Comparative  length  I  degree  ........ 

9 

«                 «              ti 

5 

IT 
I 

f 

«                 «              « 

| 

4 

j 

^5 

IT 

Degrees  of  temperature  taken  on  one  scale  can  easily  be 
reduced  to  any  other;  thus,  let  tf  be  the  temperature  of  a  body 
on  the  Fahrenheit  scale,  tc  on  the  Centigrade  scale,  and  tr  on 
the  Reamur  scale.  We  shall  have,  from  the  preceding  table, 


3*°; 
-32°); 


338 


EXPERIMEN  TA  L   ENGINEERING. 


[§  262. 


The  Fahrenheit  thermometer  is  used  principally  by  English- 
speaking  people,  and  unless  otherwise  mentioned  is  the  one 
us  id  in  this  treatise. 

The  Thermometric  Substances  principally  used  are  mercury,, 
alcohol,  and  air,  from  the  expansion  of  which  the  temperature 
is  obtained. 

Absolute  Zero. — This  quantity  is  fixed  by  reasoning  as  the 
point  where  gaseous  elasticity  or  expansion  would  be  zero. 
This  is  492°,  more  exactly  491.8°,  of  the  Fahrenheit  scale  or 
273°  -}-*  of  the  Centigrade  scale  below  the  freezing-point  of 
water,  so  that  in  the  Fahrenheit  scale  the  absolute  tempera- 
ture is  460°  +  the  reading  of  the  thermometer,  and  on  the 
Centigrade  scale  273°  -f-  the  reading  of  the  thermometer. 

Absolute  Temperature,  on  any  scale,  is  temperature  reckoned 
from  absolute  zero. 

262.  Specific  Heat. — Specific  heat  is  the  ratio  of  that  re- 
quired to  raise  a  pound  one  degree  in  temperature  compared 
with  that  required  to  raise  one  pound  of  water  from  60°  to  61° 
Fahr. 

Specific  heat  of  water  is  not  quite  constant,  but  varies  as 
follows  i  f 


Centigrade. 

Fahrenheit. 

Specific  Heat. 

Centigrade. 

Fahrenheit. 

Specific  Heat. 

0° 

32° 

1.0072 

30° 

86° 

0.9954 

5° 

41° 

1.0044 

35° 

95° 

0.9982 

10° 

50° 

I.  OOl6 

40 

104° 

I.  0000 

15° 

59° 

I  .0000 

45° 

"3° 

1.008 

20° 

68° 

0.9984 

155° 

311° 

1.046 

25° 

77° 

0.9948 

200° 

392° 

1.046 

Specific  heat  of  saturated  steam  at  atmospheric  pressure 
was  found  by  Regnault  to  equal  0.478.  Investigations  made 
at  Sibley  College  show  that  the  specific  heat  of  superheated 
steam  increases  with  the  pressure  and  temperature. 

The  heat  contained  in  different  bodies  of  the  same  tempera- 


*  Encyc.  Brit.,  Vol.  XI.  p.  573. 


f  See  Peabody's  Steam-tables. 


§  264.]     DEFINITIONS   OF    THERMODYNAMIC   TERMS.  339 

ture,  or  in  the  same  body  in  its  liquid  and  gaseous  condition,  is 
quite  different  and  cannot  be  measured  by  the  thermometer. 
Thus  in  equal  weights  of  water  and  iron  at  the  same  tempera- 
ture, the  heat  in  the  water  is  several  times  that  in  the  iron. 
This  is  known  because  in  cooling  a  degree  in  temperature, 
water  will  heat  a  much  greater  weight  of  some  other  substance. 

263.  Mechanical  Equivalent  of  Heat. — The  experiments 
made  by  Rumford  and  Joule  established  the   fact  that  heat- 
energy  could  be  transformed  into  work,  or  vice  versa.     The  re- 
sults of  Joule's  latest  determination  gave  the  mechanical  work 
equivalent  to  the  heating  of  one  pound  of  water  one  degree  Fahr. 
in  temperature  as  774  foot-pounds,  while  the  later  and  more 
refined  determinations  of  Rowland,  reduced  to  45°  of  latitude 
and  to  the  sea-level,  make  the  mechanical  work  equivalent  to 
the  raising  the  temperature  of  one  pound  of  water  from  62°  to 
63°  Fahr.  to  be  778  foot-pounds.     The  heating  of  one  pound 
of   water  one    degree,  from    39°    to   40°    Fahr.,    is    termed  a 
British  thermal  unit,  B.  T.  U.,  and  this  is  equivalent  in  me- 
chanical work  to  778  foot-pounds.     This  number  is  represented 
by  J  and  its  reciprocal  by  A  throughout  this  work. 

The  heat  needed  for  raising  one  kilogram  of  water  one  de- 
gree Centigrade  is  termed  a  calorie,  and  this  is  equivalent  to 
426.9  foot-pounds. 

In  some  treatises  a  British  thermal  unit  is  the  heat  required 
to  raise  one  pound  of  water  from  62°  to  63°  Fahr.,  which  differs 
little  from  that  defined  above. 

264.  Relations  of  Pressure  and  Temperature  of  Steam, 
— There  is   a  definite   relation  between  the  temperature  and 
pressure  of  steam  in  its  normal  or  saturated  condition.     This 
relation  was  very  carefully  investigated  1836-42  by  M.  V.  Reg- 
nault  in  Paris  by  a  series  of  careful  experiments  made  on  a  large 
scale.     These  experiments  form  the  basis  of  our  experimental 
knowledge  of  the  properties  of  steam. 

The  properties  of  steam  are  also  shown  by  the  thermody- 
namic  laws,  and  are  given  in  tables  of  Rankine,  Clausius,  M.  V. 
Dwelshauvers-Dery,  Peabody,  and  Buel. 

The  following  empirical  formula,  deduced  from  Regnault's 


34°  EXPERIMENTAL   ENGINEERING.  [§  265. 

experiments,  gives  the  relation  between  the  temperature  and 
pressure  of  steam  at  a  latitude  of  45°  : 

For  steam*  from  32°  to  212°  Fahr.  pressure  in  pounds  per 
square  inch, 


in  which  a  =  3.025908,  log  b  =  0.61174,  log  c  =  8.13204  —  10, 
log  a  =  9.998181015  —  10,  log^  =  0.0038134,  T=t  —  32°. 
For  steam  from  212°  to  428°  Fahr., 


in  which  ^  =  3.743976,  log  b,  =04120021,  log  cl  —  7.74168  — 
10,  log  #,=  9.998  56  1  83  1  —  10,  log  ^  =  0.0042454,  T=t  —  2i2°. 
265.  Properties  of  Steam.  —  Definitions.  —  Steam  occurs  in 
two  different  conditions:   I,  saturated  ;  2,  superheated. 

1.  Dry  and  Saturated  Steam,  or,  as  frequently  called,  dry 
steam,  is  the  vapor  of  water  at  point  of  precipitation,  and  may 
be  considered  the  normal  condition  of  steam. 

Saturated  steam  of  any  pressure  is  at  the  lowest  tempera- 
ture and  possesses  the  least  specific  volume  and  the  greatest 
density  consistent  with  that  pressure.  The  slightest  decrease 
in  total  heat  results  in  partial  condensation,  forming  what  is 
termed  moist  or  wet  steam,  in  distinction  from  dry  steam.  Thus 
saturated  steam  may  be  either  wet  or  dry.  The  percentage  of 
dry  steam  in  a  mass  of  wet  steam  is  termed  its  quality. 

2.  Superheated  steam  has  properties  similar  in  every  respect 
to   those    of   a   perfect   gas.      Its   temperature   is   higher,    its 
specific   volume  greater   and    its  density   less  than  saturated 
steam  of  the  same  pressure. 

Steam-tables  give  the  properties  of  dry  saturated  steam  only 
and  usually  arranged  with  absolute  pressure  as  the  argument 
or  given  quantity.  The  important  properties  are  as  follows  : 

(a)  Total  Heat  (symbol,  A).  —  This  is  the  amount  of  heat 
required  to  convert  one  pound  of  water  from  32°  into  saturated 

*  Steam-tables,  by  Prof.  Cecil  H.  Peabody. 


§265.]     DEFINITIONS   OF   THERMODYNAMIC   TERMS,         .341 

steam  at  a  pressure  P.  If  t  is  the  temperature  of  the  steam, 
the  total  heat,  A,  is  calculated  by  an  empirical  formula  based  on 
the  experiments  of  Regnault.  Expressed  in  English  units, 


(b)  Heat  of  the  Liquid  (q)  is  the  number  of  thermal  units 
used  in  heating  one  pound  of  water  from  32°  Fahr.  to  the  tern- 
perature  required  to  generate  steam.     According  to  Regnault, 

q-=.t-\-  0.00002/2  -j-  0.0000003^ 

for  Centigrade  units.     And  according  to  Rankine  for  English 
units  when  tl  is  the  initial  and  t  the  final  temperature, 

q^t-t,  +  o.oooooo  103  [(*  -  39°-03  -  Ci  -  39°-  1)8]- 

(c)  Internal    Latent    Heat    (p).  —  This    is   the   work   done, 
measured  in  thermal  units,  in  separating  the  molecules  of  the 
steam  beyond  the  range  of  mutual  attraction.     It  is  calculated 
from  the  formula 

p  =  1  06  1  —  0.79  it. 

(d)  External  Latent  Heat  (APu).  —  This   is  the  work,  ex- 
pressed   in    heat-units,   of    expanding   the    steam    against    an 
external  pressure  which  is  equal  to  that  of  the  steam  generated. 
Thus,  let  u  =  s  —  cr  be  the  difference  in  volume  of  a  pound  of 
steam,  s,  and  a  pound  of  water,  cr,  at  any  pressure  per  square 
foot,  P.    Then  the  work  of  expansion  will  be  Pu  foot-pounds  or 
APu  thermal  units.     According  to  Zeuner, 

APu  —  20.91  +  1.096(2  —  q). 

(e)  Heat  of  the  Steam  (L\—  This  is  the  heat  which  the  steam 
actually  contains  ;  it  is  the  total  heat  less  the  external  latent 
heat.     In  thermal  units, 

L  =  A  —  APu  —  q-\-p,     since     \-q-\-APu-\-p. 


342^  EXPERIMENTAL  ENGINEERING.  [§266. 

(/)  Heat  of  Vaporization,  or  total  latent  heat,  (r,)  is  that  por- 
tion of  the  total  heat  which  is  required  to  convert  one  pound 
of  water  at  any  temperature  into  saturated  steam  at  the  same 
temperature  and  at  a  pressure  P\  it  is  the  sum  of  external 
and  internal  latent  heats,  or  the  total  heat  less  the  heat  of  the 
liquid.  That  is, 


r  —  p--u  =      —  q. 
A  formula  for  calculating  r  is 

r  =  1081.4  +  0.305/  —  q. 


Specific  Volumes  and  Density  of  Steam.  —  These  quanti 
ties  are  usually  calculated  from  thermodynamic  equations, 


dt 


s  j=  volume  of  one  pound  of  steam,  <r  =  volume  of  one  pound 
of  water. 

It  will  be  noticed  that  the  different  steam  tables  differ 
principally  in  respect  to  these  quantities. 

THERMODYNAMIC   CONDITIONS,  TEMPERATURE  AND 
ENTROPY. 

266.  Isothermal  is  a  term  used  to  denote  a  condition  in 
which  the  temperature  remains  constant ;  the  total  amount  of 
heat,  or  the  pressure,  may  vary. 

Adiabatic  is  a  term  used  to  denote  the  condition  in  which 
the  total  quantity  of  heat  is  unchanged  by  heat-transfer.  It 
may,  however,  be  changed  by  transformation  into  work  and 
vice  versa. 

Temperature  is  the  scale  used  to  determine  the  relative 
values  of  different  isothermal  conditions ;  and  change  of  tern 


§266.]     DEFINITIONS   OF    THERMODYNAMIC   TERMS.  343 

perature  is  the  change  which  occurs  in  passing  from  one 
isothermal  condition  to  another. 

Entropy  is  the  scale  used  to  determine  the  relative  values 
of  different  adiabatic  conditions  ;  and  change  of  entropy  is  the 
change  which  occurs  in  passing  from  one  adiabatic  condition 
to  another. 

Change  of  temperature  can  be  measured  by  the  expansion 
of  some  thermometric  substance  ;  but  change  of  entropy,  which 
is  just  as  real,  cannot  be  measured  or  represented  in  any  sim- 
ple manner.  If  we  represent  the  entropy  by  0,  the  absolute 
temperature  by  T,  the  heat  at  any  adiabatic  condition  by  Q, 
then  by  the  second  law  of  thermodynamics 


In  case  of  a  liquid,  dQ  =  cdq,  in  which  c  is  the  specific  heat, 
and  q  the  temperature.  In  this  case  denote  the  entropy  by  6. 
Then 


•- 


For  water  this  is  readily  calculated. 

In  the  case  of  steam  the  entropy,  or  change  of  entropy 
from  water  at  the  freezing-point  to  steam  at  any  pressure  is 
equal  to  the  entropy  of  the  liquid,  0,  plus  that  of  the  steam, 

JtTT* 

-~r.     In  which  x  is  the  quality  of  the  steam,  or  per  cent  of  dry 
steam. 

* 

In  this  case 


xr   ,    n      xr 


C  cdt 
J      T' 

c/  o 


In  any  other  case 


344  EXPERIMENTAL  ENGINEERING.  [§267. 

Change  of  entropy, 


A  short  table  giving  the  value  of  the  entropy  of  the  liquid 
is  to  be  found  in  Article  230,  page  301. 

267.  Steam-tables.  —  The  numerical  values  representing 
the  various  properties  of  steam,  in  relation  to  its  pressure,  are 
arranged  in  the  form  of  tables  termed  steam-tables.  The  rela- 
tive accuracy  of  these  various  steam  tables  is  discussed  at 
length  by  Prof.  D.  S.  Jacobus  in  Vol.  XII.  Transactions  of 
American  Society  Mechanical  Engineers,  page  590,  from  which 
it  is  seen  that  the  table  compiled  by  Mr.  Chas.  T.  Porter  rep- 
resents the  experimental  investigations  of  Regnault  most  accu- 
rately ;  but  that  possibly  for  scientific  investigations  the  tables 
of  Peabody,  Dery,  and  Buel,  which  are  founded  on  thermo- 
dynamical  laws,  are  somewhat  more  accurate.  Practically  the 
tables  are  accordant  for  all  working  pressures  and  temperatures 
of  steam  ;  the  difference  is  principally  in  the  values  given  for 
the  density.  The  tables  of  Chas.  T.  Porter*  have  been  adopted 
as  the  tables  to  be  used  in  reporting  results  of  boiler  trials 
and  of  duty  trials  of  pumping  engines,  by  the  American 
Society  of  Mechanical  Engineers  (see  Transactions,  Vol.  VI., 
and  also  Vol.  XII.),  and  for  such  tests  the  standard  reports 
should  be  calculated  from  those  tables.  These  tables  are,  how- 
ever, deficient  for  scientific  purposes,  since  they  omit  values  of 
some  of  the  important  properties  of  steam.  In  the  Appendix 
is  printed  the  table  by  Porter,  and  also  the  table  by  Buel  as 
printed  in  Weisbach's  work  on  the  steam-engine  and  in  Vol.  I. 
of  Thurston's  Manual  of  the  Steam-engine. 

*  The  Richards  Steam  -engire  Indicator,  by  Chas.  T.  Porter. 


CHAPTER   XI. 


MEASUREMENT   OF   PRESSURE. 


268.  Manometers. — The   term    manometer    is    frequently 
applied   to  any  apparatus   for  the  measurement  of  pressure, 
although    it    is   the    practice    of   Ameri- 
can  engineers  to  use  this  term  only  for 

short  columns  filled  with  mercury  or 
water  and  used  to  measure  small  press- 
ures. The  pressure  is  measured,  in  all 
manometers  used  for  engineering  pur- 
poses, above  the  atmospheric  pressure,  and 
this  determination  must  be  increased  by 
the  pressure  equivalent  to  the  barometer- 
reading  to  give  absolute  pressure.  The 
manometers  in  common  use  are  glass  or 
metal  tubes,  either  U-shape  in  form  as  in 
Fig.  160,  or  straight  and  connected  to  a 
cistern  of  large  cross-section  as  shown  in 
Fig.  162. 

Pressures  below  the  atmosphere  can 
be  measured  equally  well  by  connecting 
to  the  long  branch  of  the  tube  and  leav- 
ing the  short  branch  open  to  the  atmos- 
phere. 

269.  U-shaped  Manometer. — In  the 

U-shaped  tube,  with  any  form  as  shown  in  Fig.  160  or  Fig.  161, 

345 


FIG.  160.— I/-SHAPED  MA- 
NOMETER-TUBES. 


34-6  EXPERIMENTAL   ENGINEERING.  [§  269. 

» 

water  or  mercury  is  poured  in  both  branches  of.  the  tube,  the 
pressure  is  applied  to  the  top  of  one  of  the  tubes, 
and  the  liquid  rises  a  corresponding  distance  in  the 
other.  When  no  pressure  is  applied,  the  liquid  will 
stand  at  the  same  level  in  both  tubes  ;  when  pressure 
is  applied,  it  is  depressed  in  one  tube  and  raised  in 
the  other.  The  pressure  corresponds  to  the  vertical 
distance  between  the  surface  of  the  liquid  in  the 
two  tubes  and  can  be  reduced,  as  explained  in  Arti- 
cle 260,  to  pounds  of  pressure  per  square  inch. 

An  inch  of  water  at  a  temperature  of  70°  Fahr. 
corresponds  to  a  pressure  of  0.036  pound  ;  an  inch 
of  mercury,  to  0.493  pound.  The  principle  of  ac- 
tion of  the  U-shaped  manometer-tubes  is  as  follows  : 
Consider  the  atmospheric  pressure  as  acting  on 
one  side  of  the  tube,  and  the  pressure  which  is 
to  be  measured  and  which  is  greater  or  less  than 
-  atmospheric  as  acting  on  the  other  side.  The  total 
NOMETER.  absolute  pressure  in  each  branch  of  the  tube  must  be 
equal,  consequently  enough  liquid  will  flow  from  the  side  of  the 
greater  to  the  side  of  the  less  to  maintain  equilibrium.  Thus 
let  /  be  the  atmospheric  pressure  ;  /,  ,  the  absolute  pressure 
to  be  measured,  expressed  in  inches  of  water  or  mercury  ;  //, 
the  height  of  the  column  on  the  side  of  the  atmosphere;  hlt 
the  height  on  the  side  of  the  pressure.  Then 


from  which 


The  U-shaped  tube,  in  construction  similar  to  Hoadleys 
draught-gauge,  Art.  275,  can  be  used  with  two  liquids  of  .dif- 
ferent densities,  using  the  heavier  liquid  on  the  side  of  the 
lighter  pressure.  Let  dl  denote  the  density  of  the  lighter 
liquid,  and  d  that  of  the  heavier;  //,  and  h,  the  corresponding 


§  2/O.J  MEASUREMENT  OF  PRESSURE.  347 

heights  of  the  columns.      We  shall  have  as  before,  taking  all 
measurements  from  the  lower  surface  of  the  heavier  liquid, 


from  which 

p^  —  p  —  h.d,  —  hd. 

This  instrument  is  much  more  delicate  and  is  better  suited 
for  measuring  small  differences  of  pressure  than  when  a  single 
liquid  is  used  ;  the  reason  for  which  will  be  readily  seen  if  we 
consider  an  example.  Suppose  that  water  be  used  as  the 
heavier  liquid,  of  which  the  specific  gravity  is  I,  and  that 
crude  olive-oil  be  used  as  the  lighter  liquid,  of  which  the 
specific  gravity  is  0.916.  Suppose  that  all  pressures  are  meas- 
ured in  equivalent  height  of  a  water  column  expressed  in 
inches,  and  that  h  —  6  inches,/,  —  p  =  -J  inch  ;  then  hl  ,  which 
is  the  difference  of  level  of  the  water  in  the  two  branches,  will 
be  j-  -f-  6.(o.9i6)  =  6.0  inches,  whereas  it  would  have  been  but 
one-half  inch  had  there  been  only  water,  or  0.545  if  the  liquid 
had  been  olive-oil.  By  making  the  density  of  the  liquids  more 
and  more  nearly  equal  the  instrument  will  become  more  and 
more  delicate.  A  dilute  mixture  of  water  and  alcohol  of  which 
the  density  must  be  determined  (see  Article  275,  page  354),  for 
the  heavier,  and  of  crude  olive-oil  for  the  lighter,  gives  excel- 
lent results.  If  the  instrument  can  be  so  manipulated  that 

" 


and  the  calculation  becomes  very  simple,  as  in  that  case  the 
reading  would  have  to  be  multiplied  only  by  the  differences  o£ 
the  densities  of  the  two  liquids. 

270.  Cistern-manometer.  —  In  the  case  of  a  manometer  oi 
the   form    of    Fig.  162   or  Fig.  163,  the  cistern  or  vessel  into 


348 


EXPERIMENTAL   ENGINEERING. 


[§  270. 


which  the  tube  is  connected  has  a  large 
that  of  the  tube.  Pressure  is  applied  to 
the  top  of  the  liquid  in  the  cistern,  the 
surface  of  which  will  be  depressed  a  small 
amount,  and  the  liquid  in  the  tube  will 
be  raised  an  amount  sufficient  to  balance 
this  pressure.  The  pressure  corresponds 
to  the  vertical  distance  from  the  surface 
of  the  .liquid  in  the  tube  to  that  in  the 
cistern.  As  the  liquid  is  not  usually  in 
sight  in  the  cistern,  a  correction  is  neces- 
sary to  the  readings  in  order  to  find  the 
correct  height  corresponding  to  a  given 
pressure.  This  correction  is  calculated 
as  follows :  Let  A  equal  the  area  of  sur- 
face of  the  liquid  in  the  cistern,  a  the 
area  of  the  manometer-tube,  H  the  fall 
of  liquid  in  the  cist-em,  h  the  correspond- 
ing rise  of  liquid  in  the  tube,  b  the  height 
required  for  one  pound  of  pressure  (see 
Article  260,  page  336),  p  the  number  of 
pounds  of  pressure.  We  have  then 

H4-h 


area  relative  to 


FIG.    162. — CISTERN-MANOM- 
ETER. 


and  since  the  tube  is  supplied  by  liquid  from  the  cistern, 

HA  =  ha. 

Eliminating  H  in  the  two  equations, 

Apb 


A+a 


If  p  ~  one  pound, 


MEASUREMENT  OF  PRESSURE. 


349 


which  is  the  length  the  graduation  should 
be  made  to  allow  for  fall  of  mercury  in  the 
cistern  and  give  a  value  equal  to  one  pound 
of  pressure. 

To  make  this  correction  uniformly  ap- 
plicable the  area  of  cross-section  of  both 
tube  and  cistern  should  remain  uniform. 

271.  Mercury  Columns. — Mercury    col- 
umns, as  used  in  the  laboratories,  are  usually 
made  on  the  principle  of  the  cistern-manom- 
eter.    The   tube  is  very  long  and  made  of 
glass  or  steel  carefully  bored  out  to  a  uniform 
diameter.     If  the  tube  is  of  glass,  the  height 
of    mercury  can    be    readily  perceived    and 
read  ;  if  of  steel,  the  height  of  the  mercury 
is  usually  obtained  by  a  float,  which  in  some 
instances  is   connected  to   a   needle    which 
moves  around  a  graduated  dial. 

In  some  of  these  instruments  electric  con- 
nections are  broken  whenever  the  mercury 
passes  a  certain  point,  and  an  automatic 
register  of  the  reading  is  made.  Fig.  163 
shows  the  usual  form  of  the  mercury  col- 
umn, in  which  the  pressure  is  applied  in  the 
upper  part  of  the  cistern,  so  as  to  come 
directly  on  the  top  of  the  mercury.  In  the 
case  of  a  glass  column  the  graduations  are 
usually  made  on  an  attached  scale,  and  are 
corrected  as  explained  in  Article  270  for  the 
fall  of  mercury  in  the  cistern. 

272.  Corrections  to  the  Mercury  Col- 
umn.— The  mercury  column  is  usually  the 
standard  by  which   all  pressure-gauges   are 
compared,    and     its     accuracy    should     be 
thoroughly  established  in  every  particular. 

The  requirements  for  an  accurate  mer- 
cury column  are : 


85" 


30 


EPl 


FIG.  163.— MERCURY 
COLUMN. 


350 


EXPERIMENTAL    ENGINEERING. 


272. 


1.  Uniform  bore  in  cistern  and  tube. 

2.  Accurate  graduations,  spaced  as  explained  in  Article  270. 
As  it  is  impossible  to  make  the  graduations  perfectly  accurate, 
the  error  in  this  scale  should  be  carefully  determined,  and  the 
readings  corrected  accordingly. 

The  corrections  to  the  readings  are : 

i.  For  expansion  of  the  mercury  and  tube  due  to  increase 
of  temperature. 

The  method  of  correcting  for  expansion  of  the  mercury  and 
the  material  enclosing  it  would  be  as  follows  : 

Let  A  equal  the  coefficient  of  lineal  expansion  of  the  mer- 
cury, and  3/1  that  of  the  cubical  expansion  per  degree  Fahr. ; 
let  d  equal  the  coefficient  of  lineal  expansion  of  the  metal  of 
the  cistern,  and  6'  that  of  the  metal  of  the  tube.  Let  H'  equal 
the  depression  in  the  cistern,  h'  the  corresponding  elevation  in 
the  tube  corresponding  to  a  pressure  of  one  pound,  and  a 
difference  of  level  of  b' .  Let  b  equal  the  difference  of  level 
corresponding  to  a  pressure  of  one  pound  at  a  temperature  of 
60°  Fahr.  Then,  as  before, 


h'  = 


A'V  A(i  +  26)6(1  +  3A) 


A' 


2.  Correction  for  the  capillary  action  of  the  tube.  This  force 
depresses  the  mercury  in  the  tube  a  distance  which  decreases 
rapidly  as  the  diameter  increases. 

The  amount  of  this  depression  is  given  in  Loomis's  Meteor- 
ology as  follows : 


Diameter  of 
Tube. 
Inch. 

Depression. 
Inch. 

Diameter  of 
Tube. 
Inch. 

Depression. 
Inch. 

0.05 

0.295 

0.40 

0.015 

0.10 
0.15 
O.2O 

o.  141 

0.087 
0.058 

0.45 
0.50 
0.6o 

O.OI2 
0.008 
0.004 

0.25 
0.30 

O.O4I 
0.029 

0.70 
0.8o 

O.OO23 
0.0012 

0-35 

O.O2I 

§  2/3-]  MEASUREMENT  OF  PRESSURE.  35  I 

3.  There  might  also  be  considered  a  very  slight  correction 
due  to  the  fact  that  the  force  of  gravity  in  different  latitudes 
varies  somewhat.     Since  the  weight  of  a  given  mass  of  mercury 
is  equal  to  the  product  of   the  mass  into  the  force  of  gravity,  it 
will  vary  directly  as  the  force  of  gravity,   or,  in   other  words, 
the   assumed   weight   of   mercury   may   not   be    exactly  correct. 
This  correction  is  a  refinement  not  necessary  in  usual  tests. 

4.  Difference   of   barometer-readings    at   top    and   bottom  of 
the  tube  might  make  some  difference. 

While  it  is  well  to  give  all  these  corrections  their  true 
weight,  yet  a  false  impression  should  not  be  incurred  concerning 
their  importance.  It  is  hardly  probable  that  the  corrections  for 
change  in  temperature,  or  corrections  for  the  difference  in  the 
force  of  gravity  from  that  at  the  sea-level  on  the  equator,  would 
in  any  event  make  a  sensible  difference  in  the  readings. 

273.  Direct-reading  Draught-gauges.  —  The  ascending 
force  which  causes  smoke  or  heated  air  to  rise  in  a  chimney  is 
called  the  draught.  The  pressure  in  such  a  case  is  below  that 
of  the  atmosphere,  and  is  usually  measured  in  inches  of 
water.  Draught-gauges  are  U-shaped  manometers  adapted  to 
measure  pressures  less  than  that  of  the  atmosphere.  See  Figs. 
1 60  and  161.  To  use  this  manometer,  water  is  poured  into  the 
tube  until  it  stands  at  the  point  marked  o,  Fig.  161;  one  side 
is  then  connected  by  a  pipe  to  the  flue  or  chimney  of  which 
the  draught  is  to  be  measured.  The  difference  of  level  of  the 
.water,  as  shown  by  the  manometer-tubes,  is  the  draught  ex- 
pressed in  inches  of  water.  An  inch  of  water  at  a  temperature 
of  70°  Fahr.  corresponds  to  0.036  pound. 

Allerts  Draught- gauge. — A  very  complete  draught-gauge  of 
the  U-shaped  manometer  type,  with  attached  thermometer  and 
a  movable  scale  the  zero  of  which  can  be  set  to  correspond  to 
the  lower  water  surface,  is  shown  in  Fig.  164  as  designed  by 
J.  M.  Allen  of  the  Hartford  Boiler  Insurance  Co. 

A  draught-gauge  designed  by  the  author  is  shown  in  Fig. 
1640,  which  is  arranged  so  that  one  scale  will  give  difference  in 
elevation  of  the  liquid  in  the  two  columns.  This  is  accomplished 


352 


EXPERIMENTAL  ENGINEERING. 


[§  274- 


by  setting  the  collar  F  to  the  lower  meniscus  of  the  liquid  by  the  screw 
E\  then  by  setting  the  collar  H  to  the  meniscus  of  the  liquid 
in  the  other  column  by  means  of  the  micrometer- screw  R,  the 
height  of  the  column  may  be  read  on  the  attached  scale  and  the 


FIG.  164. — DRAUGHT-GAUGE. 


FIG.  1640. — DRAUGHT-GAUGE. 


micrometer-screw  R.  The  reflection  from  the  two  edges  of  the 
meniscus  enables  the  scales  to  be  set  with  great  accuracy.  The 
inches  and  tenths  of  inches  are  read  on  the  attached  scale,  the 
hundredths  of  inches  by  the  graduations  of  the  micrometer- screw  R. 
274.  Draught-gauges  with  Diagonal  and  Level  Scales. 
—  Pedet's  Draught- gauge. — A  draught-gauge  with  diagonal  scale 
is  shown  in  Fig.  165.  It  consists  of  a  bottle,  A,  with  a  mouth- 
piece near  the  bottom  into  which  a  tube,  EB,  is  inserted  with  any 
convenient  inclination.  The  upper  end  of  the  tube  is  bent  up- 
ward, as  at  BK,  and  connected  with  a  rubber  tube,  KC,  leading 
to  the  chimney.  The  tube  is  fastened  to  a  convenient  support, 


2750 


MEASUREMENT  OF  PRESSURE. 


353 


and  a  level,  D,  is  attached.  To  use  the  instrument,  first  level 
it,  note  reading  of  scale,  then  attach  it  to  the  chimney,  and 
take  the  reading,  which  will  be,  if  the  inclination  is  one  to  five, 


FIG    166. — HIGGINS'S  DRAUGHT- 
GAUGE. 


FIG.  165. — DRAUGHT-GAUGE. 

five  times  the  difference  of  level  in  the  bottle  and  tube.  The 
scale  should  be  graduated  to  show  differences  of  level  in  the 
bottle,  and  thus  give  the  pressure  directly  in  inches  of  water. 

Higginss  Draught-gauge. — Another  form  of  this  class  of 
draught-gauges  is  shown  in  Fig.  166,  as  designed  by  Mr.  C.  P. 
Higgins  of  Philadelphia.  The  gauge  «  « 

is  filled  with  water  above  the  level  of  e 
the  horizontal  tube,  in  such  a  manner 
as  to  leave  a  bubble  of  air  about  one- 
half  inch  long  near  one  end  of  the  hori- 
zontal tube  when  the  water  is  level  in 
the  side  tubes.  The  inside  diameter 
of  the  vertical  tubes  being  the  same,  say  one-half  inch,  and  that 
of  the  horizontal  tube  one  eighth  of  an  inch,  a  draught  equivalent 
to.  one  inch  in  water,  or  which  will  cause  the  water-level  in  the 
vertical  tubes  to  vary  one  inch,  will  cause  the  bubble  in  the 
tube  to  move  eight  inches  in  the  horizontal  tube.  In  general 
the  air-bubble  moves  a  distance  inversely  proportional  to  the 
area  of  the  tubes,  and  hence  it  can  be  read  more  accurately 
than  in  case  of  the  ordinary  draught-gauge. 

275.  Hoadley's  Draught-gauge. — This  gauge  was  used  in 
the  trials  of  a  warm-blast  apparatus  described  in  Vol.  VI.  Tran- 
sactions American  Society  Mechanical  Engineers,  page  725. 
It  consists  of  two  glass  tubes,  as  shown  in  Fig.  167,  about  30 
inches  long,  and  about  0.4  inch  inside  diameter  and  0.7  inch 
outside,  joined  at  each  end  by  means  of  stuffing-boxes  to 
suitable  brass  tube  connections,  by  which  they  are  secured  to  a 


354 


EXPERIMENTAL   ENGINEERING. 


275. 


backing  of  wood.  The  glass  tubes  can  be  put  in  communica- 
tion with  each  other  at  top  and  bottom  by  opening  a  cock  in 
each  of  the  brass  connections.  Directly  over  each  tube  is  a  brass 
drum-shaped  vessel  4.25  inches  in  diameter  and 
with  heads  formed  of  plate-glass.  These  drums 
are  connected  to  the  tubes-,  and  also  provided 
with  stop-cocks  and  nipples  to  which  rubber 
tubes  can  be  attached.  Two  sliding-scales  are 
arranged  along  the  tubes,  one  to  measure  the  de- 
pression, the  other  the  elevation,  of  the  surface  of 
a  liquid  filling  the  lower  halves  of  the  tubes.  In 
the  use  of  the  instrument  two  liquids  of  different 
densities  were  used,  a  mixture  of  water  and 
alcohol  with  specific  gravity  about  0.93  being 
used  for  the  heavier  liquid,  and  crude  olive-oil 
with  a  specific  gravity  of  0.916  for  the  lighter. 
In  using  the  instrument  the  heavier  liquid  was 
first  put  into  the  tubes,  care  being  exercised  to 
avoid  wetting  the  top  attachments;  then  the 
top  connection  between  the  tubes  was  opened 
and  the  olive-oil  poured  in.  In  using  the  instru- 
ment one  branch  was  connected  to  the  chimney, 
the  other  being  opened  to  the  air,  the  bottom 
connection  opened  and  the  top  connection 
closed.  The  liquid  would  rise  in  the  tube  with 
the  lighter  pressure  a  distance  inversely  pro- 
portional to  the  respective  areas  of  exposed 
surface  of  the  tube  and  drum.  The  bottom 
connection  was  then  closed,  the  connection  to 
the  flue  removed,  and  the  top  connection  opened  ; 
the  surface  of  the  olive-oil  would  then  become 
level  in  the  two  tubes,  that  of  the  water  remaining  at  different 
heights.  It  was  then  attached  to  the  flue  and  these  operations 
repeated,  until  the  heavier  liquid  would  no  longer  flow  to  the 
side  of  the  lighter  pressure;  in  that  case  we  should  have  the 
condition  of  equilibrium  between  two  liquids  of  different  den- 
sities, Article  269,  page  347,  in  which  the  lengths  of  columns 


FIG.  167. — HOAD- 
LEY'S  DKAUGH\« 
GAUGE. 


MEASUREMENT   OF  PRESSURE. 


355 


of  the  two  liquids  are  equal.     Hence,  noting  that  p  is  here  the 
greater,  the  difference  of  pressure  in  inches  of  water  is 

P- ft  *-*&-£), 

in  which  d\   and  d  are  the  respective  specific  gravities  of  the 
liquids  used. 

276.  Multiplying  Draught-gauges.  —  Fig.  i68a  shows  a 
draught-  gauge  designed  by  Prof.  Wm.  Kent,  the  dimensions  of 
which  are  marked  on  the  figure,  although  they  are  not  material  for 
its  operation.  The  gauge  consists  of  a  cup,  B,  which  is  partly  filled 
with  water,  and  an  inverted  cup,  A,  suspended  above  the  cup  B 
by  a  spring,  C,  with  the  lower  and  open  end  submerged  in  the 
water  of  the  cup  B.  The  tube,  £,  extends  through  the  side  of 
the  cup  B,  with  its  upper  end  projecting  above  the  surface  of 
the  water  in  the  cup  B,  and  is  extended  by  suitable  connection 
to  the  flue. 


FIG.  1686. 

By  this  connection  the  pressure  in  the  inverted  cup,  A,  is  re- 
duced to  that  in  the  flue  where  the  pressure  is  to  be  measured, 
putting  a  greater  load  on  the  spring,  C,  which  causes  it  to  elongate. 
The  amount  of  elongation  will  be  proportional  to  the  reduction 
in  pressure  and  can  be  determined  by  the  use  of  a  suitable  scale, 
the  values  of  which  are  found  by  calibration.  It  is  evident  that 
the  distance  through  which  the  cup  A  will  move  is  dependent 
upon  the  area  of  its  cross-section  and  the  strength  and  length 
of  the  spring,  C,  and  the  immersion  in  the  water. 


356  EXPERIMENTAL   ENGINEERING.  [§  2/6. 

Peclet  in  his  work,  "Traite  de  la  Chaleur,"  published  in  1878, 
describes  a  similar  gauge. 

In  Vol.  XI  of  the  Transactions  of  the  Am.  Soc.  Mech.  En- 
gineers Prof.  J.  B.  Welb  describes  a  draught-gauge  of  similar 
principle,  but  in  which  the  change  in  pressure  is  weighed  on  a 
pair  of  balances. 

A  U-shaped  gauge  as  shown  in  Fig.  1686,  in  which  two  liquids 
of  different  density  are  employed,  has  been  frequently  used  to 
measure  small  pressures.  In  the  gauge  shown,  each  arm  of  the 
U  tube  is  enlarged  near  its  upper  end  for  a  short  distance.  Sup- 
posing the  liquids  employed  to  be  water  and  kerosene  oil,  water 
is  first  put  into  the  U  tube  in  one  of  the  arms,  as,  for  instance, 
the  arm  B]  kerosene  oil  is  put  in  the  arm  A,  the  surface  of  both 
liquids  being  in  the  enlarged  parts  C  and  D.  If  the  side  con- 
taining the  lighter  liquid  is  connected  to  the  flue,  the  surface  in 
the  enlarged  portion  B  will  move  in  proportion  to  the  pressure. 

If  a  be  the  point  of  junction  of  the  heavier  and  lighter  liquids, 
this  motion  will  be  as  much  greater  than  the  surface  D  as  the 
area  is  smaller;  if,  for  instance,  the  area  at  a  be  one  fourth  that 
at  D,  the  motion  will  be  four  times  as  great.  The  motion  of 
the  surface  A  could  be  determined  by  calculation,  but  it  can  be 
much  more  accurately  and  more  easily  determined  by  a  calibra- 
tion, -which  consists  of  a  comparison  with  a  direct-reading  draught- 
gauge  used  to  measure  the  same  pressure. 

A  form  of  pressure-gauge  has  been  made  in  which  the  pres- 
sure has  been  transmitted  to  the  measuring  manometer  by  a 
piston  having  faces  or  sides  of  unequal  areas  connected.  In 
this  case  the  total  pressure  acting  on  each  face  of  the  piston 
will  be  in  equilibrium ;  consequently  the  pressure  per  square  inch 
on  each  face  will  vary  inversely  as  the  areas  of  the  two  faces 
of  the  piston.  The  objection  to  the  instrument  is  the  resistance 
due  to  friction  of  the  piston,  which  can  in  large  measure  be  elimi- 
nated by  keeping  it  in  rotation  during  its  use.  In  place  of  a 
piston  two  diaphragms  of  unequal  area  with  a  connecting  solid 
part  have  in  some  cases  been  employed  for  the  purpose  of  eliminat- 
ing friction. 


§  277-]  MEASUREMENT  OF  PRESSURE.  357 

277.  Steam-gauges. — The  steam-gauges  in  general  use  are 
of  two  classes,  known  respectively  as  the  Bourdon  and  Dia- 
phragm Gauges. 

The  Bourdon  Gauge. — In  the  Bourdon  gauge  the  pressure 
is  exerted  on  the  interior  of  a  tube,  oval  in  cross-section,  bent 
to  fit  the  interior  of  a  circular  case  ;  the  application  of  pressure 
tends  to  make  the  cross-section  round  and'  thus  to  straighten 
the  tube.  This  motion  communicated  by  means  of  racks  and 
gears  rotates  an  arbor  carrying  a  needle  or  hand. 

The  various  forms  of  levers  used  for  transmitting  the 
motion  of  the  tube  to  the  needle  are  well  shown  in  the  accom- 


FIG.  169. — CROSBY  BOURDON  GAUGE. 

panying  figures,  169  to  173.  The  levers  are  in  general  adjust- 
able in  length  so  that  the  rate  of  motion  of  the  needle  with 
respect  to  the  bent  tube  can  be  increased  or  diminished  at  will. 
Thus  in  Fig,  169,  and  also  in  Fig.  170,  the  lever  carrying  the 
sector  is  slotted  where  it  is  pivoted  to  the  frame ;  by  loosen-. 
ing  a  set-screw  the  pivot  can  be  changed  in  position,  thus  alter- 
ing the  ratio  of  motion  of  hand  and  spring  in  different  parts  of 
the  dial 

Fig.  170  shows  a  gauge  with  a  steel  tube  or  diaphragm  for 
use  with  ammoniacal  vapors  which  attack  brass. 


358 


EXPERIMENTAL   ENGINEERING. 


[§  277- 


FlG.    170.— SCHAEFFER   &    I?UDENBERG    AMMONIA-GAUGE. 


FIG.  171. — BOURDON  GAUGE. 

In  nearly  all  these  gauges  lost  motions  of  the  parts  are 
to  some  extent  taken  up  by  a  light  hair-spring  wound  around 
the  needle-pivot. 


§  278.]  MEASUREMENT  OF  PRESSURE,  359 

278.  The  Diaphragm  Pressure-gauge.  —  In  the  dia- 
phragm-gauge the  pressure  is  resisted  by  a  corrugated  plate, 
which  may  be  placed  in  a  horizontal  plane,  as  in  Fig.  172,  or  in  a 
vertical  plane,  as  in  Fig.  173.  The  motion  given  the  plate  is 
transmitted  to  the  hand  in  ways  similar  to  those  just  explained. 


FIG.   172.— DIAPHRAGM-GAUGE. 

In  Fig.  172  the  pressure  is  exerted  on  the  corrugated  dia- 
phragm below  the  gauge,  and  the  motion  is  transmitted  to  the 
hand  by  the  rods  and  gears  shown  in  the  engraving. 

The  construction  shown  in  Fig.  173,  in  which  the  diaphragm 
is  vertical,  is  as  follows :  the  lever  is  in  two  parts  which  are 
pivoted  at  the  centre;  one  end  is  fixed  to  the  frame,  the  other 
connected  to  the  sector.  The  centre  pivot  is  pressed  outward 
by  the  action  of  the  diaphragm,  drawing  the  free  end  downward 
and  rotating  the  sector,  which  in  turn  moves  the  needle. 

In  gauges  of  usual  construction  of  either  class,  when  there 
is  no  pressure  on  the  gauge,  the  needle  rests  against  a  stop, 
which  is  placed  somewhat  in  advance  of  the  zero-mark,  so  that 


3^0  EXPERIMENTAL   ENGINEERING.  [§  279. 

minute  pressures  are  not  indicated  by  the  gauge.  In  the  use 
of  the  instrument  the  needle  sometimes  gets  loose  on  the  pivot, 
or  turned  to  the  wrong  position  with  reference  to  the  gradua- 
tions ;  in  such  a  case  the  needle  is  to  be  removed  entirely,  and 
set  when  the  gauge  is  subjected  to  a  known  pressure.  These 


FIG.  173. — DIAPHRAGM-GAUGE. 

gauges  are  also  affected  by  heat.  Hence,  when  set  up  for  use  a 
bent  tube,  termed  a  siphon,  or  a  vessel  which  will  always  contain 
water,  should  be  interposed  between  the  gauge  and  the  steam. 
279.  Vacuum-gauges. — Vacuum-gauges  are  constructed 
in  the  same  method  as  the  Bourdon  or  diaphragm  gauges;  the 
removal  of  pressure  from  the  interior  of  the  bent  tube  or  dia- 
phragm causes  a  motion  which  is  utilized  to  move  the  needle. 
These  are  graduated  to  show  pressure  below  that  of  the  at- 
mosphere corresponding  to  inches  of  mercury,  zero  being  at 
atmospheric  pressure,  and  29.92  a  perfect  vacuum.  The  differ- 
ence between  the  reading  by  such  a  gauge  and  that  of  the 


§  280.J 


MEASUREMENT   OF  PRESSURE. 


36! 


barometer  would  be  the  absolute  pressure  in  inches  of  mer- 
cury. 


FIG.  174.— EDSON'S  SPEED  AND  PRESSURE  RECORDING  GAUGE  AND  ALARM. 

The  principal  makers  of  steam-gauges  in  this  country  are  the 
Crosby  Steam  Gauge  and  Valve  Co.,  Boston  ;  American  Steam 
Gauge  Co.,  Boston;  Ashcroft  Steam  Gauge  Co.,  New  York; 
Schaeffer  &  Budenberg,  New  York ;  Utica  Gauge  Co.,  Utica, 
N.  Y. 

280.  Recording- gauges. — Recording-gauges  are  arranged 
so  that  the  pressure  moves  a  pencil  parallel  to  the  axis  of  a 
revolving  drum  which  is  moved  at  a  uniform  rate  by  clock- 
work. The  Edson  recording-gauge  is  shown  in  Fig.  174.  In 
this  gauge  the  steam-pressure  acts*1  on  a  diaphragm  which  oper- 


362 


EXPERIMENTAL   ENGINEERING. 


[ 


ates  a  series  of  levers  giving  motion  to  a  needle  moving  over 
a  graduated  arc  showing  pressure  in  pounds ;  also  to  a  pencil- 
arm  moving  parallel  to  the  axis  of  a  revolving  drum. 

This  instrument  has  an  attachment,  which  is  furnished 
when  required,  to  record  fluctuations 
in  the  speed,  and  consists  of  a  pul- 
ley on  a  vertical  axis  below  the  instru- 
ment that  is  put  in  motion  by  a  belt 
to  the  engine-shaft.  On  the  small 
pulley-shaft  are  two  governor-bails 
which  change  their  vertical  position 
with  variation  in  the  speed,  giving 
a  corresponding  movement  up  or 
down  to  a  pencil  near  the  lower  part 
of  the  drum.  A  diagram  is  drawn 
on  which  uniform  speed  would  be 
shown  by  a  straight  line. 

Fig.  175  shows  Schaeffer  Si  Buden- 
berg's  recording-gauge.  This  con- 
sists of  a  pressure-gauge  below  the 
recording  mechanism.  The  drum  B 
is  operated  by  clock-work,  the  piston- 
rod  C,  which  carries  the  pencil,  being 
moved  by  the  pressure.  The  pencil- 
movement  is  much  like  that  on  the 
Richards  steam-engine  indicator. 

Fig.  176  shows  a  portion  of  a  diagram  made  by  a  recording- 
gauge.     The  drum  is  operated  by  an  eight-day  clock,  and  ar- 


FIG  175. — RECORDING  PRESSURE- 
GAUGE. 


3  4  5  (5  7 

-         --   -  —     -     -  -  — 

FlG.    I70.—DIAGRAM  FROM  PRESSURE-RECORDING  GAUGE. 


§  28 1.]  MEASUREMENT  OF  PRESSURE,  363 

ranged  to  rotate  once  in  twenty-four  hours.  In  the  diagram 
the  ordinates  show  pressure,  and  the  abscissae  time  in  hours 
and  fractions  of  an  hour. 

281.  Apparatus  for  Testing  Gauges. — Apparatus  for 
testing  gauges  consists  of  a  pump  or  other  means  of  obtaining 
pressure,  and  some  method  of  attaching  the  gauge  to  be  tested, 
and  the  standard  with  which  it  is  to  be  compared.  The  form  of 
pump  usually  employed  for  producing  the  pressure  is  shown  in 
Fig.  177.  The  gauge  is  attached  at  E,  the  standard  at  El ;  the 
hand-wheel  D  is  run  back,  and  water  is  supplied  by  filling  the 
cup  between  the  gauges  and  opening  the  cock;  after  the  cylin- 
der C  is  filled  the  cock  below  the  cup  is  closed;  if  the  hand- 
wheel  D  is  turned,  an  equal  pressure  will  be  put  on  the  standard 
and  on  the  gauge. 

The  standards  used  for  testing  may  be  manometers  or  calv 
brated  gauges,  or  apparatus  for  lifting  known  weights  by  the 
pressure  acting  on  a  known  area.  Of  these  various  standards, 
the  mercury  column,  as  described  in  Article  271,  page  349,  is 
to  be  given  the  preference,  since  the  only  errors  of  any  prac- 
tical importance  are  those  due  to  graduation.  The  readings 
given  by  the  mercury  column  are  on  a  larger  scale  than  those 
given  by  any  other  instrument,  and  no  corrections  for  friction 
are  required.  The  other  standards,  of  which  the  short  mer- 
cury columns  have  been  described  (see  Article  264),  will  be 
found  to  give  excellent  results  in  practice,  since  the  graduations 
on  the  gauges  to  be  tested  are  usually  so  close  together  that 
the  friction  of  the  moving  parts  of  the  apparatus  is  inap- 
preciable. 

Apparatus  for  Testing  Gauges  with  Standard  Weights. 

There  are  two  forms  of  this  apparatus  on  the  market,  in  one- 
of  which  the  pressure  is  received  on  a  round  piston,  and  in 
the  other  on  a  surface  exactly  one  square  inch  in  area.  The 
friction  in  both  cases  is  practically  inappreciable  ;  the  errors  in 
areas  can  be  determined  by  comparison  with  a  standard  mer- 
cury column. 

The  Crosby  Steam-gauge  Testing  Apparatus. — This  is  shown 
in  Fig.  178,  from  which  it  is  seen  to  consist  of  a  small  cylinder 


EXPERIMENTAL  ENGINEERING. 


177-— TEST-PUMP  FOR  GAUGES. 


§28l.J 


MEASUREMENT  OF  PRESSURE. 


365 


in  which  works  a  nicely  fitted  piston  ;  this  cylinder  connects 
with  a  U-shaped  tube  ending  in  a  pipe  tapped  and  fitted  for 


FIG.  178. — CROSBY  STEAM-GAUGE  TESTING  APPARATUS. 

attaching  a  gauge.  The  tube  is  filled  with  glycerine,  in 
which  case  a  known  weight  added  to  the  piston  produces  an 
equal  pressure  on  the  gauge,  less  the  friction  of  the  piston  in 
the  tube.  This  is  almost  entirely  overcome  by  giving  the 
weight  and  piston  a  slight  rotary  motion. 

The  Square-inch  Gauge. — This  apparatus  consists  of  a  tube 
the  end  of  which  has  an  area  of  one  square  inch  enclosed  with 
sharp  edges.  This  is  connected  to  the  test-pumps  in  place  of 
the  standard  (see  Fig.  177,  page  364);  a  given  weight  is  sus- 
pended from  the  centre  of  a  smooth  plate  which  rests  on  the 
square  inch  orifice.  The  gauge  to  be  tested  is  connected  at 
E,  and  the  pressure  applied  until  the  plate  is  lifted  and  water 
escapes  from  the  orifice. 


366  EXPERIMENTAL  ENGINEERING.  [§  282. 

282.  Calibration  and  Correction  of  Pressure-gauges.— 

The  correctness  of  gauges  is  determined  in  each  case  by  com- 
parison with  apparatus  known  to  be  correct,  the  apparatus 
being  subject  to  a  fluid  pressure  of  the  same  intensity.  The 
calibration  may  be  done  by  comparison  with  any  of  the  stand- 
ards described. 

Calibration  of  Gauges  with  the  Mercury  Column. 

First,  with  Steam-pressure. — In  this  case  attach  the  gauge 
-with  a  siphon  connection  to  a  steam-drum,  making  the  center 
of  the  gauge  the  height  of  the  zero  of  the  column.  This  drum 
is  to  be  connected  at  one  end  to  the  mercury  column,  and  the 
steam-pressure  is  to  be  applied  to  it  so  that  it  can  be  regulated 
t>y  throttling  the  admission  or  discharge.  Admit  steam- 
pressure  to  the  gauge  and  the  mercury  column  ;  adjust  the 
Tpressure  to  a  given  reading  by  throttling  the  valves.  Starting 
-at  five  pounds  of  pressure  on  the  gauge,  note  the  correspond- 
ing reading  of  the  mercury  column,  temperature  of  the  mer- 
cury and  of  the  room.  Increase  the  pressure  and  take  readings 
once  in  five  pounds.  In  no  instance  allow  the  pressure  to  exceed 
that  at  the  time  of  making  the  reading.  In  case  the  pressure  is 
made  too  great  at  any  time,  run  it  some  distance  below  the 
required  amount  and  make  a  new  trial,  it  being  necessary  to 
keep  the  mercury  column  and  gauge  hand  moving  continually 
upward  or  downward.  Repeat  the  same  operation  in  the 
reverse  direction,  commencing  with  the  highest  pressures ;  the 
average  reading  of  the  mercury  column,  corrected  for  error  as 
explained  in  Article  272,  page  350,  and  reduced  to  pounds  of 
pressure,  is  the  correct  pressure  with  which  the  gauge-reading 
is  to  be  compared. 

Second,  with  Water-pressure. — In  this  case  a  hand  force- 
pump  (see  Article  281)  must  be  used  after  the  limits  of  pressure 
•  of  the  water-main  have  been  reached.  Proceed  as  follows : 

Run  out  the  piston  of  the  pump  attached  to  the  mercury 
-column  to  the  end  of  its  travel ;  close  drip-cock  and  open  the 
connectiag-valve.  Attach  the  gauge  to  be  tested  with  its 
centre  opposite  the  zero  of  the  column.  Open  the  cock. 


V 


§  283.] 


MEASUREMENT  OF  PRESSURE. 


367 


Draw  water  from  the  mains  until  the  gauge  indicates  5  Ibs. 
pressure.  Shut  off  the  water  and  adjust  the  pressure  exactly 
at  5  Ibs.  by  using  the  displacer.  Note  the  height  of  the  mer- 
cury in  the  tube.  Increase  the  pressure  to  10  Ibs.  and  take 
readings.  Carry  the  pressure  as  far  as  desired  by  increments 
of  5  Ibs.  Use  the  pump  alone  when  water-pressure  fails. 
From  the  maximum  pressure  attained  descend  by  increments 
of  5  Ibs.,  taking  readings  as  before.  Tabulate  data  and  plot  a 
curve,  using  gauge-readings  as  ordinates  and  actual  pressures  as 
.abscissae.  By  inspection  of  the  curve  determine  the  fault  in 
the  gauge  and  give  directions  for  correcting  it. 

In  these  tests  it  may  not  be  possible  to  set  the  centre  of 
the  gauge  as  low  as  the  zero  of  the  column.  In  that  case  the 
reading  on  the  mercury  column  should  be  greater  than  that  at 
the  centre  of  the  gauge  by  a  pressure  due  to  the  length  of  a 
column  of  water  equal  to  the  elevation  of  the  centre  of  the 
gauge  above  the  zero  of  the  mercury  column.  This  is  a  con- 
stant amount ;  it  should  be^  obtained  and  the  read- 
ings of  the  column  corrected  accordingly. 

The  method  of  calibrating  gauges  with  other 
standards  is  to  be  essentially  the  same,  except  as  to 
the  manipulation  of  the  apparatus.  Further  di- 
rections do  not  seem  necessary. 

Correction  of  Gauges. — If  an  error  appears  as  a 
result  of  calibration,  it  may  generally  be  corrected  ; 
if  the  error  is  a  constant  one,  the  hand  may  be 
removed  with  a  needle-lifter,  and  moved  an  amount 
corresponding  to  the  error,  or  in  some  gauges  the 
dial  may  be  rotated.  If  the  error  is  a  gradually 
increasing  or  diminishing  one,  it  can  be  corrected  by 
changing  the  length  of  the  lever-arm  between  the 
spring  and  the  gearing  by  means  of  adjustable  sleeves 
or  the  equivalent.  It  is  to  be  noted  that  the  pin 
to  stop  the  motion  of  the  hand  is  not  placed  at 
zero,  but  in  high-pressure  gauges  is  usually  set  at 

NOMETER. 

three  to  rive  pounds  pressure. 

283.  Calibration   of  Vacuum-gauges. — This  is  best  done 
by  a  comparison  with  a  U-shaped  mercury  manometer,  as  shown 


368 


EXPER1MEN TA  L   ENGINEERING. 


[§284. 


in  Fig.  179,  of  which  each  branch  of  the  tube  should  exceed 
30  inches  in  length.  Before  calibrating,  the  manometer  is 
filled  with  mercury  to  one  half  the  length  of  the  tubes,  and 
is  attached  near  the  gauge  to  be  tested  to  the  receiver  of  an 
air-pump.  In  case  a  condensing  engine  is  used,  both  the 
gauge  and  the  standard  may  be  connected  to  the  condenser. 
A  comparison  of  the  readings  of  the  vacuum-gauge  with  the 
difference  of  level  of  mercury  in  the  two  tubes  will  determine 
the  error  of  the  gauge. 

284.  Forms  for  Calibration  of  Gauges. 

CALIBRATION    OF   STEAM-GAUGE    BY    COMPARISON   WITH   THE 

MERCURY   COLUMN. 
Maker  and  No.  of  Gauge. 


Date 189.         Observers, 


No. 

Gauge. 
Ibs 

Mercury  Column. 

Gauge. 
Ibs 

Error. 
Ibs. 

Inches. 

Pounds. 

Up. 

Down. 

Mean. 

Temperature  of  Room  ....  deg.  Fahr. 
Centre  of  Gauge  above  o  of  column  . . 
Correction  to  column  reading  ....  Ibs. 


ft. 


CALIBRATION   OF   STEAM-GAUGE   BY   COMPARISON   WITH   THE 
SQUARE-INCH  GAUGE,  OR  WITH  CROSBY'S  GAUGE- 
TESTING   APPARATUS. 


Date  

..180  . 

Observers, 

3 

\  

No. 

Load  in  Ibs.  on 
Valve. 

Gauge. 

Error. 

Remarks. 

CHAPTER   XII. 
MEASUREMENT   OF   TEMPERATURE. 

285.  Mercurial  Thermometers. — Measurements  of  tem- 
perature are  determined  by  the  expansion  of  some  ther- 
mometric  substance,  mercury,  alcohol,  or  air  being  commonly 
employed. 

The  mercurial  thermometer  is  commonly  used  ;  this  con- 
sists of  a  bulb  of  thin  glass  connected  with  a  capillary  glass 
tube  ;  on  the  best  thermometers  the  graduations  are  cut  on 
the  tube,  and  an  enamelled  strip  is  placed  back  of  them  to  facil- 
itate the  reading.  When  the  mercury  is  inserted,  every  trace  of 
air  must  be  removed  in  order  to  insure  perfect  working.  There 
are  certain  defects  in  mercurial  thermometers  due  to  perma- 
nent change  of  volume  of  the  glass  bulb,  with  use  and  time, 
that  results  in  a  change  of  the  zero-point.  This  defect  is  so 
serious  as  to  render  the  mercurial  thermometer  useless  for  very 
minute  subdivisions  of  a  degree.  In  a  good  thermometer  the 
bore  of  the  tube  must  be  perfectly  uniform,  which  fact  can  be 
tested  by  separating  a  thread  of  mercury  and  slidirfg  it  from 
point  to  point  along  the  tube,  and  noting  by  careful  measure- 
ment whether  the  thread  is  of  the  same  length  in  all  portions 
of  the  tube  :  if  the  readings  are  the  same,  the  bore  is  uniform  or 
graduated  by  trial.  In  most  thermometers  the  graduations  are 
made  with  a  dividing  engine ;  in  some  thermometers  the  prin- 
cipal graduations  are  obtained  by  the  thread  of  mercury,  as 
described  ;  in  the  latter  case  change  in  diameter  of  bore  would 
be  compensated.  To  determine  the  accuracy  of  temperature 

369 


37°  EXPERIMENTAL   ENGINEERING.  [§286. 

measurements  thermometers  used  should  be  frequently  tested 
for  freezing-point  and  boiling-point.  The  accuracy  of  inter- 
mediate points  should  be  determined  by  comparison  with  a 
standard  mercurial  or  air  thermometer. 

The  mercurial-weight  thermometer  which  was  employed  by 
Regnault,  but  is  now  very  little  used,  consists  of  a  glass  vessel 
with  a  large  bulb  and  capillary  tube,  open  at  the  top ;  it  is  filled 
with  mercury  when  at  the  temperature  of  the  freezing-point ; 
it  is  then  heated  to  the  temperature  of  boiling  water,  and  the 
amount  of  mercury  that  runs  out  is  carefully  weighed,  and  de- 
termines the  value  of  the  thermometric  scale.  The  temperature 
of  any  enclosure  is  then  found  by  placing  in  it  the  thermome- 
ter, previously  filled  when  at  freezing-point  and  weighing  the 
amount  that  escapes ;  from  this  the  temperature  can  be  cal- 
culated by  simple  proportion. 

The  expansion  of  mercury  is  not  perfectly  uniform  for  all 
temperatures,  so  that  mercurial  thermometers  are  never  per- 
fect for  extreme  ranges  of  temperature. 

286.  Rules  for  the  Care  of  Mercurial  Thermometers. — 
The  following  rules  for  handling  and  using  mercurial  thermome 
ters,  if  carefully  observed,  will  reduce  accidents  to  a  minimum  : 

1.  Keep  the  thermometer  in  its  case  when  not  in  use. 

2.  Avoid  all  jars  ;  exercise  especial  care  in  placing  in  ther- 
mometer-cups. 

3.  Do  not  expose  the  thermometer  to  steam  heat  unless 
the  graduations  extend  to  or  beyond  350°  F. 

4.  In  measuring  heat  given  off  by  working-apparatus,  or  in 
continuous  calorimeters,  do  not  put  the  thermometers  in  place 
until  the  apparatus  is  started,  and  take  them  out  before  it  is 
stopped.      Be  especially  careful  that  no  thermometer  is  over- 
heated. 

5.  In  general  do  not  use  thermometers  in  apparatus  not 
fully  understood  or  which  is  not  in  good  working  condition. 

6.  Never  carry  a  thermometer  wrong  end  up. 

7.  See  that  the  thermometer-cups  are  filled  with  cylinder- 
oil  or  mercury.     If  cylinder-oil  is  used,  keep  water  out  of  the 
•cups  or  an  explosion  will  follow. 


§288.]  MEASUREMENT  OF    TEMPERATURE.  3/1 

8.  After  a  thermometer  is  placed  in  a  cup,  keep  it  from 
contact  with  the  metal  by  the  use  of  waste. 

287.  Alcohol-thermometers. — Other    liquids,  as    alcohol 
•or  spirits  of  wine,  are  better  suited  for  low  temperatures  than 
mercury,  but  on  account  of  the  tension  of  their  vapors  are  not 
suited  for  high  temperatures,  and  are  probably  subject  to  the 
same  objections  in  a  less  degree  as  mercurial  thermometers. 

288.  Air-thermometers. — Air-thermometers,in  which  either 
air  or  hydrogen  may  be  used,  are  not  open  to  the  objections 
which  hold  with  the  mercurial  thermometer,  as  the  expansion  for 
uniform,  increments  of  heat  is  under  all  conditions  the  same. 

There  are  two  plans  of  these  thermometers  : 
I.  Increase  of  volume  of  air  at  constant  presssure. 

II.  Increase  of  pressure  at  constant  volume. 

The  latter  plan  was  found  to  give  better  results  by  Reg- 
nault,  and  constitutes  the  principle  of  the  "  Normal  Air-ther- 
mometer." 

The  air-thermometer  in  construction  is  a  U-shaped  tube, 
one  branch  enlarged  into  a  bulb  for  the  air,  the  other  open  for 
the  mercury.  Adjacent  to  the  tube  for  the  mercury  is  a  gradu- 
ated scale  which  can  be  read  by  a  vernier  to  small  divisions  of 
an  inch  ;  a  single  mark  is  placed  in  the  air  branch,  at  a  dis- 
tance of  eight  or  ten  inches  from  its  top.  This  mark  serves  to 
define  the  limit  of  volume  used. 

There  are  various  forms  of  instrument  in  use ;  the  one 
adopted  at  Sibley  College  was  designed  by  Mr.  G.  B.  Preston 
and  is  shown  in  Fig.  180.  The  air-bulb,  C,  is  approximately 
if  inches  by  6  inches  ;  the  bulb  is  joined  by  a  capillary  tube,  F, 
straight  or  bent  into  any  convenient  form  as  may  be  required. 
In  order  that  the  bulb  may  be  conveniently  located  for  heat- 
ing, this  capillary  tube  is  joined  to  a  tube  of  glass  about  TJT  inch 
bore,  the  end  of  which  is  bent  at  right  angles  ground  true,  and 
joined  by  a  short  piece  of  rubber  tubing  to  a  glass  tee  at  B. 
The  tee  has  a  branch  provided  with  a  cock,  and  connection  for 
rubber  tubing.  The  opposite  side  of  this  tee  is  joined  in  a 
similar  way  to  a  tube,  BE,  of  the  same  bore,  which  is  given  a 
length  sufficient  to  measure  the  required  temperatures.  A  mark 


372 


EXPERIMEN  TA  L   ENGINEERING. 


[§  288. 


a  is  made  on  the  glass  near  F,  at  the  junction  of  the  capillary 
tube  with  the  larger  one  for  the  mercury,  and  serves  to  deter- 
mine the  limit  of  volume  of  air  used.  ,  The  bottle,  A,  is  filled 
with  mercury,  and  connected  by  a  rubber  tube  to  the  cock  B. 
By  opening  the  cock  and  elevating  the  bottle,  mercury  will 


FIG.  180. — PRESTON   AIR-THERMOMETER. 

pass  into  the  tubes  :  when  it  reaches  the  height  of  the  mark  a, 
the  connecting  cock  B  is  closed,  and  the  amount  that  the  col- 
umn BE  extends  above  the  level  of  this  mark,  or  fails  of 
reaching  this  level,  is  read  on  the  scale. 

Hoadley  Air-thermometer. — The  Hoadley  air-thermome- 
ter, as  described  in  the  Transactions  of  the  American  Society  of 
Mechanical  Engineers,  Vol.  VI.,  page  282,  is  shown  in  Fig.  181, 
with  all  the  dimensions  marked.  It  differs  from  the  preceding 
one  in  having  no  means  provided  for  introducing  or  removing 
mercury  to  maintain  the  volume  of  air  constant.  The  tube  con- 
nected to  the  air-bulb,  instead  of  being  capillary,  is  about 

inch  diameter.     The  instrument  consists  of  a  U-tube  about 


§  288.] 


MEASUREMENT  OF    TEMPERATURE. 


|  inch  external  diameter,  ^  bore,  having  a 
short  leg  about  39  inches  long,  and  the  other 
leg  longer  by  12  inches  or  more,  the  latter  sur- 
mounted by  a  bulb  blown  out  of  the  tube  if 
inches  in  diameter,  6f  inches  in  extreme  length. 
The  branches  of  the  U-tube  are  2  inches  apart 
and  vertical ;  these  are  separate  tubes,  each  one 
bent  to  a  right  angle  by  a  curve  of  short 
radius,  ground  square  and  true  at  the  ends 
and  united  by  a  short  coupling  of  rubber 
tubing,  ea,  firmly  bound  on  each  branch  with 
wire.  After  it  is  filled  with  dry  air  according 
to  the  directions  in  Article  290,  page  376,  it  is 
fastened  on  a  piece  of  board  by  annealed  wire 
staples,  and  paper  scales  affixed  as  shown  in 
the  figure.  The  difference  in  height  of  the 
two  columns  of  mercury  is  taken  as  the  read- 
ing of  the  thermometer,  and  no  correction  is 
made  for  slight  variations  in  the  volume  of 
air,  as  shown  by  variation  in  the  position  of  the 
height  of  the  mercury  column  in  the  branch 
BC.  The  error  caused  in  this  way  is  very  small 
and  amounts  to  only  0.0030  inch  per  inch  of 
height.  This  is  equivalent  to  an  error  of  about 
five  degrees  in  a  range  of  temperature  of  600 
degrees  F. 

The  Jolly  Air-thermometer. — An  exceedingly 
simple  form  of  the  air-thermometer,  and  one  also 
very  accurate,  consists  of  the  air-bulb  C,  and  a 
capillary  stem  attached  to  three  or  four  feet 
of  rubber  tubing,  which  replaces  the  U-tube 
in  Fig.  180;  in  the  other  end  of  the  rubber 
tubing  is  inserted  a  piece  of  glass  tube  8  to  12 
inches  long  and  about  -^  inch  bore ;  on  this 
glass  tube,  and  also  on  the  capillary  tube,  is 
etched  a  single  mark ;  the  rubber  tube  is  filled 
with  mercury,  which  extends  up  the  glass  tube  FlG.  T8l  _THE  HOAD. 
on  the  other  branch.  A  fixed  scale,  similar  to  DE 


LEY     AIR-THERMOM- 
ETER. 


374  EXPERIMENTAL   ENGINEERING.  [§  289. 

in  Fig.  1 8 1,  is  located  near  the  instrument.  To  use  the  instru- 
ment the  tube  is  manipulated  until  the  air  is  brought  to  its. 
limit  of  volume,  then  the  other  end  of  the  tube  is  held  oppo- 
site the  scale,  and  the  reading  corresponding  to  the  height  of 
the  mercury  is  taken.  This  is  repeated  for  several  tempera- 
tures, and,  if  the  constant  of  the  instrument  is  known,  gives  the 
data  for  computing  the  temperature. 

289.  Formulae  for  the  Air-thermometer  of  Constant  Vol- 
ume.— The  pressure  exerted  by  the  confined  air,  added  to  the 
weight  of  mercury,  in  the  branch  Bfr,  Fig.  180,  will  equal  the 
weight  of  mercury  in  the  other  branch  plus  the  weight  of  the 
atmosphere.  Thus  let  p  equal  the  pressure  expressed  in  inches- 
of  mercury  of  the  confined  air,  v  its  volume,  m  the  height  of 
the  mercury  in  the  branch  of  the  tube  on  the  side  of  the  air- 
bulb,  m'  the  height  in  the  other  branch,  b  the  pressure  of  the 
atmosphere  expressed  in  inches  of  mercury,  T  the  absolute 
temperature,  t  the  thermometer-reading,  h  the  height  of  mer- 
cury in  the  tube  BE  above  the  mark  #,  no  mercury  being 
above  the  point  a  in  the  tube  BF.  Let  a  equal  constant  ratio 
of  T  to  pv.  Then  we  have,  since  the  pressures  in  both  branches 
of  the  tube  are  equal, 


p  =  m'  —  m  -f-  If. 

Since     m'  —  m  =  k, (2) 

/  =  *  +  *. .    (3) 

• 

From  physics, 


-=,  =  constant ;    . (4) 


£289.]               MEASUREMENT   OF    TEMPERATURE.  375 

and  if  v  be  made  constant,/  will  vary  as  T-,  also 

T=46o  f  /;    ......     r  (5): 

p  =  r(constant)  =  (460  +  /)«;....  (6) 
hence 

=  6  +  t  .......  (7) 


Let  the  same  symbols  with  primes  denote  other  values  of  the 
corresponding  quantities.     Then 

(460  +  /')«  =  V  +  K  .......     (8) 

By  comparing  equations  (7)  and  (8), 

460  +  ' 


460  +  /' 
From  which,  by  solving, 


=  [=-(460  +  ;)    -460..    .    .    .    (10) 


To  apply  the  formula,  take  readings  of  the  instrument  at 
32°  F.,  or  some  known  temperature,  and  ascertain  the  con- 
stants of  the  instrument.  Thus  suppose  the  air-bulb  to  be 
packed  in  ice  and  the  temperature  reduced  to  32°  F.  In  this 
case  t  —  32°  ;  b  and  h  are  to  be  observed  and  recorded. 


3/6  EXPERIMENTAL   ENGINEERING.  [§  290. 

If  t  =  32°  in  equation  (10), 


(ii) 


which  is  an  equation  to  determine  any  temperature.     If  b  and  h 
are  constant,  492  -7-  (b  +  K)  is  constant  and  equals  K. 


(12) 


which  is  the  practical  equation  for  use  in  determining  tem- 
peratures. 

If  the  height  of  the  mercury  in  the  column  £fi,  Fig.  180, 
is  less  than  that  in  FB,  h  will  be  negative,  and  is  to  be  so  con- 
sidered in  the  preceding  formulae. 

In  the  use  of  the  air-thermometer  the  mercury  must  be 
maintained  constantly  at  the  point  a  in  the  branch  FB]  this 
will  require  the  addition  of  mercury  to  the  U-tube  as  the  press- 
ure increases,  which  is  readily  done  by  raising  the  bottle  A 
and  opening  the  connecting-cock  B.  By  a  reverse  process 
mercury  may  be  removed  as  the  pressure  decreases. 

290.  Construction  of  the  Air-thermometer. — The  bulb 
of  the  air-thermometer  must  be  rilled  with  perfectly  dry  air, 
as  any  vapor  of  water  will  vitiate  the  results. 

To  accomplish  this,  the  bulb  is  provided  with  a  small  open- 
ing opposite  the  capillary  tube,  which  is  fused  after  the  dry  air 
is  introduced.  To  effect  the  introduction  of  dry  air,  all  the 
mercury  is  drawn  into  the  bottle  A,  Fig.  180;  the  end  of 
the  tube  E  is  connected  to  a  U-tube  about  6  inches  long  in 
its  branches  and  about  J  inch  internal  diameter,  filled  with  dry 
lumps  of  chloride  of  calcium  and  surrounded  by  crushed  ice; 
the  opening  in  the  end  of  the  air-chamber  is  connected  by  a 
rubber  tube  to  an  aspirator  (a  small  injector  supplied  with 
water  would  act  well  as  an  aspirator),  and  air  is  drawn  through 


"1  292.]  MEASUREMENT   OF    TEMPERATURE.  377 

for  three  or  four  hours:  at  the  end  of  this  time  the  bulb  and 
tube  should  be  filled  with  dry  air.  While  the  current  of  air  is 
still  flowing,  the  cock  B  is  opened  and  mercury  allowed  to  pass 
into  the  tubes  until  it  rises  to  the  point  a  in  the  tube  BF\  the 
opening  in  the  air-chamber  is  then  hermetically  sealed  with  a 
blow-pipe,  and  the  connections  to  the  chloride-of-calcium  tube 
removed.  This  operation  fills  the  bulb  with  air  at  atmospheric 
pressure.  By  closing  the  cock  B  before  the  mercury  has  risen 
to  the  point  a  the  pressure  will  be  increased  ;  by  closing  it  after 
it  has  passed  the  point  a  it  will  be  diminished.  Packing  the 
bulb  C  in  ice;  or  heating  it,  will  also  increase  or  diminish  the 
pressure  as  required. 

291.  Corrections  to  Determinations  by  the  Air-thermom- 
eter.— The  corrections  to  the  air- thermometer  are  all  very 
small,  and  affect  the  results  but  little  if  considered.  They  are  : 

1.  Capillarity,  or  adhesion  of  the  mercury  to  the  glass.     In 
general  the  mercury  in  the  two  tubes  BF  and  BE  (Fig.  180)  is 
moving  in   opposite  directions,  and   the  effect  of  adhesion  is 
neutralized.     For  error  in  other  cases  see  table  on  page  351. 

2.  Expansion  of  the  glass.     This  is  a  small  amount,  and 
may  usually  be  neglected.     The  coefficient  of  surface  expan- 
sion of  glass  is  o.ooooi  per  degree  F. ;  it  is  entirely  neutralized 
if  the  column  of  mercury  is  not  reduced   in  area   at  the  point 
of  meeting  the  air  from  the  bulb. 

3.  Expansion  of  the  mercury  should  in  every  case  be  taken 
into  account  by  reducing  all  observations  to  32°  F.,  the  coeffi- 
cient of  expansion  being  o.oooi  per  degree  F.     Reduce  all  ob- 
servations before  applying  formulae. 

4.  Errors   in    the  fixed    scale    should    be  determined   and 
observations  reduced  before  applying  formulae. 

292.  Practical  Uses  of  the  Air-thermometer. — The  air- 
thermometer  may  be  used  as  a  standard  with  which  to  compare 
mercurial  thermometers ;  in  this  case  the  bulb  of  the  air-ther- 
mometer is  surrounded  with  a  non-conducting  chamber  (Fig. 
180),  in  which  the  thermometer  to  be  compared  is  inserted. 
For  low  temperatures  water  may  be  circulated  through  this 
chamber,  and  simultaneous  readings  taken ;  for  higher  tem- 


378  EXPERIMENTAL   ENGINEERING.  [§293. 

peratures  steam  may  be  used.  Time  must  in  each  case  be 
given  to  permit  the  fluid  in  the  air-thermometer  to  arrive  at 
the  true  temperature. 

In  comparison  with  mercurial  thermometers,  an  exact 
agreement  may  be  found  at  freezing  and  boiling  points  ;  but  at 
other  places  a  slight  disagreement  may  be  expected,  which  will 
increase  rapidly  for  high  temperatures. 

The  air-thermometer  may  also  be  used  to  measure  tempera 
tures  directly.  When  the  bulb  is  connected  with  a  long  capil- 
lary stem  it  may  be  introduced  into  flues,  and  temperatures 
below  the  melting-point  of  glass  measured.  The  melting- 
point  will  vary  from  600  to  800  degrees  F.  By  using  porcelain 
bulbs  extremely  high  temperatures  can  be  measured. 

293.  Directions  for  Use  of  the  Air-thermometer. 

First.  To  obtain  the  Constants  of  the  Instruments.  —  Enclose 
the  air-bulb  with  crushed  ice,  arranged  so  that  the  water  will 
drain  off.  Note  the  reading  of  the  mercury  column  of  the  air- 
thermometer  //  and  of  the  barometer  b  ;  by  means  of  the  at- 
tached thermometers  reduce  these  readings  for  a  temperature 
of  the  mercury  corresponding  to  32°  F.  Correct  for  errors  of 
graduation.  Divide  492  by  the  sum  of  these  corrected  readings 
for  the  constant  of  the  air-thermometer.  Call  this  constant  K. 

Second.  To  Measure  any  Temperature  t'  .  —  Note  the  corre- 
sponding reading  of  the  mercury  column  h  ',  and  that  of  a 
barometer  b'  in  the  same  room.  The  reading  of  the  mercury 
column  plus  that  of  the  barometer  will  correspond  to  b'  -\-  h' 
in  the  formula 


o  -  460  = 


Third.  To  Compare  a  Mercurial  Thermometer.  —  Make  simul- 
taneous readings  of  the  thermometer  when  hanging  in  the 
chamber  with  the  air-bulb,  and  the  height  of  the  mercury 
column.  Perform  reduction,  and  plot  a  calibration  curve  for 
each  10°  of  graduation. 

Fourth.  For  general  use  of   the  air-thermometer,  arrange 


§  294-] 


MEASUREMENT  OF   TEMPERATURE. 


379 


the  bulb  so  that  it  can  be  inserted  into  the  medium  whose 
temperature  is  to  be  measured,  with  the  U-shaped  tubes  in  an 
accessible  position  for  reading.  Obtain  the  temperature  as 
explained  above  (see  Second). 

294.  Form  for  Reducing  Air-thermometer  Determina- 
tions. 


TEMPERATURE  DETERMINATIONS  WITH  AIR-THERMOMETER. 

By 189... 

DETERMINATION  OF  CONSTANT. 


Symbol. 

i. 

II. 

III. 

IV. 

Temperature  of  air-bulb  

Reduced  to  32°  

b 

Air-thermometer  —  Reading  

Thermometer. 

Reduced  to  32°. 

h 

A 

DETERMINATION  OF  TEMPERATURE. 

t'  =  K(b'  +  h')  -460. 


No. 

Barometer. 

Air-thermometer. 

6'+*' 
Sum. 

t' 
Tem- 
pera- 
ture. 

Mercury 
Thermometer. 

Read- 
ing. 

Ther. 

b' 
re- 
duced. 

Read- 
ing. 

Ther. 

h' 
re- 
duced. 

Read- 
ing. 

Error. 

I 
2 

3 
4 
5 
6 

7 
8 

9 

10 

ii 

12 

380 


EXPERIMENTAL   ENGINEERING. 


[§  296. 


295.  Determination  of  Boiling  and  Freezing  Points. 

First.  To  test  for  Boiling-point.— Suspend 
the  thermometer  so  that  it  will  be  entirely 
surrounded  in  the  vapor  of  boiling  water 
at  atmospheric  pressure  but  will  not  be  in 
contact  with  the  water.  Note  the  reading. 
From  the  barometer-reading  calculate  the 
boiling-point  for  the  same  time.  The  dif- 
ference will  be  the  error  in  position  of  the 
boiling-point. 

The  engraving  (Fig.  182)  shows  an  in- 
strument  for  determining  the  boiling- 
point.  The  bulb  of  the  thermometer  is 
exposed  to  steam  at  atmospheric  pressure, 
which  passes  up  to  the  top  of  the  instru- 
ment around  the  tube,  and  down  on  the 
outside,  discharging  into  the  air,  or  it  may 
be  returned  directly  to  the  cup,  thus  ob- 
viating the  need  of  supplying  water.  In 
the  form  shown,  the  parts  telescope  into 
each  other  for  convenience  in  carrying, 
which  is  entirely  unnecessary  for  labora- 
tory uses. 

Secondly.  To  test  for  Freezing-point  — 
Surround  the  bulb  of  the  thermometer  by 
a  mixture  of  water  and  ice,  or  water  and 
snow ;  drain  off  most  of  the  water.  The 
difference  between  the  reading  obtained 

and  the  zero  as  marked  on  the  thermometer  (32°  for  Fahr. 

scale)  is  the  error  in  location  of  freezing-point. 

296.  Metallic  Pyrometers  are  instruments  used  for  meas- 
uring high  temperatures.     The  ordinary  instruments  sold  under 
this  name  are  made  of  two  metals  which  have  different  rates  of 
expansion,  copper  and  iron  generally  being  used.     The  differ- 
ence in  the  rate  of  expansion  is  employed  by  means  of  levers 
and  gears  to  rotate  a  needle  over  a  dial  graduated  to  degrees. 

In  using  the  metallic  pyrometer  no  reading  should  be  taken 
until  rt  has  had  sufficient  time  to  arrive  at  -:he  temperature  of 


FIG.  1 8a.— APPARATUS  TO 
TEST  SOILING-POINT. 


§  298- J  MEASUREMENT  OF    TEMPERATURE.  381 

the  medium  in  which  it  is  enclosed ;  when  one  tube  alone  is 
heated,  the  needle  may  be  stationary  on  the  dial,  or  even  have 
a  retrograde  motion. 

The  metallic  pyrometer  is  usually  calibrated  by  immersing 
in  a  pipe  filled  with  steam  under  pressure  and  comparing  the 
temperature  with  that  given  by  a  calibrated  mercurial  ther- 
mometer. The  scale  so  obtained  is  assumed  to  be  uniform 
throughout  the  range  of  the  pyrometer  and  beyond  the  limits 
of  the  calibration.  Comparison  might  be  made  with  an  air- 
thermometer.  The  extreme  range  of  such  pyrometers  is  about 
1200°  Fahr.,  but  they  are  probably  of  little  value  for  tempera- 
tures exceeding  1000°  Fahr. 

Wedgewood's  Pyrometer  is  based  on  the  permanent  contrac- 
tion  of   clay  cylinders    due   to   heating.     This   contraction  is 
determined  by  measurement  in  a  metal  groove  with  plane  sides 
^inclined  towards  each  other.     This  pyrometer  does  not  give 
Ji^niform  results. 

~  297.  Air-pyrometer. — The  air-thermometer  with  a  bulb  of 
|  porcelain,  or  platinum   or  other  refractory  material,  affords  am 
accurate  method  of  measuring  high  temperatures. 

Mr.-Hoadley*  states  that  the  ordinary  air-thermometer  made- 
of   hard  glass  can  be  used  to  determine  temperatures  of  800° 
Fahr.     With  porcelain  bulb  it  has  been  used  to  measure  tem- 
peratures of  1900°  Fahr. 

298.  Calorimetric  Pyrometers. — Pyrometers  of  this  class 
determine  the  temperature  by  heating  a  metal  or  other  refrac- 
tory substance  to  the  heat  of  the  medium  whose  temperature 
is  to  be  measured.  Suddenly  dropping  the  heated  body  into  a 
large  mass  of  water,  the  heat  given  off  by  the  body  is  equal  to 
that  gained  by  the  water ;  from  this  operation  and  the  known 
specific  heat  of  the  substance  the  temperature  is  computed. 
Thus,  let  K  equal  the  specific  heat  of  the  body,  M  its  weight ; 
let  W  equal  the  weight  of  water,  t  its  temperature  before,  and 
t'  after,  the  body  has  been  immersed  ;  let  T  equal  the  tempera- 
ture of  the  heated  body,  t'  its  final  temperature.  Then 

KM(T-tr}=  W(t'  -t). 

*  See  Vol.  VI.,  Transactions  American  Society  Mechanical  Engineers* 


382  EXPERIMENTAL   ENGINEERING.  [§  3OO. 

From  which 

W 


In  connection  with  pyrometrical  work,  the  specific  heat  of 
the  substance  used  often  has  to  be  determined. 

299.  Determination  of  Specific  Heat.  —  The  specific  heat 
of  a  body  is  determined  by  heating  it  to  a  known  temperature  ; 
for  instance,  after  heating  it  in  steam  of  atmospheric  pressure 
until    it  has  attained  a  known  temperature    T,  its  weight  M 
having   been   accurately  determined,  it  is  dropped    suddenly 
without  loss  of  heat  into  a  vessel  containing  ^pounds  of  water 
at  a  temperature  of  60°  Fahr.     Let  K  be  the  specific  heat  of 
the  body,  and  t'  the  resulting  temperature.     The  vessel  must 
be  so  made  that  there  is  no  loss  of  heat,  and  that  the  water 
can  be  thoroughly  agitated  so  that  an  accurate  measure  of  the 
temperature  t'  can  be  taken  ;   also  the  effect   of  the  vessel  in 
cooling  the  body  must  be  determined  and  considered  a  part  of 
the  weight  W.     Then  will  the  loss  of  heat  of  the  body  be  equal 
to  that  gained  by  the  water. 

K(T—  t')M=  W(t'  -  60°). 
From  which 

_  Fry  -60°) 

~  M  (T-t')' 

The  specific  heat  of  most  bodies  is  not  quite  constant  but 
is  found  to  increase  with  higher  temperatures. 

300.  Values    of   Specific    Heat    and    Melting-point— 

The  metals  required  for  pyrometrical  purposes  are  those  with 
a  high  melting-point  and  a  uniform  and  known  specific  heat. 
The  obvious  losses  of  heat  in  (i)  conveying  the  heated  body 
to  the  calorimeter,  and  (2)  radiation  of  heat  from  the  calorim- 
eter, may  be  considerable,  and  should  be  ascertained  by  radia- 
tion tests  and  the  proper  correction  made.  Nearly  all  metals 
.are  oxydized,  or  acted  on  by  the  furnace-gases,  long  before  the 
melting-point  is  reached  ;  so  that,  in  general,  whatever  metal 
is  used,  it  must  be  protected  by  a  fire-clay  or  graphite  crucible. 
Platinum,  copper  and  iron  are  usually  employed.  The  following 
table  gives  determinations  of  melting-points  and  specific  heats: 


S300.J 


MEASUREMENT  OF    TEMPERATURE. 


383 


TABLE   OF   MELTING-POINTS    AND   SPECIFIC    HEATS   OF 
METALS. 


Metal. 

Melting-point. 

Specific  Heat. 
Low  Temperatures. 

Degrees 
Fahr. 

Degrees 
Centigrade. 

2000 

415 
325 
264 
228 

425 

0.034 
0.118 
O.IIO 

0.14 
0.94 

0.170 

0.094 
0.093 

0.030  * 

0.030 
0.047 

0.030 

O.2OO 

Steel 

Wrought-iron.    ... 
Cast-iron  

2900 

3400 
2550 

Porcelain    

Brass  

1870 
700 
630 

493 
426 
-  38 
239 

Zinc      

Lead  

Bismuth      

Tin   

Sulphur               .  . 

The  mean  specific  heat  of  Platinum*  has  been  the  subject  of 
careful  investigation.  It  was  found  to  vary  from  0.03350  at 
100°  C.  to  0.0377  at  1100°  C.  by  Poullet,  the  experiment  being 
made  with  a  platinum  reservoir  air-thermometer. 

The  following  were  the  determinations : 


Platinum 

Copper. 

Range  of  Temperature. 
Degree  Centigrade. 

Mean  Specific 
Heat. 

Range  of  Temperature. 
Degree  Centigrade. 

Mean  Specific 
Heat. 

O  to     TOO 

0.03350 

15  to  IOO 

0.09331 

0           200 

.03392 

16   "  172 

0.09483 

o        300 

•03434 

17    "  247 

0.09680 

o        400 

.03476 

o        500 

•03518 

o        600 

.03560 

o        700 

.03602 

o        800 

.  03644 

o        900 

.03686 

O         IOOO 

.03728 

O         IIOO 

.03770 

*  See  Encyclopaedia  Britannica,  art.  Pyrometer. 


3  §4 


EXPERIMENTAL   ENGINEERING. 


301 


For  wrought-iron  the  true  specific  heat  at  a  temperature  t 
on  the  Centigrade  scale  is  given  as  follows  by  Weinbold : 

Ct  =  0.105907  +  0.00006538^  +  0.000000066477^. 

Porcelain  or  Fire-clay  having  a  specific  heat  from  0.17  to  o.2r 
although  not  a  metal,  is  well  adapted  for  pyrometrical  purposes. 

301.  Hoadley  Calorimetric  Pyrometer. — The  Hoadley 
pyrometer  is  described  in  Vol.  VI.,  p.  7I2>  Transactions  of 
the  American  Society  of  Mechanical  Engineers.  It  consisted 
of  a  vessel,  Fig.  183,  made  of  several  concentric  vessels  of 
copper,  with  water  in  the  inner  one,  eider-down  in  the  inter- 
mediate spaces,  and  a  cover  of  the  same  nature.  Also  a  sub- 


FIG.  183. — HOADLEY  PYROMETER. 

stance  to  be  heated  consisting  of  balls  of  platinum,  or  wrought- 
iron  and  copper  covered  with  platinum.  These  balls  were 
heated  in  a  crucible,  conveyed  to  the  calorimeter  and  suddenly 
dropped  in.  The  calorimeter  was  provided  with  an  agitator 
ma  ie  of  hard  rubber,  with  a  hole  in  the  centre  for  a  thermome- 
ter. The  balls  used  as  heat-carriers  weighed  about  three  quar- 
ters of  a  pound  each  ;  the  vessel  held  about  twelve  pounds  of 
water.  This  apparatus  is  now  at  Cornell  University. 


§  3°3-]  MEASUREMENT  OF    TEMPERATURE. 


385 


The  balls  were  heated   in   crucibles  and  conveyed  to  the 
calorimeter  in  a  fire-clay  jar  as  shown  in  Fig.  142.     The  cover 


FIG.  183.  —  PLATINUM  BALLS  ANU  CRUCIBLE. 

of  this  jar  was  quickly  removed  and  the  balls  dropped  into  the 
water  in  the  calorimeter. 

302.  Electric  Pyrometers.—  The  fact  that  electric  currents 
are  excited  by  differences  of  temperature  in  different  parts  of 
a  metallic  circuit  is  made  use  of  for  measuring  large  as  well  as 
small  differences  of  temperature. 

The  electromotive  force  of  a  circuit  at  different  tempera- 
tures is  given  by  Professor  Tait*  as 


in  which  E  =  electromotive  force  ;  Tt  a  constant  temperature, 
such  that  no  current  is  produced  if  temperatures  on  either  side 
are  equal,  and  which  depends  on  the  metal  :  for  copper  and 
iron  it  is  about  284°  C.  A  is  a  constant  depending  on  the 
metals  ;  tl  =  the  higher  temperature,  /2  the  lower. 

303.  Siemens's  Pyrometer.  —  This  instrument  is  based  on 
the  well-known  principle  of  increase  of  resistance  with  rise  of 
temperature. 

The  formula  given  by  Siemens  for  the  resistance  of  metals  is 


*  See  article  Pyrometer,  Encyc.  Britannica. 


386  EXPERIMENTAL   ENGINEERING.  [§  304. 

in  which  R  equals  the  resistance  to  be  measured,  a,  fi,  and  y 
are  coefficients,  and  T  equals  the  absolute  temperature. 

The  resistance  is  ascertained  by  a  volt-meter,  and  the  co- 
efficients a,  /?,  and  y  are  determined  by  special  calibration. 
The  heated  substance  is  a  platinum  wire  wound  around  a  clay 
cylinder  and  protected  by  a  covering  of  fine  clay;  this  is  in- 
serted into  the  furnace  or  medium  whose  temperature  is 
required.  The  current  is  passed  alternately  in  different  direc- 
tions, and  the  resistance  is  measured  by  the  gas  accumulating 
in  a  volt-meter  at  either  pole. 

The  instrument  is  very  sensitive  to  slight  changes  of  tem- 
perature, and  is  well  suited  for  accurate  measurements  of 
moderate  temperatures.  In  the  measurement  of  high  tem- 
peratures considerable  difficulty  was  experienced  because  of 
change  in  the  coefficients  due  to  the  extreme  heat. 

Callendar's  platinum  thermometer  is  an  electrical  pyrometer 
of  the  resistance  type  arranged  so  that  one  portion  is  maintained 
at  constant  temperature  by  being  kept  in  a  vessel  of  water  contain- 
ing melting  ice,  while  the  other  part  is  subjected  to  the  tempera- 
ture to  be  measured.  The  difference  in  resistance  of  these  two 
parts  affords  a  basis  for  determining  the  temperature.  This 
apparatus  is  exceedingly  accurate  and  capable  of  measuring 
very  small  subdivisions  of  a  degree. 

Professor  Brown  of  McGill  University  has  devised  a  form  of 
the  Callendar  instrument  in  which  the  difference  of  temperature 
is  determined  by  equalizing  the  resistance  through  two  circuits 
until  they  are  the  same,  which  fact  is  indicated  by  the  use  of  a 
telephone  whjch  transmits  no  sound  at  that  instant. 

304.  Optical  Pyrometers. — From  the  fact  that  the  color  of 
an  incandescent  body  varies  with  the  wave  length  and  this  again 
with  the  temperature,  it  is  possible  to  determine  the  temperature 
of  such  bodies  by  then  appearance. 

For  ihis  purpose  a  number  of  optical  pyrometers  have  been 
devised.  The  Mesure*  and  Nouel's  pyrometric  telescope  meas- 
ures the  temperatures  by  taking  advantage  of  the  rotation  of  the 
plane  of  polarization  of  light  passing  through  a  quartz  plate  cut 


MEASUREMENT   OF   TEMPERATURE. 


387 


perpendicular  to  its  axis.  The  angle  of  rotation  is  directly  pro- 
portional to  the  thickness  of  the  quartz,  and  approximately  in- 
versely proportional  to  the  square  of  the  wave  length. 

Light    from    an    incandescent    object,    passing    through    the 
slightly  ground  diffusing-glass  G  (Fig.  185),  enters  a  polarizing 


FlG.    185. — MESURfi  AND   NOUEL  PYROMETRIC  TELESCOPE. 

nicol  P,  and,  traversing  the  quartz  plate  Q,  strikes  the  analyzer  A, 
and  is  seen  through  the  eye  piece  OL. 

In  the  use  of  the  instrument  the  analyzer  is  turned  until  the 
object  appears  to  have  a  lemon-yellow  color.     The  position  of 


.Milli.Ammetei- 

FIG.  186. — THE  MORSE  THERMO-GAUGE. 

the  analyzer  is  indicated  by  the  graduated  circle  C,  the  reading 
of  which  may  be  referred  to  a  temperature  scale.  Because  of 
the  variations  due  to  personal  errors  of  different  observers  the 
uncertainties  of  observations  are  likely  to  amount  to  fully  100°  C. 
The  instrument  is  very  convenient  for  use  and  is  approximately 
accurate. 


388  EXPERIMENTAL   ENGINEERING.  [§  304. 

The  Morse  thermo-gauge  is  shown  in  Fig.  186.  It  employs 
an  incandescent  lamp  with  a  rheostat  arranged  so  that  the  current 
flowing  through  it  and  its  consequent  brightness  may  be  regu- 
lated. The  amount  of  current  flowing  through  is  shown  by  a 
milli-voltmeter  connected  in  circuit,  the  reading  of  which  can  be 
referred  to  a  scale  for  the  determination  of  temperature.  The 
lamp  is  adjusted  from  an  experimental  scale  for  its  degree  of 
brightness  at  different  ages. 

In  using  this  instrument  the  incandescent  lamp  is  located 
between  the  eye  and  the  object  whose  temperature  is  to  be  meas- 
ured, and  the  current  is  regulated  until  the  lamp  is  invisible.  This 
instrument  is  designed  for  use  in  hardening  steel  and  has  an 
extensive  use  in  that  industry. 

General  Remarks  regarding  Pyrometers.  —  An  ex- 
tended series  of  experiments  with  the  different  pyrometers 
described  has  led  the  author  to  believe  that  the  calorimetric 
forms,  as  described  in  Articles  298  and  301,  despite  their  in- 
convenience and  the  losses  from  radiation  which  attend  their 
use,  give,  if  we  except  the  air-pyrometer,  more  uniform  and  re- 
liable results  than  the  others.  The  electrical  pyrometers  are 
subject  to  the  same  inaccuracy  as  the  calorimetric  pyrometers, 
due  to  complex  changes  in  the  electrical  resistances  of  the 
thermometric  substance,  so  that  the  results  are  quite  uncer- 
tain for  high  temperatures. 

The  electrical  pyrometers  also  need  for  their  successful 
use  a  command  of  electrical  energy  and  the  possession  of  a  set 
of  electrical  measuring  instruments.  While  these  pyrometers 
may  give  reliable  results  with  skilled  electricians,  they  are  of 
little  practical  use  to  the  engineer.  The  calorimetric  pyrom- 
eters are  cheap,  portable,  and  easy  to  use,  and  with  careful 
handling  give  uniform  and  fairly  reliable  results.  The  best 
substance  for  use  in  these  instruments  as  a  heat-conveyer  is, 
in  the  opinion  of  the  author,  a  porcelain  or  fire-clay  ball 
about  2  inches  in  diameter.  The  metals,  not  even  excepting 
platinum,  are  readily  attacked  by  the  furnace-gases,  and  wher> 


§  304-] 


MEASUREMENT  OF    TEMPERATURE. 


389 


employed  need  to  be  protected  in  a  crucible  of  refractory 
material.  If  used  by  heating  directly  in  the  furnace,  wrought- 
iron  is  perhaps  as  good  as  any  of  the  metals.  It  may  be  oxi- 
dized and  fall  in  pieces,  but  since  the  oxide  has  about  the  same 
specific  heat  as  the  original  metal,  determinations  may  be  made 
with  the  residue  without  any  great  error.  The  porcelain  or 
fire-clay  balls  seem  to  be  unaffected  by  the  furnace-gases,  and 
do  not  radiate  heat  as  rapidly  as  the  metals,  so  that  were  the 
specific  heat  as  accurately  determined  they  would  be  superior 
in  every  way  to  the  metallic  balls.  The  determination  of  the 
specific  heat  of  burned  fire-clay  as  made  by  Mr.  D.  J.  Jenkins 
at  Sibley  College  was  0.1702  at  temperature  of  boiling  water. 
By  comparison  with  results  obtained  with  a  metal 
whose  specific  heat  was  known,  the  specific  heat 
at  1000°  C.  (1832°  F.)  is  calculated  as  about  0.20. 
The  latter  quantity  is  subject  to  correction. 

The  air -py- 
rometer with  a 
porcelain  or  plat- 
inum bulb  can  be 
used  convenient- 
ly, and  the  cor- 
responding tern 
peratures  so  read- 
ily and  easily 
deduced  from  the 
determinations 
that  it  is  worthy 
a  much  more  ex- 
tended use.  The 
bulb  may  be 
made  in  any  de- 
sired form  and  ELEMENT  OF  LE  CHATELIER'S  PYROMETER. 

a  long  capillary  stem  can  be  led  from  the  bulb  to  the  meas- 
uring tubes  a  long  distance  without  sensible  error,  so  that  it 
may  be  adapted  to  a  variety  of  uses. 


LE   CHATELIER'S   ELECTRICAL  PYROMETER. 


CHAPTER   XIII. 

METHODS  OF  DETERMINING  THE  AMOUNT  OF  MOISTURE 

IN  STEAM. 

305.  Quality    of   Steam.—  Degree  of   Superheat.— Steam 
may  be  dry  and  saturated,  wet  or  superheated,  as  described  in 
Article  265,  page  340.     The  term  quality  is  used  to  express 
the  relative  condition  of  the  steam  as  compared  with  dry  and 
saturated  steam  of  the  same  pressure.     It  is  in  any  case  the 
total  heat  in  a  pound  of  the  sample  steam,  less  the  heat  of  the 
liquid,  divided  by  the  total  latent  heat  of  evaporation  of  one 
pound  of  dry  steam  at  the  same  pressure,  see  page  343. 

For  moist  or  wet  steam,  which  is  to  be  considered  as  made 
up  of  a  mixture  of  water  and  dry  steam,  the  quality  would 
equal  the  percentage  by  weight  of  dry  steam  in  the  mixture. 

For  superheated  steam  the  quality  would  exceed  unity,  and 
is  to  be  considered  as  that  weight  of  dry  and  saturated  steam, 
the  heat  in  which  is  equivalent  to  that  in  one  pound  of  the 
superheated  steam,  neglecting  in  both  cases  the  heat  of  the 
liquid. 

In  case  of  superheated  steam,  its  temperature  is  higher 
than  that  of  dry  and  saturated  steam  at  the  same  pressure ; 
this  excess  of  temperature  is  termed  degree  of  superheat. 

306.  Importance   of  Quality  Determinations. — The  im- 
portance of  correctly  determining  the  quality  of  steam  is  great, 
because  the  percentage  of  water  carried  over  in  the  steam  in 
the  form  of  vapor  or  drops  of  water  may  be  large,  and  this 
water  is  an  inert  quantity  so  far  as  its  power  of  doing  work  is 
concerned,  even  if  not  a  positive  detriment  to  the  engine.     Any 
tests  for  the  efficiency  of  engine  or  boiler  not  accompanied 
with  determinations  of  the  amount  of  water  carried  over  in  the 

390 


§  309-]        THE  AMOUNT  OF  MOISTURE  IN   STEAM.  39! 

steam  would  be  defective  in  essential  particulars,  and  might 
lead  to  erroneous  or  even  absurd  results. 

307.  Methods  of  Determining  the  Quality.— The  methods 
of  measuring  the  amount  of  moisture  contained  in  steam  may 
be  considered  under  three  heads:  first,  Calorimetry proper,  in 
which  the  method  is  based  on  some  process  of  comparing  the 
heat  actually  existing  in   a  pound   of  the  sample  with   that 
known  to  exist  in  a  pound  of  dry  and  saturated  steam  at  the 
same  pressure.     Secondly,  Mechanical  Separation  of  the  water 
from  the  steam,  involving  the  processes  of  separation  and  of 
weighing.     Thirdly,  a  Chemical  Method,  in  which  case  a  soluble 
salt  is  introduced  into  the  water  of  the  boiler.     This  salt  is  not 
absorbed  by  dry  steam,  and  if  it  is  found  in  the  steam  it  indi- 
cates the  presence  of  water.     The  quality  is  equal  to  the  ratio 
of  salt  in  the  steam  to  that  in  an  equal  weight  of  water  drawn 
from  the  boiler. 

All  methods  for  determining  the  quality  of  steam  are 
included  under  the  head  of  calorimetry,  and  instruments  for 
determining  the  quality  are  termed  calorimeters. 

308.  Classification  of  Calorimeters. — The  following  clas- 
sification of  different  forms  of  calorimeter  is  convenient  and 
comprehensive: 

Barrel  or  Tank. 
Continuous. 

Condensing  ...  \  ,  Barrus_Continuous< 

Surface  , . .  \  Hoadley  Calorimeter. 

Tank  Calorimeter. 


Calorimeters  . . . .  < 


SBarrus- 
Hoadlei 
Kent—' 

c         ,        .  (   External — Barrus  Superheating. 

Superheating j   Internal-Peabody  Throttling 

I  Directly  determining  moisture j   ChSScSi 

309.  Error  in  Calorimetric  Processes. — The  calorimetric 
processes  proper  depend  on  the  method  of  measuring  the  heat 
actually  existing  in  a  pound  of  the  sample  steam  at  a  known 
pressure.  This  measurement  is  then  compared  with  the  re- 
sults given  in  a  steam-table  for  dry  and  saturated  steam,  and 
the  quality  is  computed  as  will  be  explained  later. 


392 


EXPERIMEN  TA  L   ENGINEERING. 


[§310. 


In  nearly  every  calorimetric  process  the  heat  of  the  sample 
is  determined  by  -condensing  the  steam  at  atmospheric  press- 
ure, or  at  least  measuring  the  heat  when  its  conditions  of 
pressure  and  temperature  are  different  from  its  original  state. 
This  process  involves  no  error.  The  following  is  a  statement  of 
an  investigation  concerning  it  made  by  Sir  William  Thomson:* 

"  If  steam  have  to  rush  through  a  long  fine  tube  or 
through  a  fine  aperture  within  a  calorimetric  apparatus,  its 
pressure  will  be  diminished  before  it  is  condensed ;  and  there 
will,  therefore,  in  two  parts  of  the  calorimeter  be  saturated 
steam  at  different  temperatures;  yet  on  account  of  the  heat 
developed  by  the  fluid  friction,  which  would  be  precisely  the 
equivalent  of  the  mechanical  effect  of  the  expansion  wasted  in 
the  rushing,  the  heat  measured  by  the  calorimeter  would  be 
precisely  the  same  as  if  the  condensation  took  place  at  a  press- 
ure not  appreciably  lower  than  that  of  the  entering  steam." 

310.  Use  of  Steam-tables. — In  reducing  calorimetric  ex- 
periments steam-tables  will  be  required.  The  explanation  of 
the  terms  used  will  be  found  in  Article  265,  page  340,  and 
tables  will  be  found  in  the  Appendix  of  the  book. 

Students  will  please  notice,  that  the  pressures  referred  to  in 
the  steam-tables  are  absolute,  not  gauge  pressures,  and  that 
gauge  pressures  are  to  be  reduced  to  absolute  pressures,  by 
adding  the  barometer-reading  reduced  to  pounds  per  square 
inch,  before  using  the  tables. 

The  following  symbols  will  be  employed  to  represent  the 
different  properties  of  steam  : 

TABLE  OF  SYMBOLS. 


Properties  of  Steam. 

Symbol. 

Properties  of  Steam. 

Symbol. 

•b 

Total  heat  B    T   U 

/I  or  If 

Pressure,  pounds  per  sq.  foot 
Temperature,  degrees  Fahr. 

*e 

t 
T 

Weight  of  cu.  ft.  of  steam  Ibs. 
Vol.  of  i  Ib.  steam,  cubic  ft. 
Vol    of  i  Ib   water   cubic  ft 

dor  W 
v  or  C 
(j 

Heat  of  the  liquid     •    .      .  . 

a  or  S 

Change  in  volume  v  -—  <r. 

14 

y   ui    o 

p  or  J 

Quality  of  steam   

x 

APuor  E 

Per  cent  of  moisture    .  .  . 

I  —  X 

Total  latent  heat       . 

r  or  L 

Degree  of  superheat  

D 

*  Mathematical  Papers,  XLVIII.,  p.  194. 


§  3*2.]        THE  AMOUNT  OF  MOISTURE  IN  STEAM.  393 

The  quantities  q,  p,  APu,  r,  and  A  are  given  in  B.  T.  U. 
per  pound  of  saturated  steam  reckoned  from  32°  Fahr. 

311.  General  Formula  for  the  Heat  in  One  Pound  of 
Steam.  —  The  heat  existing  in  one  pound  of  steam  with  any 
quality  x  can  be  expressed  by  the  formula 


(i) 


The  heat,  however,  which  is  required  to  raise  water  from 
32°  F.  and  convert  it  into  steam  at  a  given  temperature  will 
include  the  external  latent  heat,  and  will  be  expressed  by  the 
formula 

xr  +  q  =  h'  ........     (2) 

The  heat  that  may  be  given  out  by  condensation  or  change 
of  pressure  is  expressed  in  equation  (2)  ;  that  which  exists  in 
the  steam  without  change  of  pressure  or  external  work,  by 
equation  (i). 

Since  in  all  calorimetric  processes  the  steam  is  condensed, 
or  at  least  the  pressure  changed,  equation  (2)  is  to  be  employed 
to  represent  the  available  heat. 

If  the  pressure  of  the  steam  is  known,  r  and  q  can  be  found 
from  the  steam-tables.  If  the  heat  h  in  B.  T.  U.  above  32° 
can  be  found  for  the  sample  steam,  all  the  quantities  in  the 
above  equation  with  the  exception  of  x  are  known,  and  we 
shall  find 

//'-  q 
— 


(3) 


In  case  x  is  greater  than  unity,  the  steam  is  superheated,  and 
the  degree  of  superheat 


when  0.48  equals  the  specific  heat  of  steam,  cp. 

312.  Methods  of  Determining  the  Heat  in  a  given 
Sample  of  Steam.  —  There  are  two  methods  of  determining 
the  heat  //  in  a  given  sample  of  steam. 


394  EXPERIMENTAL   ENGINEERING.  [§  312. 

I.  Condensing  the  Steam  at  Atmospheric  Pressure.  —  In  this 
case  the  weight  of  the  steam  is  obtained  by  weighing  the  con- 
densing water  before  and  after  condensation  has  taken  place 
and  determining  the  corresponding  temperatures.  Thus  let 
the  weight  of  condensing  water  be  represented  by  W,  that  of 
the  condensed  steam  by  w\  the  temperature  of  the  condensing 
water  cold  by  /,  ,  the  condensing  water  warm  by  t^  ;  the  original 
temperature  of  the  steam  by  t,  that  of  the  condensed  steam  by 
£,  .  Suppose  that  the  calorimeter  absorb  heat  to  the  same 
extent  as  k  pounds  of  water;  then  the  heat  added  by  con- 
densing one  pound  of  steam  is  equal  to 


The  original  heat  above  32°  from  equation  (2),  page 
is  xr-\-q.  Since  in  equation  (5)  the  temperature  is  reck- 
oned above  zero,  it  will  be  more  convenient  to  use,  instead  of 
xr-\-  q-\-  32,  xr  -\-  1,  which  is  very  nearly  identical. 

Since  the  heat  lost  in  condensing  one  pound  of  steam  is 
equal  to  that  gained  by  the  water,  we  shall  evidently  have 


from  which 


w 


If  the  temperature  of  condensed  steam  equal  that  of  the 
warm  condensing  water,  /,  =  /a,  which  is  the  usual  condition  of 
condensation. 

2.  Superheating  the  Steam. — If  the  pressure  and  tempera- 
ture of  superheated  steam  is  known,  the  degree  of  superheat  D 
can  be  found  by  deducting  the  normal  temperature,  as  given 
in  the  steam-table  for  that  pressure,  from  the  observed  tem- 
perature. The  total  heat  in  a  pound  of  the  superheated  steam 


§  3  1 3-]        THE  AMOUNT  OF  MOISTURE   IN  STEAM. 


395 


is  equal  to  that  in  a  pound  of  saturated  steam,  as  given  by  the 
steam-tables,  plus  the  product  of  the  degree  of  superheat  into 
the  specific  heat  cp  of  the  steam  ;  that  is, 


The  superheating  may  be  done  by  extraneous  means,  as  in 
the  Barrus  superheating  calorimeter,  or  by  throttling,  as  in 
the  throttling  calorimeter.  In  the  latter  the  heat  required  for 
superheating  is  obtained  by  reducing  the  pressure,  which,  being 
accompanied  by  a  corresponding  reduction  of  boiling  point, 
liberates  heat  sufficient  to  evaporate  a  small  percentage  of 
moisture  only. 

In  the  case  of  the  superheating  calorimeter,  the  heat  re- 
quired to  evaporate  the  moisture  and  superheat  the  steam  is 
measured  by  the  loss  of  temperature  n  in  an  equal  weight  of 
superheated  steam,  so  that 


=  r(i  —  x}-\-cpD\ 


I  —  x  =  c. 


(n-D) 


(7) 


In  the  case  of  the  throttling  calorimeter  there  is  no  change 
in  the  total  amount  of  heat,  but  there  is  a  change  of  pressure,  so 
that  the  quantities  in  the  first  member  of  (8)  correspond  to  the 
original  pressures  of  steam  before  throttling,  and  those  in  the 
second  member  to  the  calorimeter  pressures  after  throttling,  and 


xr 


q  — 


cpD, 


(8) 


313.  Condensing  Calorimeters.— Condensing  calorimeters 
ire  of  two  general  classes  :  I.  The  jet  of  steam  is  received  by 
:he  condensing  water,  and  the  condensed  steam  intermingles 
lirectly  with  the  condensing  water.  2.  The  jet  of  steam  is 
:ondensed  in  a  coil  or  pipe  arranged  as  in  a  surface  condenser. 


EXPERIMENTAL  ENGINEERING.  [§  314. 

and  the  condensed  steam  is  maintained  separate  from  the  con- 
densing water. 

The  principle  of  action  of  both  classes  of  condensing  calo- 
rimeter is  essentially  the  same,  and  is  expressed  by  equation 
(6): 


w 


In  the  first  class  /3  =  /a,  and 


x  = 


w 


Both  forms  of  condensing  calorimeter  can  be  made  to  act  con- 
tinuously or  at  intervals,  and  there  are  several  distinct  types  of 
each. 

The  most  common  type  of  condensing  calorimeter  is  one 
in  which  the  condensing  water  is  received  in  a  barrel  or  tank, 
and  hence  is  termed  a  barrel  calorimeter.  The  special  forms 
will  be  described  later. 

314.  Effect  of  Errors  in  Calorimeter  Determinations. 

First.  Condensing  Calorimeters. — To  determine  the  effect 
of  error,  suppose  in  each  case  the  quantity  under  discussion  to 
be  a  variable  and  differentiate  the  equation 


w 


r 

We  have 

Ax  -±  A  W=  (/a  —  /,)  ~  wr ; 


Ax  +  At,    =[( fF-*- w)  +  i] -5- r; 
Ax  ~  At.,     =  W+wr. 


§314-]        THE   AMOUNT   OF  MOISTURE   IN  STEAM. 


397 


Since  Ar  ~  —  At,  nearly,  for  ordinary  pressures  of  steam,  and 
further  is  a  function  of  the  pressure,  we  have  approximately 

Ap  =  Ap  =  —  Ar  ; 


[W 
—  (^-O-'- 


The  weight  of  condensing  water  usually  held  by  the  barrel- 
calorimeters  is  from  300  to  400  Ibs.,  while  the  weight  of  the 
steam  condensed  varies  from  1  6  to  20  Ibs.,  and  the  correspond- 
ing temperatures  have  a  range  of  50°  to  70°  F.  For  these  cases 
it  will  be  found  that  the  percentage  of  error  in  quality,  sup- 
posing other  data  correct,  is  approximately  the  same  as  the 
percentage  of  error  in  the  weights.  The  error  in  thermometer- 
determination  has  nearly  the  same  effect,  whether  made  before 
or  after  the  steam  has  been  condensed.  For  the  amounts  usu- 
ally employed  the  error  of  one  fifth  of  one  degree  in  tempera 
ture  has  about  the  same  effect  as  one  half  of  one  per  cent  error 
in  weight  ;  that  is,  it  makes  an  error  of  about  the  same  amount 
in  the  quality  of  steam. 

The  following  shows  in  tabular  form  the  effect  of  errors 
with  condensing  calorimeters  in  which  the  ordinary  weights  of 
water  and  of  steam  are  used  : 

TABULATION  OF  ERRORS. 


Error  in 
Condensing  Water. 

Error  in 
Condensed  Steam. 

Error 
in 
Temperature, 
Cold  Water. 

Error 
in 
Temperature, 
Warm  Water. 

Error 
in 
Steam- 
pressure. 

ting  Error  in 
y.  Per  cent.  | 

Lbs. 

Per  ct. 

Lbs. 

Per  ct. 

Degs. 

Per  ct. 

Degs. 

Per  ct. 

Lbs. 

Perc. 

s:5 

S3 
*c* 

Total  wt. 

=  360  Ibs. 

Total  wt. 

=  20  Ibs. 

Temp. 

=50°  F. 

Temp. 

=110°  F. 

Pr.  = 

88  Ibs. 

?i 

I-  5 

*  3 

Total  wt. 

i  .0 

o-5 
0.40 
o.oS 

O.2 
O.I 
O.oS 
O.Olti 

I.O 

o-S 
0.4 
0.08 

°-53 
0.27 
0.18 
0.045 

1.2 

0.6 
0-5 

O.I 

0.65 
0.30 
0.25 
0.05 

0.60 
0.30 

2-5 

0.50 

7.0 
3-5 
3-o 
0.6 

8.0 
4.0 
3-5 
07 

I  2 

0.6 

05 

O.I 

=  300  Ibs. 

Total  wt. 

=  20  Ibs. 

0.25 

1-5 

0.5 

O.I 

o-5 

0.2 

2.2 

r-  5 

EXPERIMENTAL   ENGINEERING.  [§  314. 

In  the  table,  the  errors  in  the  various  observations  ex- 
pressed in  the  same  horizontal  line  have  the  same  effect  on 
the  result, 

From  the  table  it  is  seen,  for  the  given  weights,  that  an 
error  of  3.6  pounds  in  condensing  water,  of  0.2  pound  in  con. 
densed  steam,  of  0.53°  F.  in  temperature  of  cold  water,  of  0.65° 
F.  in  warm  water,  or  of  7  pounds  in  steam-pressure  will  sever- 
ally make  an  error  in  the  result  of  1.2  per  cent.  Expressed  in 
percentages,  an  error  of  I  per  cent  in  weight  or  1.2  and  0.6 
per  cent  in  thermometer-readings  makes  an  error  in  the  quality 
of  1.2  per  cent. 

The  conditions  for  determination  of  moisture  within  one 
half  of  one  per  cent  require — 

1.  Scales  that  weigh  accurately  to  half  of  one  per  cent  of 
the  quantity  to  be  weighed. 

2.  Thermometers    that    give    accurate    determinations    to 
about  one  fifth  of  one  degree  F. 

3.  An  accurate  pressure-gauge. 

4.  Correct  observations  of  the  resulting  quantities. 

5.  Determination  of  loss  caused  by  calorimeter. 

Secondly.  Superheating  Calorimeters. — The  Barrus  Super- 
heating Calorimeter. — In  this,  if  /3  —  /  is  the  gain  of  tempera- 
ture of  the  sample  steam,  and  /,— /,  is  the  loss  of  temperature 
in  the  superheated  steam,  we  have,  neglecting  radiation, 

I  -  x  —  o.48[/2  —'/,.—  (/,  —  /)]  -T-  r. 

In  the  Throttling  Calorimeter,  where  the  steam  is  super- 
heated by  expanding,  we  have  by  equation  (7),  making  cp  = 
0.48, 

_  A  +  0.48£>  —  q 


In  either  form  of  superheating  calorimeter  the  effect  of  an 
error  of  one  degree  in  temperature  is  to  make  an  error  in  x  of 
O.o6  of  one  per  cent,  while  an  error  of  9°  in  temperature  will 
affect  the  value  of  x  but  0.5  per  cent.  The  boiling-point 


§  3I50        THE  AMOUNT  OF  MOISTURE  IN  STEAM.  399 

should  be  correctly  determined,  however,  especially  if  the 
amount  of  superheating  is  small. 

An  error  in  gauge-reading  has  about  one  half  the  effect  on 
the  quality  of  the  steam  as  in  the  other  class  of  calorimeters. 

315.  Method  of  Obtaining  a  Sample  of  Steam. — It  is 
usually  arranged  so  as  to  pass  only  a  very  small  percentage  of 
the  total  steam  through  the  calorimeter,  and  it  is  important 
that  this  sample  shall  fairly  represent  the  entire  quantity  of 
steam.  From  experiments  made  by  the  author,  it  is  quite  cer- 
tain that  the  quality  varies  greatly  in  different  portions  of  the 
same  pipe,  and  that  it  differs  more  in  horizontal  than  in  verti- 
cal pipes.  Steam  drawn  from  the  surface  of  the  pipe  is  likely 
to  contain  more  than  the  average  amount  of  moisture ;  that 
from  the  centre  of  the  pipe  to  contain  less.  The  better 
method  for  obtaining  a  sample  of  steam  is  to  cut  a  long 
threaded  nipple  into  which  a  series  of  holes  may  be  drilled, 
and  screw  this  well  into  the  pipe.  Half-inch  pipe  is  gen- 
erally used  for  calorimeter  connections,  and  it  may  be  screwed 
into  the  main  pipe  one  half  or  three  quarters  of  the  distance  to 
the  centre,  with  the  end  left  open  and  without  side-perfora- 
tions, as  shown  in  Fig.  187,  or  screwed  three  fourths  the 


«  pine 


FIG.  i87.  COLLECTING-NIPPLES.  FIG.  188. 

distance  across  the  pipe,  a  series  of  holes  drilled  through  the 
sides,  and  the  end  left  open  or  stopped,  as  shown  in  Fig.  144. 
A  lock-nut  on  the  nipple,  which  can  be  screwed  against  the 
pipe  when  the  nipple  is  in  place,  will  serve  to  make  a  tight 
joint  The  best  form  of  nipple  is  not  definitely  determined, 
although  many  experiments  have  been  made  for  this  purpose; 
a  form  extending  nearly  across  the  pipe  and  provided  with  a 


400 


EXPERIMENTAL  ENGINEERING. 


[ 


slit  or  with  numerous  holes  is  probably  preferable.  When 
the  current  of  steam  is  ascending  in  a  vertical  pipe,  the  water 
seems  to  be  more  uniformly  mixed  than  when  descending  in 
a  vertical  pipe  or  when  moving  in  a  horizontal  one0  There 
is,  however,  considerable  variation  tor  this  condition? 
especially  if  the  steam  contains  more  than  3  per  cent  of  water0 
316.  Method  of  Inserting  Thermometers.— In  the  use  of 
calorimeters  it  is  frequently  necessary  to  insert  thermometers 


FIG.  189. — STEAM-THERMOMETER.  FIG  190.— THERMOMETER-CUP. 

into  the  steam  in  order  to  correctly  measure  the  temperature. 
For  this  purpose  thermometers  can  be  had  mounted  in  a 
brass  case,  as  shown  in  Fig.  189,  which  will  screw  into  a 
threaded  opening  in  the  main  pipe. 

The  author  prefers  to  use  instead  a  thermometer-cup  of  the 
form  shown  in  Fig.  190,  which  is  screwed  into  a  tapped  open- 


§  3I7-]         THE  AMOUNT  OF  MOISTURE  IN  STEAM.  4OI 

ing  in  the  pipe.  Cylinder-oil  or  mercury  is  then  poured  into 
the  cup,  and  a  thermometer  with  graduations  cut  on  the  glass 
inserted.  The  thermometer-cups  are  usually  made  of  a  solid 
brass  casting,  the  outside  being  turned  down  to  the  proper  di- 
mensions and  threaded  to  fit  a  f-inch  pipe-fitting.  The  inside 
hole  is  drilled  \  inch  in  diamciter,  and  the  walls  are  left  -fa  inch 
thick.  The  total  length  varies  from  4^  to  6  inches — depending 
on  the  place  where  it  must  be  used.  In  either  case  it  is  essen- 
tial that  the  thermometer  be  inserted  deep  into  the  current  of 
steam  or  water,  and  that  no  air-pocket  forms  around  the  bulb 
of  the  thermometer.  The  thermometer  should  be  nearly  ver- 
tical, and  as  much  of  the  stem  as  possible  should  be  protected 
from  radiating  influence. 

If  the  thermometer  is  to  be  inserted  into  steam  of  very  little 
pressure,  the  stem  of  the  thermometer  can  be  crowded  into  a 
hole  cut  in  a  rubber  cork  which  fits  the  opening  in  the  pipe. 
In  case  the  thermometer  cannot  be  inserted  in  the  pipe  it  is 
sometimes  bound  on  the  outside,  being  well  protected  from 
radiation  by  hair- felting;  but  this  practice  cannot  be  recom- 
mended, as  the  reading  is  often  much  less  than  is  shown  by  a 
thermometer  inserted  in  the  current  of  flowing  steam.  In  the 
use  of  thermometers,  breakages  will  be  lessened  by  carefully 
observing  the  directions  as  given  in  Article  286,  p.  370. 

317.  Determination  of  the  Water-equivalent  of  the 
Calorimeter.  —  The  calorimeters  exert  some  effect  on  the 
heating  of  the  liquid  contained  in  them,  since  the  inner  sub- 
stance of  the  calorimeter  must  also  be  heated.  This  effect  is 
best  expressed  by  considering  the  calorimeter  as  equivalent  to 
a  certain  number  of  pounds  of  water  producing  the  same 
result.  This  number  is  termed  the  water- equivalent  of  the 
calorimeter.  The  water-equivalent,  k,  can  be  found  in  three 
ways: 

i.  By  computing  from  the  known  weight  and  specific  heat 
of  the  materials  composing  the  calorimeter.  Thus  let  c  be  the 
specific  heat,  Wc  the  weight;  then 

k=cWc. 


402  EXPERIMENTAL   ENGINEERING.  [§  318. 

2.  By  drawing  into  the  calorimeter,  when  it  is  cooled  down 
to  a  low  temperature,  a  weighed  quantity  of  water  of  higher 
temperature  and  observingvthe  resulting  temperature.  Thus 
let  W  equal  the  weight  of  water,  tl  the  first  and  t^  the  final 
temperatures,  and  k  the  water-equivalent  sought.  Since  the 
heat  before  and  after  this  operation  is  the  same, 


From  which 

„ 

fC   •  - 


3.  By  condensing  steam  drawn  from  a  quiescent  boiler,  and 
thus  known  to  be  dry  and  saturated,  with  a  weighed  quantity 
of  water  of  known  temperature  in  the  calorimeter  ;  the  tempera- 
ture, pressure,  and  weight  of  the  steam  being  known.  The  con- 
ditions are  the  same  as  for  equation  (6),  page  394,  all  the 
quantities  being  known  excepting  k. 

By  solving  equation  (6), 


For  the  barrel  and  jet  condensing  calorimeters  generally,  £,  =  /2 , 
and  we  have 

,  _  w(rx  +  /  — -  *a)        ,,, 

The  cooling  effect  of  superheating  calorimeters  is  generally 
expressed  in  degrees  of  temperature  in  the  reading  of  one  of 
the  thermometers. 

SPECIAL  FORMS   OF   CALORIMETERS. 

318.  Barrel  or  Tank  Calorimeter.— The  barrel  calorim- 
eter belongs  to  that  class  of  condensing  calorimeters  in  which 
a  jet  of  steam  intermingles  directly  with  the  water  of  conden- 
sation. It  is  made  in  various  ways ;  in  some  instances  the 


§  3I8.J        THE  AMOUNT  OF  MOISTURE   IN  STEAM. 


403 


walls  are  made  double  and  packed  with  a  non-condensing 
substance,  as  down  or  hair-felting,  to  prevent  radiation,  and 
the  instrument  is  provided  with  an  agitator  consisting  of 
paddles  fastened  to  a  vertical  axis  that  can  be  revolved  and 
the  water  thoroughly  mixed  ;  but  it  usually  consists  of  an  ordi- 
nary wooden  tank  or  barrel  resting  on  a  pair  of  scales,  .is 
shown  in  Fig.  191. 


FIG.  191. — THE  -BARREL  CALORIMETER. 

A  sample  of  steam  is  drawn  from  the  main  steam-pipe  by 
connections,  as  explained  in  Article  315,  page  36$,  and  con- 
veyed by  hose,  or  partly  by  iron  pipe  and  partly  by  hose,  to 
the  calorimeter.  In  the  use  of  the  instrument,  water  is  first 
admitted  to  the  barrel  and  the  weight  accurately  determined. 
The  pipe  is  then  heated  by  permitting  steam  to  blow  through 
it  into  the  air ;  steam  is  then  shut  off,  the  errd  of  the  pipe  is 
submerged  in  the  water  of  the  calorimeter,  and  steam  turned 
on  until  the  temperature  of  the  condensing  water  is  about  1 10° 
F.  The  pipe  is  then  removed,  the  water  vigorously  stirred,  the 
temperature  and  the  final  weight  taken.  If  the  effect  of  the 
calorimeter,  k,  expressed  as  additional  weight  of  water,  is 
known,  the  quality  can  be  computed  as  in  equation  (6),  page  394. 


X  = 


iv  r 


-^.  . . .  (6) 


404  EXPERIMENTAL   ENGINEERING.  L§ 

A  tee  screwed  crosswise  of  the  pipe,  as  shown  in  Fig.  189, 
forms  an  efficient  agitator,  provided  the  temperature  be  taken 
immediately  after  the  steam  is  turned  off. 

The  pipe  may  remain  in  the  calorimeter  during  the  final 
weighing  if  supported  externally,  and  if  air  be  admitted  so  that 
it  will  not  keep  full  of  water ;  in  such  a  case,  however,  it  should 
also  be  in  the  barrel  during  the  first  weighing,  or  else  the  final 
weight  must  be  corrected  for  displacement  of  water  by  the 
pipe.  The  effect  of  displacement  is  readily  determined  by 
weighing  with  and  without  the  pipe  in  the  water  of  the  calo- 
rimeter. 

The  determination  of  the  water-equivalent  of  the  barrel 
calorimeter  will  be  found  very  difficult  in  practice,  and  it  is 
usually  customary  to  heat  the  barrel  previous  to  using  it,  and 
then  neglect  any  effect  of  the  calorimeter.  This  nearly  elimi- 
nates the  effect  of  the  calorimeter.  The  accuracy  of  this 
instrument,  as  shown  in  Article  314,  page  397,  depends  prin- 
cipally on  the  accuracy  with  which  the  temperature  and  the 
weight  of  the  condensed  steam  are  obtained.  The  conditions 
for  obtaining  the  temperature  of  the  water  accurately  are 
seldom  favorable,  as  it  is  nearly  impossible  to  secure  a  uniform 
mixture  of  the  hot  and  cold  water;  the  result  is  that  deter- 
minations made  with  this  instrument  on  the  same  quality  of 
steam  often  vary  3  to  6  per  cent.  From  an  extended  use  in 
comparison  with  more  accurate  calorimeters,  the  author  would 
place  the  average  error  resulting  from  the  use  of  the  barrel 
calorimeter  at  from  2  to  4  per  cent. 

Example. — Temperature  of  condensing  water,  cold,  tl ,  is 
52°. 8  F.;  warm,  /2 ,  IO9°.6  F.  Steam-pressure  by  gauge,  79.7; 
absolute,  94.4.  Entering  steam,  normal  temperature,  from 
steam-table,  • /,  323°.$  F.  Latent  heat,  r,  888.2  B.  T.  U. 
Weight  of  condensing  water  cold,  W,  360  pounds ;  warm, 
W-\-w,  379.1  pounds,  wet  steam,  w,  19.1  pounds.  Calorim- 
eter-equivalent eliminated  by  heating.  The  quality 

^60  (1096-  52.8)  _  323.5  -  109.6 
"  19.1"         888^2  888.2 


§  320,]        THE  AMOUNT  OF  MOISTURE   IN  STEAM.  405 

319.  Directions  for  Use   of  the   Barrel  Calorimeter.— 

Apparatus. — Thermometer  reading  to  \  degree  F.,  range  32° 
to  212°  ;  scales  reading  to  -fa  of  a  pound  ;  barrel  provided  with 
means  of  filling  with  water  and  emptying ;  proper  steam  con- 
nections ;  steam-gauge  or  thermometer  in  main  steam-pipe. 

1.  Calibrate  all  apparatus. 

2.  Fill  barrel  with  360  pounds  of  water,  and  heat  to   130 
degrees  by  steam  ;  waste  this  and  make  no  determinations  for 
moisture.     This  is  to  warm  up  the  barrel. 

3.  Empty   the    barrel,    take    its   weight,   add    quickly   360 
pounds  of  water,  and  take  its  temperature. 

4.  Remove  steam-pipe  from  barrel ;  blow  steam  through  it 
to  warm  and  dry  it ;  hang  on  bracket  so  as  not  to  be  in  contact 
with  barrel ;  turn  on  steam,  and  leave  it  on  until  temperature 
of  resulting  water  rises  to   110°  F.     Turn  off  steam  ;  open  air- 
cock  at  steam-pipe  as  explained. 

5.  Take  the  final  weights  with  pipe  in  barrel,  in_  nrnir  FJQ 
sition  as  in  previous  weighings ;  also  take  weights  with  the  pipe 
removed  :  calculate  from  this  the  displacement  due  to  pipe,  and 
correct  for  same. 

Alternative  for  fourth  and  fifth  operations. — Supply  steam 
through  a  hose,  which  is  removed  as  soon  as  water  rises  to  a 
temperature  of  110°  F.  Weigh  with  the  hose  removed  from 
the  barrel.  Stir  the  water  while  taking  temperatures. 

6.  Take  five  determinations,  and  compute   results  as   ex- 
plained.    Fill  out  and  file  blank  containing  data  and  results. 

7.  Compute  the  value  of  the  water-equivalent,  £,  in  pounds 
by  comparing  the  different  sets  of  observations. 

320.  The    Continuous-jet    Condensing    Calorimeter.-— 
A  calorimeter  may  be  made  by  condensing  the  jet  of  steam  in 
a  stream  of  water  passing  through  a  small  injector  or  an  equiva- 
lent instrument.     The  method  is  well  shown  in  Fig.  193.     A 
tank  of  cold  water,  B,  placed  upon  the  scales  R,  is  connected 
to  the  small  injector  by  the  pipe  C\  the  injector  is  supplied 
with  steam  by  the  pipe  S,  the  pressure  of  which  is  taken  by 
the  gauge  P\  the  temperature  of  the  cold  water  is  taken  at  ey 
that  of  the  warm  water  at  g.     Water  is  discharged  into  the 


406 


EXPERIMENTAL  ENGINEERING. 


[§  320. 


weighing-tank  A.  The  amount  taken  from  the  tank  B  is  the 
weight  of  cold  water  W\  the  difference  in  the  respective 
weights  of  the  water  in  tanks  A  and  B  is  the  weight  of  the 
steam  w. 

The  quality  is  computed  exactly  as  for  the  barrel  calorim- 
eter. 

In  case  an  injector  is  used,  as  shown  in  Fig.  192,  the  tank 
B  is  not  needed :  water  can  be  raised  by  suction  from  the  tank 
A  through  the  pipe  d.  The  original  weight  of  A  will  be  that 


FIG.  19*.— THE  INJECTOR  CALORIMETER. 

of  the  cold  water;  the  final  weight  will  be  that  of  steam  added 
to  the  cold  water. 

In  case  an  injector  is  not  convenient,  and  the  water  is  sup- 
plied under  a  small  head,  a  very  satisfactory  substitute  can  be 
made  of  pipe-fittings,  as  shown  in  Fig.  193.  In  this  case,  steam 
of  known  pressure  and  temperature  is  supplied  by  the  pipe  A 
cold  water  is  received  at  S',  and  the  warm  water  is  discharged 
at  S.  The  temperature  of  the  entering  water  is  taken  by  a 
; thermometer  in  the  thermometer-cup  T',  that  of  the  discharge 
by  a  thermometer  at  T.  The  steam  is  condensed  in  front  of 
the  nozzle  C. 

This  class  of  instruments  present  much  better  opportunities 
of  measuring  the  temperatures  accurately  than  the  barrel 
calorimeter,  and  the  results  are  somewhat  more  reliable. 


§  321.]        THE   AMOUNT  OF  MOISTURE  IN  STEAM. 


407 


In  the  use  of  continuous  calorimeters  of  any  class,  the  in- 
strument should  be  put  in  operation  before  the  thermometers 
are  put  in  place  or  any  observations  taken.  The  poise  on  the 
weighing-scale  can  be  set  somewhat  in  advance  of  its  bal- 
ancing position,  and  when  sufficient  water  has  been  pumped 
out  the  scale-beam  will  rise ;  this  may  be  taken  as  the  signal 


FIG.  193.— JET  CONTINUOUS  CALORIMETER. 


for  saving  the  water  which  has  been  previously  wasted,  and 
of  commencing  the  run. 

The  water-equivalent  of  the  calorimeter,  k,  will  be  smallt 
and  due  principally  to  radiation.  It  can  be  found  by  passing 
hot  water  through  the  calorimeter  and  noting  the  loss  in  tem- 
perature. 

321.  The  Hoadley  Calorimeter. — This  instrument  be. 
longs  to  the  class  of  non-continuous  surface  calorimeters.  The 


408 


EXPERIMENTAL   ENGINEERING. 


instrument  is  described  in  Transactions  of  the  American  So- 
ciety of  Mechanical  Engineers,  Vol.  VI.,  page  716,  and  consisted 
of  a  condensing  coil  for  the  steam,  situated  in  the  bottom  of  a 
tank-calorimeter,  very  carefully  made  to  prevent  radiation- 
losses.  The  dimensions  were  17  inches  diameter  by  32  inches 
deep,  with  a  capacity  of  about  200  pounds  of  water.  The 


FIG.   194. — HOADLEY'S  CALORIMETER. 

calorimeter  was  made  of  three  concentric  vessels  of  galvanized 
iron,  the  spaces  being  filled  with  hair-felt  and  eider-down. 
The  condenser  consisted  of  a  drum  through  which  passed 
a  large  number  of  half-inch  copper  tubes,  the  steam  being 
on  the  outside,  the  water  on  the  inside,  of  these  tubes ;  the 
agitator  consisting  of  a  propeller-wheel  attached  to  an  axis 
that  could  be  rotated  by  turning  the  external  crank  K,  effectu- 
ally stirring  the  water.  The  thermometer  for  measuring  the 
temperature  was  inserted  in  the  axis  of  the  agitator  at  T. 


§  322,]        THE  AMOUNT  OF  MOISTURE   IN  STEAM. 


409 


In  the  hands  of  Mr.  Hoadley  the  instrument  gave  accurate 
determinations. 

In  practice  the  instrument  was  arranged  as  in  Fig.  195;  the 
calorimeter  E  was  placed  on  the  scales  F,  and  supplied  by 
cold  water  from  the  elevated  barrel  A.  The  temperature  of 
the  entering  water  was  taken  at  C.  Steam  was  admitted  to 
the  condensing-coil  until  the  temperature  of  the  condensing 
water  reached,  say,  1 10°  F.  The  weights  before  and  after 


FIG.  195. — HOADLEY'S  CALORIMETER  ARRANGED  FOR  USE. 

adding  steam  were  taken  by  the  scales  F\  the  temperature  ot 
the  warm  condensing  water  was  taken  by  a  thermometer,  Gt 
inserted  in  the  axis  of  the  agitator.  The  water-equivalent  was 
determined  as  explained  in  Article  317,  page  401,  and  the 
quality  computed  by  equation  (6),  page  394.  The  rate  of 
cooling  was  determined,  and  an  equivalent  amount  added  as  a 
correction  for  any  loss  of  heat  by  radiation. 

322.  The  Kent  Calorimeter. — This  instrument  differs 
from  the  Hoadley  instrument  principally  in  the  arrangement  of 
the  condensing  coil.  This  when  filled  with  steam  could  be 
removed  from  the  calorimeter,  so  as  to  enable  the  weight  ot 


EXPERIMENTAL   ENGINEERING. 


[§  323. 


steam  to  be  taken  on  a  smaller  and  more  delicate  pair  of  scales 
than  those  required  for  the  condensing  water,  thus  giving 
more  accurate  determinations  of  the  weight  of  the  steam  con- 
densed. 

323.  The  Barrus  Continuous  Calorimeter. — This  calo- 
rimeter is  shown  in  Fig.  196  in  section  and  in  Fig.  197  in  per- 
spective. It  consists  of  a  steam-pipe,  aj,  surrounded  by  a 


Condensed  Steam 
FIG.  196. — BARRUS  CONTINUOUS  CALORIMETER. 

tub  or  bucket,  O,  into  which  cold  water  flows;  the  condensing 
water  is  received  as  it  enters  the  bucket  in  a  small  brass  tube, 
k,  surrounding  the  pipe  a,  and  is  conveyed  over  and  under 
baffle-plates,  m,  so  as  to  be  thoroughly  mixed  with  the  water 
in  the  vessel,  and  is  finally  discharged  at  c.  Thermometers  are 
placed  at  /and  at  g  to  take  the  temperature  of  the  water  as  it 


323.]        THE  AMOUNT  OF  MOISTURE   IN  STEAM. 


411 


enters  and  leaves,  and  finally  the  condensing  water  is  caught 
from  the  overflow  and  weighed.  The  condensed  steam  falls 
below  the  calorimeter  ;.  by  means  of  the  water-gauge  glass  at  * 


FIG    197. — THE  BARRUS  CONTINUOUS  AND  SUPERHEATING  CALORIMETERS. 

it  may  be  seen  and  kept  at  a  constant  height.  The  temperature 
of  the  condensed  steam  while  it  is  still  under  pressure  is  shown 
by  a  thermometer  at  h.  In  order  to  use  the  calorimeter  it  is 
necessary  to  weigh  the  condensed  steam  ;  this  cannot  be  done 
without  further  cooling,  as  it  would  be  converted  into  steam 
were  the  pressure  removed.  For  this  purpose  it  is  passed 
through  a  coil  of  pipe  immersed  in  a  bucket  filled  with  water, 


412  EXPERIMENTAL   ENGINEERING.  [§  324. 

shown  at  5  in  Fig.  197.  The  water  used  in  the  cooling  bucket 
5  has  no  effect  on  tne  quality  of  the  steam  and  is  not  con- 
sidered in  the  results  ;  it  is  allowed  to  waste,  but  the  condensed 
steam  is  caught  at  IV,  Fig.  197,  and  weighed. 

The  quality  of  steam   is  computed  by  omitting  k  in  for- 
mula (6),  page  394.     Hence 


w 


w  is  the  weight  of  condensed  steam  after  correction  for  radia- 
tion-loss as  explained  in  Article  324  ;  w  being  equal  to  w'  —  u. 

324.  Directions  for  Using  the  Barrus  Continuous  Calo- 
rimeter.— Apparatus  needed. — Thermometers  ;  pail  for  receiv- 
ing condensed  steam  ;  tank  and  scales  for  the  condensing  water. 

Directions. —  I.  Fill  the  thermometer-cups  with  cylinder- 
oil.  (Do  not  put  thermometers  in  place  until  apparatus  is 
working.) 

2.  Turn  on  condensing  water  and  steam  ;  regulate  the  flow 
of  condensing  water  so  as  to  keep  the  bucket  O  nearly  full,  and 
the  temperature  of  the  discharge-water  as  much   above  tem- 
perature of  the  room  as  injection  is  below :    this  should   be 
about  110°  F.     Regulate  the  flow  of  condensed  steam  so  as  to 
keep  the  water  in  the   glass  e  at  a  constant  level.     Turn  water 
on  to  the  cooling  coil  in  the  bucket  S,  and   reduce   the   con- 
densed steam  to  a  temperature  of  about  120°. 

3.  After   the  apparatus  is  working  under  uniform   condi- 
tions, put  the  thermometers   in  the  cups  for  temperature  of 
injection  and  discharge  water,  and   having  previously  weighed 
the  vessels,  at    a   given    signal,  note    time    and  commence   to 
catch  the  condensed  steam   and   the  condensing  water.     Con- 
tinue   the  run  until  about   360  or  400  pounds  of  condensing 
water  has   run   into   the   receiving  tank.     Without  disturbing 
the   condition  of  the   apparatus,  commence  simultaneously  to 
waste  the   discharge  from  both  pipes.     Find  the  weights  of 


§  324-l        THE  AMOUNT  OF  MOISTURE   IN  STEAM.  413 

condensed  steam  (wf)  and  condensing  water  (W) ;  note  time  of 
ending  run. 

4.  Make  three  more  runs  similar  to  the  first. 

5.  To   find   the    radiation-correction    of    the    instrument: 
Empty  the  bucket  O  of  condensing  water,  and  surround  the 
condensing  tube  a  with  hair-felting ;  make  a  run  of  the  same 
length,  and  with  steam  of  same  pressure  as  in  the  previous 
runs.     The  weight  of  steam  condensed  will  be  the  radiation- 
loss,  which  we  call  u,  and  is  to  be  deducted  from  the  weight  of 
condensed  steam  obtained  in  the  previous  runs  of  the  same 
length.     Find  the  condensation  per  hour. 

6.  Work  up  quality  of  steam  by  the  formula 


X  = 


Make  report  as  described  for  other  calorimeters. 

Example. — The  following  is  the  result  of  a  trial  with  the 
Barrus  continuous  calorimeter:  Temperature  of  injection-water, 
/,  =  37°.5  Fahr.;  temperature  of  discharge-water,  /,  =  83°.8 
Fahr. ;  temperature  of  condensed  steam,  /3  =  304.9  Fahr. ; 
steam-pressure  by  gauge,  72.4  Ibs.  ;  temperature  of  entering 
steam,  /  =  3i7°.9  ;  length  of  test,  40  minutes ;  weight  of  cool- 
ing water,  W  =  573.5  Ibs. ;  weight  of  condensed  steam,  w'  = 
29.89  Ibs.';  radiation-loss  u  =  o.  13  Ib.  Neglecting  value  of  ut 

=  573.5  (83.8  ~  37.5)  _  (3I7.9-3Q4.9) 
29.89   "891  891 

_  19.21  X  46.3— I3-Q  _  876.4  _ 


=  98.4  if  not  corrected  for  radiation-loss.     If  corrected, 

X  =   {  ^46.3  —   I30J  -r-  891   =  98.9. 


414  EXPERIMENTAL   ENGINEERING.  [§  325. 

325.  Forms  for  Use  with  Condensing  Calorimeters. 

MECHANICAL   LABORATORY,  SIBLEY   COLLEGE,  CORNELL 
UNIVERSITY. 

PRIMING  TEST  WITH  CONDENSING  CALORIMETER. 

Made  by 189. . 

T^st  cf. ,  ,o Steam 

at.,. '. ,         N.  Y. 

Kind  of  calorimeter 


I. 

II. 

III. 

IV. 

V 

Symbols. 

P 

Scale-readings,  tare,  Ibs  

V 

W-r  V 

Quantities  : 
Condensing1  water   Ibs               . 

w 

Condensed  steam    Ibs  

w 

Temperatures,  deg.  Fahr.  : 

t\ 

Condensing  water    warm     .... 

ti 

Condensed  steam      .    .  .  •  •    .... 

/3 

/ 

W  -*-  iv 

Quality    per  cent       

X 

Degree  of  super-heat   .    . 

D 

Correction  due  to  displacement  of  water  by  hose Ibs. 

Calorimeter-equivalent Ibs.         How  found 


Temp,  r^cm deg.  Fahr.         Barometer-reading inches. 

Quality  x 

Degree  of  super-heat  D  =  (x  —  i)r  •*-  0.48. 


\'W  ~1 

=     --(**  —  *0  ~  (*  ~  *>)     -»•  r. 


§  325-]        THE  AMOUNT  OF  MOISTURE  IN  STEAM.  415 

CALORIMETER    TEST. 
Date No 

Condensing          Condensed       ^noSe'   ***    8 

Water.  Water.  **$££*      2%        2  Q       £ 

&£  .         —  -iis  ! 

|      I      Weight.    D*.     Weight.    ™-      Hot.       Cold.    Jog    ^      ^ 

Total . 

Aver. 

Cor.. 

Duration  of  test min. 

Weight  of  steam  condensed Ibs. 

Weight  of  condensing  water «• 

Average  temperature  of  hot  condensing  water. . .  .C.;    ...  .Fahr.;    . . .  .B.T.U. 

«  «  <t     pQl(l  '>  ««  «  '«  " 

"  condensed  steam "     ««        " 

"  "  "room "        deg.  C. 

"        pressure  of  air Ibs.  per  sq.  in. 

"        absolute  pressure  of  the  steam "      "      " 

Thermal  units  in  water  corresponding  to  absolute  pressure  of  steam.. .  .B.T.Uo 

Heat  acquired  by  condensing  water 

Heat  given  up  by  condensed  steam  in  cooling  to  temperature  of  ther- 
mometer in  same.   te 

Weight  of  water  condensed  by  radiation Ibs 

Heat  given  up  by  each  pound  of  steam  in  condensing B.T.U. 

Latent  heat  of  one  pound  of  steam  at  average  absolute  pressure " 

Per  cent  of 

Signed 


416 


EXPERIMENTAL   ENGINEERING. 


[§  326. 


326.  Barrus  Superheating  Calorimeters. — In  the  Barrus 
Superheating  Calorimeter,  Fig.  198,  the  steam-pipe  leading  from 
the  main  is  bifurcated,  one  branch,  E,  .•» 
passing  over  the  flames  of  a  large 
Bunsen  burner,  the  other  passing  up- 
ward, and  finally  downward,  when  it 
is  jacketed  by  the  enlargement  of  the 


,-STEAM    FOR    SUPERHEATER 


SUPERHEATEF 


temp 


first  branch.  The  branches  discharge 
separately,  each  through  equal  orifices, 
about  one-eighth  inch  in  diameter. 

This  instrument  is  shown  in  Fig.  198 
in  elevation,  and  on  the  left-hand  side  of 
Fig.  197  in  perspective.  The  steam  in 
one  branch  is  superheated  at  G\  that  in 
its  normal  condition  is  received  at  H,  and 
is  discharged  at  N.  The  superheated 
steam  forms  a  jacket  from  /  to  K  outside 
the  sample  to  be  tested,  and  is  discharged 
at  the  orifice  M.  The  temperature  of  the 
jacket  steam  is  taken  at  A  and  at  B ;  that 
of  the  normal  steam  is  measured  at  C,  as 
it  is  discharged ;  it  is  found  as  it  enters  from  its  pressure  taken 
at  H,  by  reference  to  the  steam-table. 

The  theory  of  this  calorimeter  is  as  follows: 


FIG.   198.— BARRUS  SUPER- 
HEATING CALORIMETER. 


§  326.]        THE  AMOUNT  OF  MOISTURE   IN   STEAM.  417 

1.  An  equal  weight  of  steam  flows  through  each  branch  of 
the  pipe. 

2.  The  steam,  superheated  by  the  gas-flame,  is  used  as  a 
jacket  for  the  other  branch,  and  parts  with  as  much  heat,  ex- 
cept for  radiation,  as  the  other  gains. 

3.  This  amount  may  be  measured  provided  the  steam  dis- 
charged from  the  central  tube  is  superheated. 

To  measure  this  gain  or  loss  of  heat,  thermometers  are 
placed  to  take  the  temperature  of  steam  as  it  enters  and  leaves 
the  jacket,  and  on  the  central  pipe  near  the  same  places. 

Formula. — Let  (i  —  x)  be  the  amount  of  water  to  be  evap- 
orated;  in  so  doing  it  will  take  up  from  the  jacket-steam 
r(\  —  x)  heat-units.  Let  t  be  the  normal  temperature  of  the 
steam  at  the  gauge  pressure ;  let  7\  be  the  temperature  of  the 
superheated  jacket-steam  at  entering,  and  T9  as  it  leaves ;  let 
T3  be  the  temperature  of  the  superheated  steam  discharged 
from  the  sample  pipe,  and  let  radiation-loss  in  degrees  F.  be 
/.  If  the  specific  heat  of  steam  be  0.48,  since  gain  and  loss  of 
heat  are  equal,  we  have 

0.48(7;  _ T,  _  /)  =  KI  -  *)  +.048(7;  -  /). 


from  which  x  may  be  found. 

To  find  /,  the  radiation-loss  in  degrees,  shut  off  steam  in 
the  branch  leading  to  the  centre  steam-pipe,  and  find  reading 
of  thermometers  7^  and  T9 .  After  a  run  of  same  length  as  in 
test,  take  /  =  T,  —  T9. 

Directions  for  using  Barrus  Superheating  Calorimeter. — Ap- 
paratus needed. — Three  thermometers  reading  400°  F.  each, 
and  pressure-gauge,  superheating  lamps,  etc. 

First.  Calibrate  instruments,  and  ascertain  by  a  run  of 
twenty  minutes  that  equal  amounts  of  steam  are  discharged 
from  each  orifice.  This  may  be  done  by  condensing  the  steam. 

Second.  Put  cylinder-oil  in  oil-cups ;  attach  gauge. 


EXPERIMENTAL   ENGINEERING. 


[§  328. 


Third.  Put  in  working  order ;  after  thermometer  at  end  of 
sample-steam-pipe  shows  superheat,  commence  the  run. 

Fourth.  Take  readings  once  in  two  minutes  for  twenty 
minutes. 

Fifth.  Obtain  radiation-loss  /as  explained. 

Sixth.  Work  up  results  as  explained,  and  make  report  as 
in  previous  cases. 

327.  Form  for  Determination  with  Barrus  Superheat- 
ing Calorimeter. 


No. 


BARRUS   SUPERHEATING  CALORIMETER. 

DATE.  . 


Time. 

Temp. 
Jacket-steam 
Entering. 

Temp. 
Jacket  steam 
at  Exit. 

Temp. 
Sample  Steam 
at  Exit. 

Steam- 
pressure  by 
Gauge. 

Barometer. 

Total 

Corrected  . 

Duration  of  test min. 

Barometer in. ;   Ibs.  per  sq.  in. 

Sample  steam,  gauge  pressure Ibs.  per  sq.  in. 

"  "        absolute     "       , Ibs.  per  sq.  in. 

"  "       temperature  at  absolute  pressure C. ; F. 

"outlet C.;   F. 

Superheated  steam,  temperature  at  inlet C.;  F. 

"outlet C.;  F. 

Latent  heat  of  steam  at  absolute  pressure ., . .  B.  T.  U. 

Specific  heat  of  superheated  steam B.  T.  U. 

Correction  for  condensation 

"  "   radiation , . 

Per  cent  of  moisture  in  steam 

328.  The  Throttling  Calorimeter. — This  instrument  was 
designed  in  1888  by  Prof.  C.  H.  Peabody  of  Boston,  and  rep- 


§  328.]        THE  A  MO  UN  7"  OF  MOISTURE   IN  STEAM. 


419 


resents  a  greater  advance  than  any  previously  made  in  practical 
calorimetry.  The  equations  for  its  use  and  limitations  of  the 
same  were  given  by  Prof.  Peabody  in  Vol.  IX.,  Transactions 
Am.  Society  Mechanical  Engineers.  As  designed  originally, 
it  consisted  of  a  small  vessel  four  inches  in  diameter  by  six  to 
eight  inches  long,  and  connected 
to  the  steam-supply  with  a  pipe 
containing  a  valve,  b,  used  to 
throttle  the  steam  supplied  the 
calorimeter.  Fig.  199  shows  the 
original  form  of  the  calorimeter, 
which  is  arranged  so  that  any  de- 
sired pressure  less  than  that  in  the 
main  steam-pipe  can  be  maintained 
in  the  calorimeter  A.  The  press- 
ure in  the  calorimeter  is  shown  by 
a  steam-gauge  at  g,  and  the  tem- 
perature by  a  thermometer  at  D\ 
the  main  steam-pipe  is  provided 
with  a  drip  at  /,  to  drain  the  pipe 
before  making  calorimetric  tests. 
In  using  the  calorimeter,  any  desired  pressure  can  be  main- 
tained in  the  vessel  A  by  regulating  the  opening  of  the  ad- 
mission and  exhaust  valves. 

The  effect  of  this  operation  will  be  to  admit  the  heat  due 
to  high-pressure  steam  into  a  vessel  rilled  with  steam  of  lower 
pressure.  The  excess  of  heat  is  utilized  firstly  in  evaporating 
moisture  in  the  original  steam  ;  secondly,  if  there  is  sufficient 
heat  remaining,  in  raising  the  temperature  in  the  vessel  A 
above  that  due  to  its  pressure,  thus  superheating  the  steam. 
Unless  the  steam  in  the  chamber  A  is  superheated,  no  deter- 
minations can  be  made  with  the  instrument.  The  equation  for 
its  use  is  obtained  as  follows :  the  heat  in  one  pound  of  high- 
pressure  steam  before  reaching  the  calorimeter  is  expressed 
as  in  formula  (2),  Article  311,  page  393,  by  xr  -\-  q.  After 
reaching  the  calorimeter  the  heat  is  that  due  to  the  press- 


FIG.  199. — PEABODY'S  THROTTLING 
CALORIMETER. 


420 


EXPERIMENTAL  ENGINEERING. 


[§  328. 


ure  in  the  calorimeter  added  to  that  due  to  the  superheat,  or 
A, +  o.48(7i  —  Tc).     Since  these  quantities  are  equal, 


from  which 


=  [A,  -  2  +  0.48(7;  -  T;)]  -  r; 


.    (ii) 


in  which  r  equals  latent  heat,  and  q  heat  of  liquid  due  to 
pressure  in  main  pipe  as  given  in  the  steam-table. 

\c  =  total  heat  in  one  pound  of  dry  steam  at  calorimeter 
pressure ;  Tl  =  reading  of  thermometer  in  calorimeter,  and 
Tc  =  normal  temperature  of  steam  in  calorimeter  due  to  calo- 
rimeter pressure.  Care  must  be  taken  that  both  A,  and  q  are 
given  in  the  same  units. 

Example. — Suppose  that  the  gauge  pressure  on  the  main 
steam-pipe  is  80  pounds,  that  on  the  calorimeter  8  pounds 
atmospheric  pressure  14  pounds,  as  reduced  from  the  barom- 
eter-reading, and  that  the  thermometer  in  the  calorimeter 
reads  274°. 2  F.  Required  the  quality  of  the  steam. 

In  this  case  we  obtain  the  following  quantities  from  the 
steam-table : 


/ 
Absolute 
Pressure. 

T 
Temperature 
Deg.  F. 

q 
Heat  of 
Liquid, 
B.T.  U. 

A 
Total 
Heat, 
B.  T.  U. 

r 
Latent 
Heat. 
B.  T.  U. 

F'nterinc'  steam       . 

Od 

<52'l     I 

2na    2 

887    7 

TO  calorimeter.  .  .    .  . 

y*r 

22 

2-2-J    I 

2O2   O 

T  TCa    O 

°0/  •  3 

QC  T       O 

From  which 

*  =  ["53  —  293.2  +  0.48(274.2  -  233.1)]  -7-  887.3; 


Per  cent  of  moisture,  100  —  x  =  0.9. 


§  329-J 


THE  AMOUNT   OF  MOISTURE  IN  STEAM. 


42 


329.  Recent  Forms  of  Throttling  Calorimeters. — These 
instruments  differ  from  Peabody's  principally  in  size  and 
form.  They  all  work  in  the  same  general  manner  and 
detailed  descriptions  are  hardly  necessary. 


FIG.     »oo.— HEISLER'S  THROTTLING  CALORIMETER. 

Heisler's  throttling  calorimeter  is  shown  in  Fig.  200, 
with  attached  manometer  for  measuring  the  pressure  in  the 
calorimeter  chamber,  it  is  of  small  size  and  keeps  the  current 
of  steam  intimately  in  contact  with  the  thermometer. 

Carpenter's  throttling  calorimeter,  shown  in  Fig.  201,  is  pro- 
vided with  an  attached  nozzle  for  spraying  the  sample  of 
steam  over  the  themometer-bulb.  The  instrument  may  be 
used  with  or  without  a  thermometer-cup,  but  in  every  case 
the  thermometer  must  be  deeply  immersed  in  the  steam. 
This  instrument  is  made  by  Schaff  er  and  Budenberg,  New  York. 


422 


EXPERIMENTAL  ENGINEERING. 


[§330 


FIG.  201.— CARPENTER'S  CALORIMETER. 


Throttling  Calorimeter  of  Pipe-fittings.— A  very  sat- 
isfactory calorimeter  can  be  made  of  pipe-fittings,  as  shown 


FIG.     202.— THROTTLING  CALORIMETER  OF  PIPE-FITTINGS. 
in  Fig.  202.     Connection    is    made   to    the   main   steam-pipe, 
as    explained    already    elsewhere.     The    calorimeter    is    made 


§33i] 


THE  AMOUNT  OF  MOISTURE   IN  STEAM. 


423 


of  f  inch  fittings  arranged  as  shown  ;  the  steam-pipe  W  is  of 
J-inch  pipe,  and  the  throttling  orifice  is  made  by  screwing  on  a 
cap,  in  which  is  drilled  a  hole  -J  or  -fa  inch  in  diameter. 

A  thermometer-cup,  Fig.igo,  page  400. is  screwed  into  the 
top,  and  an  air-cock  inserted  opposite  the  supply  of  steam.  A 
manometer,  B,  for  measuring  the  pressure  is  attached  by  a 
piece  of  rubber  tubing  as  shown.  The  exhaust  steam  is  dis- 
charged at  E.  The  back-pressure  on  the  calorimeter  can  be 
increased  any  desired  amount  by  a  valve  on  the  exhaust-pipe; 
when  no  valve  is  used  the  pressure  is  so  nearly  atmospheric 
that  a  manometer  is  seldom  required. 

Method  of  rinding  Normal  Temperature  in  the  Calor- 
imeter.— It  is  essential  to  know  the  normal  temperature 
within  the  calorimeter ;  this  will  vary  with  the  pressure  on  the 
calorimeter,  which  pressure  is  equal  to  the  barometer-reading 
plus  the  manometer-reading. 

The  following  table  gives  the  normal  temperature  corre- 
TABLE  OF  BOILING-POINTS. 


Normal 
Temperature. 
Degrees  F. 

Total  Pressure 
on  Calorimeter. 
Inches  Hg. 

Normal 
Temperature. 
Degrees  F. 

Total  Pressure 
on  Calorimeter. 
Inches  Hg. 

209.5 

28.466 

•  7 

•744 

.6 

.523 

.8 

.803 

•7 

.580 

•9 

.863 

.8 

.637 

212.  0 

.922 

•9 

.695 

.1 

.982 

2IO.O 

•752 

.2 

30.041 

.1 

.810 

•  3 

.101 

.2 

.867 

•4 

.161 

•  3 

•925 

•5 

.221 

•4 

-933 

.6 

.281 

•5 

29.041 

•7 

•341 

.6 

.099 

.8 

.401 

•  7 

•157 

•9 

.462 

.8 

.215 

213.0 

.522 

•9 

.274 

.8 

3L004 

211.  0 

•332 

214.0 

.107 

.1 

.391 

215.0 

.692 

.2 

•449 

216.0 

32.277 

•3 

•  508 

217.0 

.862 

•4 

.567 

218.0 

33-447 

•  5 

.626 

219.0 

34.032 

.6 

.685 

220.0 

.617 

Difference  i°  F  —  0.585  inch.       Difference  I  inch  =  i".7OQ. 


424  EXPERIMENTAL   ENGINEERING.  [§332 

spending  to  various  absolute  pressures  nearly  atmospheric,  ex- 
pressed in  inches  of  mercury: 

In  the  use  of  the  instrument  the  total  pressure  in  the 
calorimeter  is  to  be  taken  as  the  sum  of  the  barometer-reading 
and  the  attached  manometer.  The  degree  of  superheat  of  the 
steam  in  the  calorimeter  is  the  difference  between  the  tempera- 
ture as  shown  by  the  pressure  and  that  shown  by  the  inserted 
thermometer. 

Graphical  Solution  for  Throttling-Calorimeter  Deter- 
minations.— In  the  practical  use  of  this  instrument  it  is 
customary  to  exhaust  at  atmospheric  pressure,  so  that  the 
normal  temperature  in  the  calorimeter  is  the  boiling-point  at 
atmospheric  pressure,  and  \  is  1146.6;  in  which  case  formula 
(n)  becomes 

1146.6  +  0.48(7;  —  212)  —  q 
1146.6  —  q      0.48(7^  —  212) 

T~  ~         • 


If  in  this  form  we  suppose  the  steam-pressure  constant,  and 
the  degree  of  superheat  and  quality  of  steam  alone  to  vary, 
r  and  q  will  both  be  constant,  and  we  shall  have  the  equation 

of  a  right  line,  in  which —  is  the  distance  above  the 

origin  that  the  line  cuts  the  axis  of  ordinates,  and  0.48  -f-  r  is 
the  tangent  of  the  angle  that  the  line  makes  with  the  axis  of 
abscissae.  Drawing  lines  corresponding  to  the  different  gauge 
or  absolute  pressures,  a  chart  may  be  formed  from  which  the 
values  of  x  may  be  obtained  without  calculation. 

Using  degrees  of  superheat  in  the  calorimeter  as  abscissae 
and  absolute  steam-pressure  as  ordinates,  and  drawing  lines 
corresponding  to  various  percentages  of  moisture,  we  have  a 
diagram  shown  in  Fig.  203,  from  which  the  results  of  observa- 
tions made  with  the  throttling  calorimeter  may  be  taken  at 
once  without  further  calculation. 


iiiiiii  jiiiinigjjiii  «••»••» 


FIG.     203.— DIAGRAM  GIVING  RKSULTS  FROM  THROTTLING  CALORIMETER 
WITHOUT  COMPUTATION. 


426  EXPERIMENTAL   ENGINEERING.  [§333 

Use  of  the  Diagram.  —  To  find  the  percentage  of  moisture  in 
the  steam  from  the  diagram,  pass  in  a  horizontal  direction  along 
the  base-line  until  you  arrive  at  the  number  corresponding  to 
the  degree  of  superheat  in  the  calorimeter;  then  pass  in  a  ver- 
tical direction  until  you  reach  the  required  absolute  pressure 
of  steam.  The  position  with  reference  to  the  curved  lines 
shows  at  once  the  percentage  of  moisture,  and  can  be  read 
easily  to  one  tenth  of  one  per  cent.  Thus,  for  example,  sup- 
pose  that  we  have  the  following  readings  :  Barometer,  29.8 
inches;  attached  manometer,  1.5  inches  —  making  a  total  press- 
ure  in  the  calorimeter  of  31.3  inches,  corresponding  to  a  tem- 
perature of  2  14°.  27  Fahr.  Steam-gauge,  80  pounds;  absolute 
pressure,  94.7  pounds  ;  thermometer-reading  in  calorimeter, 
254°  Fahr.  From  which  the  degree  of  superheat  is  found  to 


Following  the  directions  as  given,  the  percentage  of  moist- 
ure is  seen  from  the  diagram  to  be  1.66  per  cent.  The  quality 
would  be  i.oo  —  1.66  =  98.34  per  cent.  While  the  diagram  is 
especially  computed  for  determinations  when  the  pressure  in 
the  calorimeter  is  atmospheric  or  but  slightly  above,  it  will  be 
found  to  give  quite  accurate  results  when  the  calorimeter  is 
underpressure,  by  considering  that  the  ordinates  represent  the 
difference  of  pressures  on  the  steam  and  in  the  calorimeter. 
Thus,  in  the  example,  Article  328,  page  390,  the  steam-pressure 
was  80  pounds,  calorimeter-pressure  8  pounds  ;  degree  of  super* 
heat  274.2  —  233.1  =41.1  ;  resulting  quality  by  calculation  99.  1, 
indicating  0.9  per  cent  of  moisture.  Using  difference  of  press- 
ure 80  —  8  =  72  as  ordinate,  and  41.1  as  abscissa,  we  find  from 
the  chart  that  the  percentage  of  moisture  is  0.92  ;  from  which 
x  =  99.08. 

The  results  for  the  throttling  calorimeter  may  be  com- 
puted from  the  temperatures  instead  of  the  pressure  of  the 
original  sample  of  steam  as  compared  with  the  temperature 
in  the  calorimeter  when  at  atmospheric  pressure.  Carpenter's 
calorimeter,  Fig.  201,  is  especially  adapted  for  such  determina- 
tions, since  it  provides  an  easy  method  of  calibrating  the 
thermometer  when  in  position.  This  is  especially  important; 
since  thermometers  will  ordinarily  read  two  or  three  degrees 
low  when  there  is  a  portion  of  the  stem  exposed. 


§  333-]         THE  AMOUNT  OF  MOISTURE   IN  STEAM.  427 

For  using  the  instrument  in  this  manner,  the  boiling- 
point  in  the  calorimeter  is  first  determined  by  opening  both 
the  supply  and  discharge  valves  C  and  D  and  showering  the 
instrument  and  connections  with  water  until  the  steam  in  the 
calorimeter  is  moist,  in  which  case  the  reading  of  the  ther- 
mometer will  be  that  due  to  the  boiling-point.  Second,  close 
the  discharge-valve  with  the  supply-valve  open  and  obtain 
full  boiler  pressure  in  the  calorimeter;  when  the  thermometer 
has  become  stationary  note  the  temperature  :  this  will  be  the 
boiling-temperature  for  the  given  pressure  as  read  by  the 
given  thermometer.  Third,  open  the  discharge-valve  of  the 
instrument,  and  after  the  mercury  has  become  stationary  note 
the  reading  of  the  thermometer.  Deduct  from  this  latter 
reading  the  reading  first  taken  and  we  shall  have  the  degree 
of  superheat  in  the  calorimeter.  From  these  two  numbers 
the  quality  may  be  computed  by  reference  to  steam  tables  as 
explained,  but  it  is  more  easily  done  by  reference  to  the 
following  diagram,  in  which  the  temperature  of  the  steam  is 
the  ordinate  and  is  that  given  when  the  discharge-valve  is 
closed,  and  the  temperature  in  the  calorimeter  is  the  abscissa, 
on  the  supposition  that  the  boiling-temperature  at  calorimeter 
pressure  is  2  12  degrees.  If  the  boiling-temperature  is  more  or 
less  than  this  amount,  a  corresponding  correction  must  be 
made  to  the  result.  As  an  illustration,  suppose  that  the 
boiling-temperature  in  the  calorimeter  is  2  1  1  or  one  degree 
low,  that  the  actual  temperature  in  the  calorimeter  when  both 
valves  are  open  is  265,  and  that  the  temperature  of  the  steam 
obtained  with  the  discharge-valve  closed  is  320.  To  find  the 
quality  we  look  in  the  line  over  266  and  opposite  330,  and 
read  the  results  by  the  diagonal  lines,  the  quality  as  shown 
on  the  diagram  being  98.8  (see  Fig.  204). 

Limits     of    the    Throttling    Calorimeter.  --  To    deter- 

mine   the    amount    of    moisture    that    can    be   evaporated  by 
throttling,  make  Tl  =  Tc  in  formula  (u);  then 


The  amount  of  moisture  that   can  be  determined  by  the 


220        230 


TEMPERATURE  IN  CALORIMETER 

250    260    270    280    290    300    310    320    330   3 


*  TEMPERATURE  IN  CALORIMETER 
FIG.  204.— DIAGRAM  FOR  COMPUTING  RESULTS  WITH  THROTTLING  CALORIMETER. 


;55l 


THE  AMOUNT   OF  MOISTURE  IN  STEAM. 


429 


throttling  calorimeter  in  expanding  from  the  given  pressure 
to  atmospheric,  as  computed  by  substituting  in  formula  (12), 
is  as  follows  : 

LIMITS  OF  THE  THROTTLING  CALORIMETER. 


Pressure,  pounds  per  square  in. 

Maximum  per 
cent  of  prim- 
ing 

Quality  of  the 
steam,  per  cent. 

Absolute. 

Gauge. 

iii&- 

300 

2S5.3 

07.7 

92-3 

250 

235-3 

7.0 

93-o 

200 

185.3 

6.1 

93.9 

175 

160.3 

5-8 

94.2 

150 

135-3 

5.2 

94.8 

125 

110.3 

4.6 

95.4 

IOO 

85.3 

4.0 

96.0 

75 

60.3 

3-2 

96.8 

50 

35-3 

2.3 

97.7 

By  reducing  the  pressure  below  the  atmosphere,  the  limits 
of  the  instrument  may  be  somewhat  increased. 

Directions    for     Use     of   Throttling    Calorimeter.  — 

Apparatus.— Steam-thermometer ;  pressure-gauge;  manometer 
for  measuring  pressure  in  calorimeter  in  inches  of  mercury. 

1.  Attach  the  calorimeter  to  a  perforated  pipe  extending 
well  into  the  main  steam-pipe  to  secure  a  fair  sample  of  steam.. 
Calibrate  all  the  apparatus. 

2.  Fill  thermometer-cup  with  cylinder-oil,  having  first  care- 
fully removed  any  moisture  from  the  cup.     Place  thermometer 
in  the  cup,  and  after  it  has  reached  its  maximum  commence 
to  take  observations. 

3.  Read  steam-pressure,  attached  manometer,  and  tempera- 
ture at  frequent  intervals. 

4.  Compute  the  quality  of  the  steam  for  each  observation. 
Forms  for  Throttling-Calorimeter  Determinations. 

Priming  tests  of 

Made  by 


189. 


at N.  Y.,   

with Throttling  Calorimeter. 

Barometer-reading .inches.         Steam  used  during  run. .  .  .Ibs.. 


430 


EXPERIMENTAL   ENGINEERING. 


[§336 


Number 

6 

8 

o 

Steam-pressure,         main 
pipe             

V       V>' 

M 

Manometer  reading  calo- 
rimeter     

7  °5- 
n  6 

^s 

/I 
? 

*C 

Observed       temperature 
calorimeter  
Heat  at  steam-pressure  P. 
Normal  temperature     in 
calorimeter  

•••• 

... 

'.'.'.'. 

II 

*        Q      . 

p 

Absolute       pressure      in 
main  

3       3 

o.48(/-/') 
Ac 

Total  heat   pressure  tn.  . 

.... 

!  1 

r 

Latent  heat  for  pressure 
p       

3 

\f       a 

5                B) 

?  £ 

;        & 

1  —  X 

Ac—  ?  +  o.48(  /!—/•<?)  
Per    cent     of    entrained 

... 

5      8? 

Quality  of  steam  

X      Q 

2) 

Degrees  of  superheat  .  . 

AVERAGE  RESULTS  OF  CALORIMETER  TEST. 

Date 

Duration  of  test.   min. 

Barometer in. ;     . .    Ibs.  per  sq.  in. 

Boiler-pressure  by  gauge 

"         absolute "         " 

Calorimeter-pressure  by  gauge  "         •' 

"        absolute "         " 

Calorimeter-temperature C.;     F. 

Per  cent  of  moisture  in  steam « 

Signed 

336.  The  Separating  Calorimeter.  -  -  The  separating 
calorimeter  is  an  instrument  which  removes  all  water  from 
the  sample  of  steam  by  some  process  of  mechanical  separa- 
tion, and  provides  a  method  of  determining  the  amount  of 
water  so  removed  and  also  the  weight  of  the  sample.  This 
process  is  dependent  upon  the  greater  density  of  water  as 
compared  with  that  of  steam.  Thus,  for  instance,  steam  at 
100  Ibs.  absolute  pressure  is  more  than  260  times  lighter  than 
water  at  the  same  temperature,  and  if  the  sample  of  steam 
when  moving  with  considerable  velocity  can  be  made  to 
change  its  direction  of  motion  abruptly,  the  water  will  be 
deposited  by  the  action  of  inertia. 


§336 


THE  AMOUNT  OF  MOISTURE   IN  STEAM. 


431 


The  accuracy  of  this  instrument  depends  on  the  possibility 
of  completely  separating  the  water  from  the  steam  by 
mechanical  methods.  To  determine  this  a  series  of  tests 
were  conducted  for  the  author  by  Messrs.  Brill  and  Meeker 
with  steam  of  varying  degrees  of  quality.  The  range  in 
moisture  was  from  33  to  I  per  cent,  yet  in  every  case  the 
throttling  calorimeter  attached  to  the  exhaust  gave  dry  steam 
within  limits  of  error  of  observation.  The  following  were  the 
results  of  this  examination. 

SEPARATING   CALORIMETER. 


Examination  of  Exhaust 

Observations  on  Entering  Steam. 

Steam  from  Calorimeter  by 

Throttling  Calorimeter. 

T 

P 

W 

IV 

X 

t 

X 

Calori- 
meter. 

Duration 
Run, 
minutes. 

Gauge 
Pressure, 
pounds. 

Pounds 
Separated 
Water  in 
Run. 

Pounds 
Condensed 
Steam  in 
Run. 

Quality 
Steam, 
per  cent. 

Temp,  in 
Calori- 
meter. 

Quality 
Steam  in 
Exhaust. 

No.  of 
Obser- 
vations 

*\ 

25 

8l.5 

I-I5 

4-45' 

79.46 

28l 

99-95 

6 

B\ 

25 

78.2 

0.15 

5.20 

97.2 

281.3 

100.00 

6 

A\ 

25 

80.8 

0.525 

4-25 

89.005 

286.5 

IOO.OO 

6 

B\ 

25 

79-5 

0.150 

4-75 

96.94 

281.8 

99-95 

6 

A\ 

25 

78-5 

0.300 

5.000 

94-34 

282.8 

100.00 

6 

B\ 

25 

77-6 

.150 

5-45 

97-32 

282.3 

100.00 

6 

A\ 

24 

79-5 

1.8 

4-55 

71.65 

2SO.I 

99-94 

6 

B\ 

24 

78.5 

1.4 

4.90 

77-77 

279-5 

99-9 

6 

A\ 

2O 

83.5 

i-i5 

4.1 

77.67 

286.5 

100.00 

5 

B\            20 

81.6 

1.70 

4-75 

73.64 

282.7 

99.98 

5 

20 

74-8 

0.65 

3-95 

85.87 

283.7 

100.05 

5 

2O 

82.0 

0.85 

3-95 

82.29 

286.8 

100.05 

5 

20 

82.6 

0-35 

4-15 

92.22 

285.6 

IOO.O 

5 

20 

81.5 

O.20 

3-95 

95-15 

285.2 

100.05 

5 

A  (            20 

81.4 

2.  2O 

4-325 

66.28 

283.1 

IOO.O 

5 

B\            20 

80.3 

0.30 

4-55 

93.81 

282.8 

IOO.O 

5 

A  i 

2O 

82.0 

0.2O 

4.65 

95-8 

282.8 

99.98 

5 

•B\\       20 

81.1 

0.20 

4.40 

95-7 

284.0 

IOO.O 

5 

Average  of  18  trials,  involving  98  observati 

ons  

99.998 

This  experiment  indicates  that  the  complete  separation  of 
moisture  from  steam  is  possible  by  mechanial  means. 

Any  radiation  in  the  instrument  will  increase  tne  apparent 
moisture  in  the  steam,  and  must  also  receive  consideration, 
especially  if  it  .be  sufficient  in  amount  to  sensibly  affect  the 
results. 


432 


EXPERIMENTAL   ENGINEERING. 


[§  337- 


337.  Description  of  Various  Forms. — The  earliest  form 
of  separating  calorimeter  used  in  experimental  work,  in  the 
Sibley  College  laboratory,  consisted  of  a  vessel  with  an  interior 


FIG.  205.— THE  SEPARATOR  CALORIMETER. 

nozzle,  extending  below  the  outlet  and  so  arranged  that  the 
current  of  steam  would  abruptly  change  direction  and  deposit 
the  moisture  into  the  bottom  portion  of  the  vessel.  The  dry 
steam  was  allowed  to  escape  near  the  top.  Fig.  205  shows 


§  337-]  THE  AMOUNT  OF  MOISTURE  IN  STEAM.  433. 

a  form,  used  in  the  early  experiments,  which  was  constructed 
of  pipe-fittings. 

This  instrument,  even  when  covered  with  hair  felt,  gave 
off  sufficient  amount  of  heat  to  sensibly  affect  the  results,  and 
a  correction  for  radiation  was  essential.  The  amount  of  radia- 
tion was  determined  by  using  two  instruments  of  the  same 
kind  and  size,  arranged  so  that  the  discharge  from  one  was 
the  supply  to  the  other. 

The  second  instrument  receives  perfectly  dry  steam  from 
the  first,  the  water  deposited  is  due  to  the  radiation  loss, 
which,  being  the  same  in  both  instruments,  provides  a  method 
of  determining  its  amount.  In  figuring  the  percentage  of 
moisture,  the  amount  thrown  down  by  radiation  in  the  second 
instrument  is  to  be  deducted  from  the  total  amount  caught 
in  the  first  calorimeter. 

In  later  forms  of  the  instrument  the  amount  of  radiating 
surface  has  been  made  so  small  as  to  render  the  correction  for 
radiation,  in  all  ordinary  cases,  negligible,  by  constructing 
the  instrument  in  such  a  manner  as  to  be  jacketed  by  steam 
of  the  same  pressure  and  temperature  as  in  the  sample.  The 
form  of  this  instrument  is  shown  in  Fig.  207,  in  which  the 
steam  is  supplied  through  the  pipe  D,  the  moisture  being 
received  in  the  interior  vessel  E,  the  discharge  steam  passing 
out  of  the  chamber  E  at  the  top,  into  the  jacket  F,  and  thence 
out  of  the  instrument  through  a  small  opening  at  L\  the 
opening  at  L  being  made  sufficiently  small  to  maintain  the 
pressure  in  the  jacket  the  same  as  that  in  the  sample.  The 
discharged  steam  is  then  condensed  in  a  can,  J.  This  can  is 
provided  with  a  small  top  in  which  is  set  a  gauge-glass  with 
attached  scale,  graduated  so  as  to  read  to  pounds  and  tenths 
of  pounds  of  water.  A  gauge-glass  N  attached  to  the 
calorimeter  is  provided  with  index,  mn,  arranged  to  move 
over  a  graduated  scale,  S,  which  shows  the  weight  of  water  in 
the  vessel  E  in  pounds  and  hundredths.  In  using  this 
instrument  the  condensing  can  J  is  filled  with  water  to  the 
zero-point  of  the  scale.  The  amount  of  condensed  steam  is 


434  EXPERIMENTAL   ENGINEERING.  [§  337. 

read  on  the  scale  of  the  can,  /;  the  amount  of  water  in  the 
sample  of  steam  for  the  same  time  is  read  on  the  scale  5. 
The  percentage  of  moisture,  in  case  radiation  is  neglected,  is 
the  quotient  of  the  reading  of  the  calorimeter  scale  S 
divided  by  the  sum  of  the  readings  on  both  scales. 

The  latest  form  of  the  instrument  is  shown  complete  with 
all  accessories  in  Fig.  206,  and  is  a  great  improvement  over 
the  earlier  forms  in  points  of  portability  and  convenience.  It 
differs  principally  from  the  form  last  described  in  the  con- 
struction of  the  steam-separating  device,  which  has  been 
increased  in  efficiency  and  in  the  substitution  of  a  gauge 
attached  to  the  outer  jacket,  which  registers  the  total  flow  of 
steam  through  the  instrument  in  ten  minutes  of  time. 

The  flow  of  steam  through  a  given  orifice  is  proportional 
to  the  absolute  steam-pressure,  by  Napier's  law*  which  has 
been  proved  correct  for  pressures  above  2£  pounds  absolute; 
and  hence  it  is  possible  to  calibrate  by  trial  a  pressure-gauge 
in  such  a  manner  that  the  graduations  will  show  the  flow  of 
steam  in  a  given  time.  The  only  error  which  is  produced  in 
this  graduation  is  that  due  to  changes  in  barometric  pressure, 
which  is  never  sufficient  to  sensibly  affect  the  results  obtained 
in  the  use  of  the  instrument.  Should  any  doubt  arise,  the 
accuracy  of  the  readings  of  the  gauge  are  easily  verified  by 
condensing  the  discharged  steam  for  a  given  period  of  time. 
This  should  be  done  occasionally  to  test  the  gaduations. 

The  instrument  may  be  described  as  follows:  It  consists 
of  two  vessels,  one  being  interior  to  the  other;  the  outer 
vessel  surrounds  the  interior  one  so  as  to  leave  a  space  which 
answers  for  a  steam-jacket.  The  interior  vessel  is  provided 
with  a  water-gauge  glass  10  and  a  graduated  scale  12.  The 
sample  of  steam  whose  quality  is  to  be  determined  is  supplied 
through  the  pipe  6  into  the  upper  portion  of  the  interior 
vessel.  The  water  in  the  steam  is  thrown  downward  into 


*  See  Transactions  American  Society  Mechanical  Engineers,  Vol.  XL, 
1887,  paper  by  Prof.  C.  H.  Peabody. 


337-]       THE  AMOUNT  OF  MOISTURE  IN  STEAM. 


435 


the  cup  14,  together  with  more  or  less  of  the  steam;  the 
course  of  the  steam  and  water  is  then  changed  through  an 
angle  of  nearly  180  degrees,  which 
causes  the  entire  amount  of  water  to 
•  be  thrown  outward  through  the  meshes 
in  the  cup  into  the  space  3,  which  con- 
stitutes the  inner  chamber.  The  cup 
serves  to  prevent  the  current  of  steam 
from  taking  up  any  moisture  which  has 
already  been  thrown  out  by  the  force 
of  inertia.  The  meshes  or  fins  project 
upward  into  the  inside  of  the  cup,  so 
that  any  water  intercepted  will  drip  into  I2" 
the  chamber  3.  The  steam  then  passes 
upward,  and  enters  the  top  of  the  out- 
side chamber.  It  is  discharged  from 
the  bottom  of  the  outside  chamber 
through  an  orifice  8  of  known  area, 
which  is  much  smaller  than  any  section 
of  the  passages  through  the  calorimeter, 
so  that  the  steam  in  the  outer  chamber 
suffers  no  sensible  reduction  in  pressure.  The  pressure  in 
the  outer  chamber,  being  the  same  as  in  the  interior,  has 
the  same  temperature,  and  consequently  no  loss  by  radia- 
tion can  take  place  from  the  interior  chamber  except,  that 
which  takes  place  from  the  exposed  surface  of  the  gauge- 
glass  and  fittings.  The  pressure  in  the  outer  chamber,  and 
also  the  flow  of  steam  in  a  given  time,  is  shown  by  suitably 
engraved  scales  on  the  attached  gauge.  The  scale  for  show- 
ing the  flow  of  steam  is  the  outer  one  on  the  gauge,  and  is 
graduated  by  trial,  and  gives  the  discharge  of  steam  in  pounds 
in  ten  minutes  of  time.  The  readings  on  the  scale  12  show 
the  weight  of  water  in  the  interior  vessel  3,  and  should  be  taken 
at  the  beginning  and  end  of  the  interval. 

The  total  size  of  the  instrument  is  about  12  X  2f  inches, 
and  its  weight  about  8  pounds. 


FIG.  206. —  IMPROVED  SEPA- 
RATING CALORIMETER. 


43^ 


EXPERIMENTAL   ENGI1VEERING* 


[§338. 


FIG.    207. — SEPARATING  CALORIMETER  WITH  CONDENSING  CAN. 

• 

338.  Formula  for  Use  of  the  Separating  Calorimeter. 

— Let  w  equal  the  weight  of  dry  steam  discharged  at  the 
exhaust-orifice,  W  the  water  drawn  from  the  separator,  R  the 
water  thrown  down  during  the  run  by  radiation.  Then  the 
quality  of  the  steam  is 


X  =  -; 


the  amount  of  moisture 


I  —  x  = 


W+w* 


w  —  R 


§  339-]          THE   AMOUNT  OF  MOISTURE  IN  STEAM.  437 

To  reduce  the  radiation  loss  as  much  as  possible  the  in- 
strument should  be  thoroughly  covered  with  hair  felt  to  the 
thickness  of  1/2  to  3/4  inch.  In  this  case  the  total  loss  by 
radiation  will  be  about  0.4  B.  T.  U.*  per  square  foot  per  hour 
for  each  degree  difference  of  temperature  between  the  steam 
and  the  surrounding  air.  This  will  amount  to  about  220 
B.  T.  U.  per  square  foot  per  hour,  or  about  1/5  of  a  pound 
of  steam  under  usual  conditions  of  pressure  and  temperature. 
In  the  instrument  described  the  actual  exposed  surface 
amounts  to  about  1/12  sq.  ft.,  so  that  the  condensation  loss 
may  be  considered  as  from  1/50  to  1/60  of  a  pound  of  steam 
per  hour.  The  total  flow  of  steam  through  the  instrument 
usually  varies  from  40  to  60  Ibs.  of  steam  per  hour,  so  that  if 
the  instrument  is  covered,  the  radiation  loss  would  be  less 
than  1/20  of  one  per  cent.  If  the  instrument  be  not  covered, 
the  loss  would  be  about  five  times  this  amount,  or  under  usual 
conditions  about  1/5  of  one  per  cent. 

The  radiation  loss  can  in  every  case  be  determined  by 
using  steam  of  known  quality  as  determined  by  the  throttling 
calorimeter,  or  better  still  by  arranging  two  separating  calori- 
meters of  exactly  the  same  size  in  series  so  that  the  steam 
exhausted  from  the  first  is  used  as  a  supply  to  the  second  in 
a  manner  already  explained. 

The  Limits  of  the  Instrument. — The  instrument  will  give 
correct  determinations  with  any  amount  of  moisture  that  the 
sample  of  steam  may  contain.  With  steam  containing  a  very 
small  amount  of  moisture,  the  radiation  loss  will  have  more 
effect  than  with  steam  containing  a  great  amount.  When  the 
fact  is  considered,  however,  that  a  sample  of  steam  cannot 
probably  be  obtained  but  what  differs  more  than  1/2  per  cent 
from  the  average,  the  futility  of  making  this  correction 
becomes  at  once  apparent. 

339.  General  Method  of  Using. — The  general  method  of 
using  is  given  only  for  the  latest  instrument  described,  which 

*  See    numerous    experiments,    Carpenter's    Heating    and    Ventilation 
(N.  Y.,  J.  Wiley  &  Sons),  Chapter  IV. 


43$  EXPERIMENTAL   ENGINEERING.  [§  34.0. 

is  briefly  as  follows:  First,  attach  the  instrument  to  a  pipe 
leading  to  the  main  steam-pipe  as  already  explained,  and  so 
as  to  obtain  the  fairest  sample  of  steam. 

Second,  wrap  the  instrument  and  connections  thoroughly 
with  hair  felt,  to  prevent  loss  of  heat  by  radiation,  leaving  only 
the  scales  visible. 

Third,  permit  the  steam  to  blow  through  the  instrument 
until  it  is  thoroughly  heated,  before  making  any  determina- 
tions. 

Fourth,  take  the  initial  and  final  readings  on  the  scale  12 
at  beginning  and  end  of  a  period  of  ten  minutes  of  time  and 
note  the  average  position  of  the  hand  on  the  gauge-dial  during 
this  time.  The  pressure  should  be  kept  as  nearly  constant 
as  possible  during  the  period  of  discharge,  in  which  case  this 
hand  will  remain  constant. 

Fifth,  compute  the  percentage  of  moisture  as  explained  by 
dividing  the  reading  on  the  scale  12  by  the  sum  of  the  read- 
ings on  scale  12  and  the  gauge-dial. 

Attention  is  again  called  to  the  difficulty  of  obtaining  an 
average  sample  of  steam  for  the  calori metric  determination.  The 
principal  cause  of  this  difficulty  is  due  to  the  great  difference  in 
specific  gravity  of  water  and  steam,  as,  for  example,  at  a  pressure 
of  100  pounds  absolute  per  square  inch  a  cubic  foot  of  steam 
weighs  0.23  pound;  a  cubic  foot  of  water  at  the  corresponding 
temperature  weighs  about  56  pounds,  or  more  than  225  times 
as  much.  If  any  great  amount  of  water  is  contained  in  the 
steam,  it  is  likely,  if  moving  in  a  horizontal  pipe ,  to  be  concen- 
trated on  the  bottom;  if  moving  downward  in  a  vertical  pipe, 
to  fall  under  the  influence  of  gravity  and  inertia;  if  moving  upward 
in  a  vertical  pipe,  it  tends  to  remain  at  the  bottom  until  absorbed 
or  taken  up  by  the  current  of  steam.  The  amount  of  water  by 
weight  that  will  be  absorbed  as  a  mist  or  fog  and  carried  by  the 
steam  is  not  definitely  known,  but  it  depends  in  a  large  measure 
on  the  velocity  of  flow. 

Because  of  the  great  difference  in  weight  of  water  and  steam 
nearly  all  the  water  can  be  deposited  from  a  current  of  steam. 


§  340-}         THE  AMOUNT  OF  MOISTURE  IN  STEAM. 


439 


in  a  vessel  or  reservoir  conveniently  connected  to  the  steam-pipe, 
by  action  of  gravity  or  inertia.  Such  a  device  is  known  com- 
mercially as  a  steam-separator.  The  water  is  removed  from  the 
separator  either  by  an  automatically  controlled  pump  or  trap  or 
by  hand. 

In  the  determination  of  quality  it  is  desirable  to  remove  the 
free  water  by  a  steam-separator  before  making  the  connection 
to  obtain  the  sample,  as  in  that  case  the  sample  is  more,  likely 
to  be  an  average  one.  See  papers  on  this  subject  in  the  Trans- 
actions of  Am.  Soc.  Mechanical  Engineers,  Vol.  XIII,  by  Prof. 
D.  S.  Jacobus,  and  Vol.  XII,  by  the  author. 

MECHANICAL   LABORATORY,  SIBLEY   COLLEGE,  CORNELL 

UNIVERSITY. 


PRIMING  TEST  WITH  SEPARATOR  CALORIMETER. 


Made  by, 

Test  of 

at.. 


189.. 


Steam. 
N.  Y. 


No.  of 
Run. 

Dura- 
tion of 
Run. 

Gauge 
Pressure. 

Absolute 
Pressure. 

Weight  of 
Exhaust. 

Weight 
of 
Water. 

Total 
Weight  of 
Steam. 

Radia- 
tion- 
loss. 

Mois- 
ture. 

>, 

13 

3 

a 

X 
per  ct. 

min. 

Ibs. 

P 
Ibs. 

IV 

Ibs. 

W 
Ibs. 

W4-w 
Ibl 

R 
Ibs. 

^-X 
per  ct. 

I 

2 

3 
4 

6 

7 
8 

9 

10 

440  EXPERIMENTAL   ENGINEERING.  [§  341. 

Diameter  of  orifice in.       Area  of  orifice sq.  in.        Symbol  A. 

Barometer-reading in. 

Formula  of  instrument,  i—  x  —  (W  —  £)-*-(  W-\-  w). 
Napier's  Rule,  Flow  of  Steam,  pounds  per  second  =  ^  PA. 

Method  of  determining  R 

Results 

Method  of  determining  W 

341.  The  Chemical  Calorimeter. — This  instrument  de- 
pends on  the  fact  that  certain  soluble  salts  will  not  be  absorbed 
by  dry  steam,  but  will  be  carried  over  by  water,  so  that  if  the 
salt  appears  in  the  steam  its  presence  indicates  water. 

Various  salts  have  been  used,  but  common  salt,  chloride  of 
sodium,  gives  as  good  results  as  any. 

The  proportion  that  the  salt  in  a  given  weight  of  con- 
densed steam  bears  to  that  in  a  given  weight  of  water  drawn 
from  the  boiler,  is  the  percentage  of  moisture  in  the  steam. 
The  method  of  analysis  is  a  volumetric  one,  and  is  as  follows : 

Add  three  or  four  ounces  of  common  salt  to  the  water  in 
the  boiler;  after  it  is  dissolved,  draw  from  the  boiler  a  small 
amount  of  water  and  condense  an  equal  weight  of  steam,  which 
are  to  be  kept  in  separate  vessels.  Add  to  each  of  them  a  few 
drops  of  neutral  chromate  of  potash,  but  in  each  case  an  equal 
quantity,  which  amount  may  be  measured  by  a  pipette  ;  the 
same  amount  should  also  be  added  to  a  vessel  containing  an 
equal  weight  of  distilled  water,  in  order  to  obtain  a  standard 
or  zero-point  foi  the  scale  used  in  the  analysis. 

By  means  of  a  graduated  pipette  a  triturated  solution  of 
nitrate  of  silver  is  permitted  to  flow,  a  single  drop  at  a  time, 
into  each  of  the  three  solutions.  The  effect  is  to  cause  the 
formation  of  the  chloride  of  silver,  and  until  that  formation 
completely  takes  place  the  resulting  liquid  will  be  whitish  or 
milky;  but  because  of  the  presence  of  the  bichromate,  the  in- 
stant the  chloride  has  all  been  precipitated  the  liquid  turns 
red.  The  amount  of  nitrate  of  silver  required  is  measured  by 
the  graduated  pipette,  and  gives  the  information  regarding  the 
salt  present. 


§  342-]        THE  AMOUNT  OF  MOISTURE  IN  STEAM. 


441 


The  detailed  directions  for  the  test  are  as  follows : 
Take  in  each  case  100  cubic  centimeters  of  liquid  contain- 
ing a  few  drops  of  neutral  chromate  of  potassium,  and  drop 
from    a»  triturated  solution  holding    10.8    grams  of  silver   to 
the  liter;  the  following  data  were  obtained  in  a  test: 

AMOUNT   OF   NITRATE   OF   SILVER   REQUIRED   TO   TURN 
100  c.  c.  RED. 


100  C.  C.  Of 

First  Trial. 

Second  Trial. 

Third  Trial. 

O  I  C     C 

o  05  c   c 

O  I  C     C 

\\/pter  from  the  boiler  «... 

13  6  c    c. 

14  o  c.  c 

1-2     -5  C    C       C 

£ 

0.05  c.  c. 

0.05  c.  c. 

o  05  c   c 

Letting  the  results. with  these  three  samples  be  denoted  by 
#,  b,  and  c  respectively,  and  the  amount  of  moisture  by  I  —  x, 
we  have 


I  —  x  = 


a  —  c 


This  gives  the  following  results  : 


First  Trial. 

Second  Trial. 

Third  Trial. 

Amount  moisture  

o.i  —  0.05 

0.05  —  0.05 

o.i  —0.05 

13.6  -  .05 

14.0  —  0.05 

13-35  —0.05 

Average  =  0.0025. 

This  method  is  evidently  applicable  only  in  determining 
the  amount  of  moisture  in  the  steam  as  it  leaves  the  boiler,  and 
will  give  no  information  regarding  the  additional  moisture  that 
may  be  added  to  the  steam  by  condensation. 

Instead  of  common  salt,  sulphate  of  soda  is  sometimes  used, 
and  the  percentage  of  moisture  determined  by  the  percentage 
of  sulphuric  acid  present  in  the  steam  as  compared  wfth  that 
in  water  from  the  boiler. 

342.  Comparative  Value  of  Calorimeters. — These  instru- 
ments, arranged  in  order  of  accuracy,  are  no  doubt  as  follows: 


442  EXPERIMENTAL  ENGINEERING.  [§  342. 

throttling  ;  separating  ;  Barrus  superheating  ;  Hoadley  ;  con- 
tinuous condensing ;  chemical ;  and  lastly  the  barrel. 

The  ease  with  which  the  throttling  and  separating  instru- 
ments can  be  used,  their  small  bulk,  and  great  accuracy,  render 
them  of  chief  practical  importance. 

The  throttling  calorimeter  can  be  used  only  for  steam  with 
a  small  amount  of  moisture,  as  explained  in  Article  333  ;  but 
the  separating  instrument  is  not  limited  by  the  amount  of 
moisture  entrained  in  the  steam.  It  is  not,  however,  as  well 
adapted  for  superheated  steam,  nor  can  the  results  be  deter- 
mined as  quickly  as  with  the  throttling  instrument ;  when 
carefully  handled  the  accuracy  is,  however,  substantially  the 
same. 


CHAPTER  XIV. 


DETERMINATION  OF  THE   HEATING  VALUE  OF 
FLUE-GAS  ANALYSIS. 


343.  Combustion. — Combustion  or  burning  is  a  rapid 
chemical  combination.  The  only  kind  of  combustion  which  is 
used  to  produce  heat  for  engineering  purposes  is  the  combina- 
tion of  fuel  of  different  kinds  with  oxygen.  In  the  ordinary 
sense  the  word  combustible  implies  a  capacity  of  combining 
rapidly  with  oxygen  so  as  to  produce  heat.  The  chief  elemen- 
tary constituents  of  ordinary  fuel  are  carbon  and  hydrogen. 
Sulphur  is  another  combustible  constituent  of  ordinary  fuel, 
but  its  quantity  and  its  heat-producing  power  are  so  small  that 
it  is  of  no  appreciable  value. 

The  chemical  elements  are  those  which  have  not  been  de- 
composed; these  unite  with  each  other  in  various  definite 
proportions,  which  may  be  represented  by  certain  numbers 
termed  chemical  equivalents  or  atomic  weights.  These  for 
gaseous  bodies  are  very  nearly  proportional  to  their  densities 
at  the  same  pressure  and  temperature. 

The  atomic  weight  of  a  chemical  compound  equals  the  sum  of 
the  atomic  weights  of  all  the  elements  entering  into  the  com- 
bination. Air  is  not  a  chemical  compound,  but  a  mechanical 
mixture  of  nitrogen  and  oxygen. 

The  following  table  gives  the  properties  of  the  principal 
elementary  and  compound  substances  that  enter  into  the  com- 
position of  ordinary  fuels  :  443 


444 


EXPERIMENTAL   ENGINEERING. 


[§344- 


Substance. 

Symbol. 

Chemical 
Equivalent 
by  Weight. 

Chemical 
Equivalent 
by  Volume. 

Properties  of 
Elements 
by  Volume. 

Oxvgen      

o 

16 

I 

N 

14 

I 

Hydrogen  

H 

I 

I 

c 

12 

? 

P 

T.I 

s 

32 

? 

Silicon  

Si 

14. 

Air     

77N  -1-  230 

IOO 

IOO 

7QN  _j_  2lO 

Water  

H2O 

18 

2 

H  4-  O 

Ammonia.  ...                        .  . 

NH3 

1  7 

2 

H  -f-  N 

Carbonic  oxide   

CO 

28 

2 

C  -f-  O 

CO2 

A  A 

2 

C  -4-  Do 

Olefiant  gas                          •  . 

CH2 

H' 

2 

C  4-  Ho 

Marsh  gas  

CH4 

16 

2 

C  -1-  Hi 

SO2 

64 

2 

S    H-  Oo 

Sulphuretted  hydrogen.. 

SH2 

^j. 

2 

S   4-  Ho 

Bisulphuret  of  carbon   

S2C 

^6 

2 

C   4-  So 

344.   Calorific    Power    or    Heat    of   Combustion. — The 

calorific  value  of  a  fuel  is  expressed  in  British  thermal  units 
or  in  calories,  according  as  Fahrenheit  or  Centigrade  therm  o- 
metric  scales  are  used.  The  calorific  value  may  be  deter, 
mined  by  direct  experiment,  or  it  may  be  computed  from  a 
chemical  analysis  as  follows  : 

The  carbon  is  credited  with  its  full  heating  power,  due 
to  its  complete  oxidation  as  determined  by  a  calorimeter  ex- 
periment. The  hydrogen  is  credited  with  its  full  heating  power, 
after  deducting  sufficient  to  form  water  with  the  oxygen 
present  in  the  compound ;  since  when  hydrogen  and  oxygen 
exist  in  a  compound  in  the  proper  proportion  to  form  water, 
the  combination  of  these  constituents  has  no  effect  on  the 
total  heat  of  combustion. 

The  calorimetric  value,  determined  experimentally,  of  one 
pound  of  hydrogen  is  62,032  B.  T.  U. ;  that  of  one  pound  of 
carbon,  14,500  B.  T.  U.  Hence  the  combustion  of  one  pound 
of  hydrogen  is  equivalent  to  that  of  4.28  pounds  of  carbon. 

A  formula  for  the  total  heat,  k,  of  combustion  in  B.  T.  U. 


§  344-]  THE  HEATING    VALUE   OF  FUELS.  .  445 

for  each  pound   of  the  compound   containing  hydrogen  and 
carbon  would  be 


For  theoretical  evaporative  power,  in  pounds  of  water  from 
and  at  212  F., 


The  number  of  pounds  of  air  required  to  supply  the  oxygen 
necessary  for  the  combustion  of  one  pound  of  fuel  to  CO2  can 
be  computed  from  the  formula 


and  the  corresponding  volume  in  cubic  feet  can  be  found  by  mul- 
tiplying by  the  specific  volume  of  one  pound  at  70  degrees  Fr. 
In  which  case  the  volume  in  cubic  feet  is 


In  the  above  formulae,  C,  H,  and  O  represent  the  number 
of  pounds  respectively  of  carbon,  hydrogen,  and  oxygen  in  the 
product  of  combustion. 

When  in  the  combustion  of  hydro-carbon  fuels  in  an  ordi> 
nary  furnace  hydrogen  is  consumed,  the  water  formed  passes 
off  in  the  state  of  vapor,  hence  the  latent  heat  of  evaporation 
is  not  available.  One  pound  of  hydrogen  burns  to  9  pounds 
of  water,  the  latent  heat  of  which  at  212°  is  966  units;  hence 
we  must  deduct  966  X  9  =  8694  units  from  the  tabular  value 


446 


EXPERIMENTAL  ENGINEERING. 


[§  345- 


of  the  heat  due  to  the  combustion  of  hydrogen.  This  leaves 
53,338  units  available.  Therefore  the  actual  value  in  terms  of 
carbon  is  H  =  3.6/C,  instead  of  4.28C  as  stated  in  (i),  and  the 
heat  of  combustion  actually  available  is 


•    .    .    (5) 


The  following  table  gives  the  heat  of  combustion  of  the 
principal  combustible  substances: 

TOTAL  HEAT  OF  COMBUSTION  WITH  OXYGEN. 


Substance. 

Pounds  of  Oxygen 
required  per  Pound 
of  Combustible. 

Pounds  of  Air  re- 
quired per  Pound 
of  Combustible 
(nearly). 

Total  Heat,  B.  T.  U. 

per  Pound. 

Pounds  of  Water 
evaporated  per 
Pound  of  Combus- 
tible from  212°. 

Product  of 
Combustion. 

8 

36 

62  032 

62  6 

H2O 

i  •  33 

6 

4  4OO 

4   en 

CO 

Carbon  burned  to  CO2  

2.t>7 
•3.4-1 

12 

14,450 
21  344 

14.67 
22    I 

C02 
CO2  and  H2O 

j  19,000 

20        ) 

i 

4e 

}  21,700 
•i  740 

22    51 

SO2 

2.2Q 

IO.  2 

14  ooo 

14    24 

SiOa 

Phosphorus  to  PaOs       .         . 

I    44 

6  5 

10  250 

p.Q, 

•2    ec 

16  2 

26  400 

26  68 

COa  and  H2O 

2.8 

1  8  600 

T8  53 

19,200 

IQ    71 

Wax         

1  8  800 

IO    OJ 

Ether  

1  6  i  o<> 

16  41 

Tallow  <  

16,000 

16  37 

1-7.06 

Methyl  alcohol  (wood-spirit)...  . 

Q  2OO 

Bisulphide  of  carbon    CSa.  •  •  • 

I    28 

57 

5  75o 

6'  18 

CO»   and    SO 

i  «33 

6 

IO  IOO 

10  4 

CO2 

345.    Determination    of   the    Heating    Value    by    the 
Oxygen   required.  —  It  was  observed  by  Welter*  that  those 


*  Chemical  Technology,  Vol.  I.,  p.  336  :  Graves  and  Thorp. 


§  345-]  THE  HEATING    VALUE   OF  FUELS.  447 

constituents  of  a  compound  which  require  an  equal  amount  of 
oxygen  for  combustion  evolve  also  equal  quantities  of  heat ; 
from  which  he  concluded  that  since  the  oxygen  required  for 
the  combustion  of  a  body  is  in  the  same  relation  as  the  quan- 
tity cf  heat  evolved,  it  might  fairly  be  made  the  measure  of 
the  heating  power.  When,  therefore,  oxygen  is  consumed  by 
the  burning  of  carbon,  wood,  hydrogen,  etc.,  the  heat  which 
is  evolved  must  increase  with  the  quantity  that  is  consumed ; 
or  the  same  amount  of  heat  is  generated  by  a  certain  given 
weight  of  oxygen,  whether  that  quantity  be  employed  in  con- 
verting carbon  into  carbonic  acid,  or  hydrogen  into  water. 

The  oxygen  required  is  2f  for  one  part  of  carbon ;  8  for  one 
part  of  hydrogen. 

One  part  by  weight  of  carbon  will  raise  the  temperature  of 
80.5  parts  of  water  from  freezing  to  boiling. 

One  part  by  weight  of  hydrogen  will  raise  234  parts  of 
water  from  freezing  to  boiling. 

One  part  by  weight  of  oxygen  in  burning  carbon  will  heat 

— ~  =  29.  i  parts  of  water. 

One  part  by  weight  of  oxygen  in  burning  hydrogen  will 
heat  -^f4-  =  29.3  parts  of  water  from  the  freezing  to  the  boiling 
point. 

In  round  numbers,  therefore,  the  heating  effect  of  oxygen 
may  be  assumed  as  sufficient  to  raise  29.2  parts  of  water  from 
the  freezing  to  the  boiling  point.  This  is  equivalent  to  2920 
Centigrade  heat-units,  or  to  5230  B.  T.  U. 

Calorific  Value. — The  calorific  value  of  the  fuel  would 
therefore  be  the  product  of  this  number  by  the  number  of 
parts  of  oxygen  required.  Thus  let  a  equal  the  number  of 
parts  of  oxygen  required  for  each  combustible ;  then  the  heat 
produced  by  the  combustion  is 

h  =  29200:     in  Centigrade  units ; 
h  =  52300:     in  B.  T.  U. 

Thus,  for  example,  in  the  combustion  of  carbon  to  COt, 


448  EXPERIMENTAL   ENGINEERING.  j_§ 

2j  parts  by  weight  of  oxygen  are  required  for  ea^i  one  of 
carbon  ;  hence  for  this  case  a  =  2f  ,  and 


h=  5230  X  2j  =  14,100. 

In  the  combustion  of  hydrogen  to  water  8  parts  by  weight  of 
oxygen  are  required,  and  in  this  case  a  =  8  ;  hence 

h  =  5230  X  8  =  41,840. 

This  is  about  two  thirds  of  the  actual  value  of  the  calorific 
power  of  hydrogen,  but  does  not  differ  much  from  the  heat 
available  in  ordinary  combustion. 

In  case  of  a  compound  body,  let  a  fuel  contain  a,  b,  c,  and 
d  parts  by  weight  of  different  combustible  ingredients  ;  and 
let  «,  «,,  <*3,  ^3  be  the  parts  by  weight  of  oxygen  required 
by  each.  Then 

h  —  2g2o(aa  4-  for,  -f-  caz  -f  dot^     in  Centigrade  units  ; 
=  5230(0^  +  bal  -\-  cct^  -\-  da^     in  Fahrenheit  units. 

346.   Temperature   produced  by  Combustion.  —  In   the 

determination  of  the  calorific  value  of  a  fuel  two  principal 
factors  are  involved,  namely,  the  calorific  power,  or  the  total 
amount  of  heat  to  be  obtained  from  the  perfect  combustion  of 
its  constituents,  and  the  calorific  intensity,  or  the  temperature 
attained  by  the  gaseous  products  of  combustion.  The  calorific 
power  will  be  the  same  regardless  of  the  method  of  combustion  ; 
that  is,  a  unit  of  carbon  or  of  hydrogen  will  give  the  same  heat 
whether  burned  with  the  oxygen  of  the  air  or  of  a  metallic  oxide. 
The  calorific  intensity  or  temperature,  however,  will  be  greater 
as  the  volume  of  gases  heated  is  less.  Thus  carbon  burned  to 
CO2  will  produce  a  much  higher  temperature  when  burned  in 
oxygen  gas  than  when  in  the  air,  since  in  the  latter  case  it 
must  heat  an  additional  quantity  of  nitrogen  equal  to  rather 
more  than  three  times  the  weight  of  the  oxygen. 


§  346-]  THE   HEATING    VALUE    OF  FUELS.  449 

The  maximum  temperature  cannot  be  either  computed  or 
determined  experimentally  with  complete  accuracy,  partly  be- 
cause the  total  combustion  of  a  quantity  of  fuel  in  a  given 
time  at  one  operation  is  practically  impossible,  but  more  par- 
ticularly from  the  fact  that  dissociation  of  gaseous  compounds 
produced  in  burning  takes  place  at  temperatures  far  below 
those  indicated  as  possible  by  calculation. 

The  maximum  temperature  is  calculated  as  follows : 
The  value  of  one  pound  of  carbon  is  8080  Centigrade  heat- 
units,  or  14,500  B.  T.  U.     The  heat  absorbed  by  any  body  is 
equal  to  the  product  of  its  weight,  w,  specific  heat,  s,  and  rise 
of  temperature,  t.     Hence 

wst  —  8080,     or     /  —  8080  -r-  ws'  in  Centigrade  degrees, 

and 

t  •=•  14,550  -r-  ws,  in  Fahrenheit  degrees. 

In  the  case  of  combustion  of  carbon  to  CO3  in  oxygen  gas, 
the  oxygen  required  for  each  part  of  carbon  is  2f  parts ;  the 
specific  heat  of  CO2  is  0.216.  Hence  the  maximum  temperature 

8080         =  ,o,r87°  C, 


3.67  X  0.216 
or 


3.67  X  0.216 


In  case  it  is  burned  in  air  an  additional  weight  of  8.88 
pounds  of  nitrogen,  with  a  specific  heat  of  0.24,  must  be 
raised  to  the  temperature  of  combustion.  Hence  the  maxi- 
mum rise  of  temperature  will  be 

8080  =273i°C.     or    4860°  F. 


3.67  X  0.216  +  8.888  X  0.24 

The  maximum  temperature  to  be  attained  by  combustion 
of  the  following  substances,  as  calculated  by  R.  Bunsen,  is : 


450 


EXPERIMENTAL   ENGINEERING. 


[§  347- 


Combustible. 

In  Oxygen. 

In  Air. 

Carbon          

9873°  C. 

7067 
9187 

7851 
8061 

17,803°  F. 
12,752 
16,568 
14,103 
14,542 

2458°  C. 
3042 
5413 
5329 
3259 

4456°  F. 
5507 
9775 
9624 
5898 

defiant  gas.  

Hydrogen           .  .  .  . 

If  the  air  supplied  to  the  fuel  be  in  excess  of  that  required 
for  perfect  combustion,  the  temperature  will  be  less. 

When  the  excess  of  air  is  50  per  cent,  the  maximum  tem- 
perature from  combustion  of  carbon  is  3515°  F. ;  when  the 
excess  is  100  per  cent,  the  maximum  temperature  is  2710°  F. 

The  specific  heats  under  constant  pressure  of  the  gases  usu- 
ally occurring  in  connection  with  combustion  are 

Carbonic-acid  gas 0.217 

Steam 0.475 

Nitrogen 0.245 

Air 0.238 

Ashes  (probably) 0.200 

Oxygen .  .  0.241 

Carbonic  oxide , 0.288 

Hydrogen 0.235 

347.  Composition  of  Fuels. — The  fuels  in  ordinary  use 
contain,  in  addition  to  the  combustible  compounds,  more  or 
less  mineral  or  earthy  matter  that  remains  as  ash  after  the 
combustion  has  taken  place  ;  there  is  also  frequently  water  in 
the  hygroscopic  state.  The  presence  of  these  incombustible 
substances  and  the  fact  that  perfect  combustion  can  rarely  be 
secured  tend  to  make  the  actual  heating  effect  less  than  that 
indicated  by  the  theory.  The  percentage  of  ash  as  given  in 
various  boiler  trials  shows  a  wide  variation,  as  follows: 

American  coals 5     to  22     percent 

English  coals 2.9  to  27.7        " 

Prussian  coals 1.5  to  1 1.6        " 

Saxon  coals 7.4  to  63.4       " 


§  348.] 


THE  HEATING    VALUE    OF  FUELS. 


451 


The  following  table  gives  the  composition  of  the  principal 
fuels  and  the  weight  of  air  required  to  produce  perfect  com- 
bustion: 

AVERAGE  COMPOSITION   OF   FUELS. 


Fuel. 

Carbon. 
C 

Hydrogen. 
H 

Oxygen. 

Ach. 

Pounds  of 
Air  required 
for  one  of 
Fuel. 

ii  .  16 

"          from  peat 

o  80 

o  6 

Coke    good             

O.  Q4 

ii   3 

Coal    anthracite  

O.QIS 

0.035 

0.026 

0.03  to  0.05 

12    17 

'       drv  bituminous     .  .  . 

o  87 

o  cm 

O  O4. 

O   04  tOO  .  22 

12    06 

'       coking       .  ..... 

o.8=> 

O   Of, 

O.O6 

<(        1  1       « 

II    73 

o.  75 

0.05 

O   OS 

«       «       « 

io.qS 

o  84 

o  06 

o  08 

«        «       « 

ii  88 

'        dry    long-flaming1  . 

O   77 

O   (X 

O    15 

IO    32 

o.  70 

0.05 

O.2O 

Q.3O 

Peat    dry   

0.58 

0.06 

O.  31 

$  to  it; 

7.68 

Wood    dry         .         .... 

o.  c  j 

O  <X7 

4.2   O 

O   OI 

6  oo 

"        air-dried,  20$  H2O. 

39.  6 

0.85 

4.8 

O.  I*? 

34-8 

0.01 

6.00 
jc  .  7 

348.  Principle  of  Fuel-calorimeters. — The  caloric  value 
of  a  fuel  is  determined  by  its  perfect  combustion  under  such 
conditions  that  the  heat  evolved  can  be  absorbed  and  measured. 
It  is  essential  in  such  cases  that  (i)  the  combustion  be  perfect, 
and  that  (2)  the  heat  evolved  be  absorbed  and  measured. 

The  combustion  may  take  place  in  atmospheric  air,  in  oxy- 
gen gas,  or  in  combination  with  a  chemical  that  supplies  the 
oxygen  required.  It  is  essential  in  all  cases  that  the  supply  of 
oxygen  be  adequate  for  perfect  combustion. 

The  heat  evolved  by  combustion  is  determined  by  the  rise 
in  temperature  of  a  given  weight  of  water  in  a  calorimeter  of 
which  the  cooling  effect,  Ky  has  been  carefully  determined,  and 
in  which  the  escaping  gases  are  reduced  to  the  temperature  of 
the  room.  Let  w  equal  the  weight  of  fuel,  E  the  heat  evolved 
in  heat-units  by  the  combustion  of  one  part,  IV  the  number  of 
parts  by  weight  of  water  heated  from  a  temperature  /7  to  /. 
Then  if  the  escaping  gases  be  reduced  in  temperature  to  that 
of  the  room, 

wE  -  (K+  W)(t  -  /'), 


452  EXPERIMENTAL   ENGINEERING.  1§35I- 

from  which 

E_  (K+W)(t-t'\ 

W 

349.  Method  of  Obtaining  Sample  of  the  Fuel.— The 

calorimetric  determination  is  made  only  on  a  very  small  portion 
of  the  fuel,  and  care  should  be  exercised  to  have  the  se- 
lected sample  fairly  represent  the  fuel  to  be  tested.  To 
select  a  sample  of  coal  for  calorimetric  examination  several 
lots  of  ten  pounds  each  should  be  chosen  from  different  por- 
tions of  the  coal  to  be  tested.  These  should  be  put  in  one  pile, 
thoroughly  mixed,  and  from  the  mixture  several  lots  of  one 
pound  each  taken.  These  latter  quantities  are  to  be  pulver- 
ized, thoroughly  mixed  into  one  pile,  and  from  this  the  required 
sample  selected.  It  is  recommended  that  the  sample  be  sub- 
jected to  a  considerable  pressure  by  placing  it  in  a  cylinder 
and  compressing  it  by  means  of  a  piston  moved  by  hydraulic 
pressure  or  by  a  screw :  this  is  of  especial  importance  if  the 
fuel  is  to  be  burned  in  oxygen  gas,  since  small  particles  are 
likely  to  form  an  explosive  mixture ;  and  further,  soot  and  tarry 
masses,  which  under  the  most  favorable  circumstances  might 
be  burned,  will  be  found  in  the  residue. 

350.  Heat-equivalent  of  the  Calorimeter. — The  effect  of 
the  calorimeter  is  most  conveniently  expressed  as  equivalent  to 
a  given  weight  of  water ;  this  is  obtained,  as  for  calorimeters 
used  in  determining  the  quality  of  steam  (see  Article  317,  page 
401),  either  by  rinding  the  sum  of  the  products  of  the  weights 
and  specific  heats  of  the  various  constituents  of  the  calorimeter, 
or  by  comparing  the  results  obtained  with  those  which  should 
have  been  found  by  the  combustion  of  some  fuel  whose  calo* 
rific  power  is  known — as  for  instance  pure  carbon  in  oxygen 
gas — or  again  by  its  cooling  effect  on  steam  of  known  pressure 
arid  weight,  or  on  warm  water  as  explained  on  page  372. 

351.  Method  of  Determining  Perfect  Combustion. — Ths 
quality  of   the  combustion   is   only  to  be  determined   by  an 
analysis  of  the  resulting  gases  and  of  the  products  of  combus- 
tion0     In  case  of  perfect  combustion  all  carbon  is  reduced  tc 


§  352-j  THE   HEATING    VALUE   OF  FUELS.  453 

CO2,  all  available  hydrogen  to  water,  sulphur  to  sulpharic  acid; 
and  further,  the  sum  of  the  weights  of  all  the  products  of  com- 
bustion should,  after  deducting  the  air  and  oxygen  obtained 
from  the  atmosphere,  equal  the  original  weight  of  the  coal. 

The  method  adopted  by  Favre  and  Silbermann  *  of  ascer- 
taining  the  weight  of  the  substances  consumed  by  calculation 
from  the  weight  of  the  products  of  combustion  was  as  follows : 
Carbonic  acid  was  absorbed  by  caustic  potash,  carbonic  oxide 
was  first  oxidized  to  carbonic  acid  by  heated  oxide  of  copper 
and  then  absorbed  by  caustic  potash  ;  water  vapor  was  absorbed 
by  sulphuric  acid.  This  system  showed  that  it  was  necessary 
to  analyze  the  products  of  combustion  in  order  to  detect  im= 
perfect  action.  Thus  in  the  case  of  substances  containing  car* 
bon,  CO  was  always  present  to  a  variable  extent  with  CO2,  and 
corrections  were  necessary  in  order  to  determine  the  total 
heat  due  to  the  complete  combination  with  oxygen.  The 
conclusion  arrived  at  by  these  experimenters  was  that  in  gen- 
eral there  was  an  equality  in  the  heat  disengaged  or  absorbed 
in  the  respective  acts  of  chemical  combination  or  of  decom- 
position of  the  same  elements ;  that  is,  the  heat  evolved  during 
the  combination  of  two  simple  elements  is  equal  to  the  heat 
absorbed  at  the  time  of  the  chemical  separation,  and  the  quan- 
tity of  heat  evolved  is  the  measure  of  the  sum  of  the  chemical 
and  mechanical  work  accomplished  in  the  reaction. 

352.  Favre  and  Silbermann's  Fuel-calorimeter. — This 
apparatus,  as  shown  in  Fig.  208,  consisted  of  a  combustion- 
chamber,  A,  formed  of  thin  copper,  gilt  internally,  and  fitted 
with  a  cover  through  which  solid  combustibles  could  be  intro- 
duced into  the  cage  C.  The  cover  was  traversed  by  a  tube,  £, 
connected  bv  means  of  a  suitable  pipe  to  a  reservoir  of  the  gas 
to  be  used  in  combustion,  and  by  a  second  tube,  D,  the  lower 
end  of  which  was  closed  with  alum  and  glass,  transparent  but 
adiathermic  substances  which  permitted  a  view  of  the  process 
of  combustion  without  any  loss  of  heat.  • 

For  convenience  of  observation  a  small  inclined  mirror  was 
placed  above  the  peep-tube  D. 

*See  Conversion  of  Heat  into  Work  :  Anderson. 


454 


EXPERIMENTAL  ENGINEERING. 


[§352. 


The  products  of  combustion  were  carried  off  by  a  pipe,  1? 
the  lower  portion  of  which  constituted  a  thin  copper  coil,  and 
the  upper  part  was  connected  to  the  apparatus  in  which  the 
non-condensible  products  were  collected  and  examined.  The 
whole  of  this  portion  of  the  calorimeter  was  plunged  into  a  thin 
copper  vessel,  G,  silvered  internally  and  filled  with  water,  which 


FIG.  208. — FAVRE  AND  SILBERMANN'S  FUEL-CALORIMETER. 

was  kept  thoroughly  mixed  by  means  of  agitators,  H.  The 
second  vessel  stood  on  wooden  blocks  inside  a  third  one,  /,  the 
sides  and  bottoms  of  which  were  covered  with  swan-skins 
with  the  down  on,  and  the  whole  was  immersed  in  a  fourth 
vessel,/,  filled  with  water  kept  at  the  average  temperature  of 
the  laboratory.  Thermometers,  K,  K,  of  great  delicacy  were 


§  353-]  THE  HEATING    VALUE   OF  FUELS.  455 

used  to  measure  the  increase  of  temperature  in  the  water  sur- 
rounding the  combustion-chamber.  The  quantity  of  heat 
developed  by  the  combustion  of  a  known  weight  of  fuel  was 
determined  by  the  increase  of  temperature  of  the  water  con- 
tained in  the  vessel  G.  For  finding  the  calorific  value  of  gases 
only,  the  cage  C  was  removed  and  a  compound  jet,  NO,  sub- 
stituted for  the  single  gas-pipe,  ignition  being  produced  by  an 
electric  spark  or  by  some  spongy  platinum  fixed  at  the  end  of 
the  jet. 

353.  Thompson's  Calorimeter. — Thompson's  Calorimeter* 
is  often  employed  for  determination  of  the  heating  values  of 
fuels.  It  consists  of  a  glass  jar  graduated  to  contain  1934 
grams  of  water;  in  this  are  inserted  (i)  a  thermometer  to  indi- 
cate elevation  of  temperature,  and  (2)  a  cylindrical  combustion- 
chamber  with  a  capacity  of  about  200  grams  of  water.  This 
chamber  is  capped  at  the  top,  and  a  small  tube  furnished  with  a 
valve  is  screwed  into  it,  to  hold  the  fuel.  The  combustible  to 
be  examined,  2  grams,  is  mixed  as  intimately  as  possible  with  22 
grams  of  a  very  dry  mixture  of  3  parts  of  potassic  chlorate  and 
i  part  of  potassic  nitrate,  and  introduced  into  the  combus- 
tion-tube ;  a  nitrate-of-lead  fuse  is  added  and  lighted.  This 
tube  is  introduced  into  the  combustion-chamber,  the  cap 
screwed  on,  and  the  whole  placed  without  delay  in  the  water 
of  the  calorimeter.  The  combustion  takes  place  directly  in  the 
water,  and  the  gases  disengaged  rise  to  the  surface.  The  water 
is  proportioned  to  the  fuel  as  966  is  to  i,  so  that  the  rise  in 
temperature  in  degrees  F.  is  proportional  to  the  evaporative 
power.  The  oxygen  required  for  the  combustion  is  supplied 
by  the  chemicals  added.  The  water-equivalent  of  the  calorim- 
eter as  above  described  is  about  ten  per  cent.  When  com- 
bustion has  ceased,  the  rise  in  temperature  of  the  water  is 
observed  ;  to  this  one  tenth  is  added  for  the  water  value  of  the 
calorimeter. 

The  corrected  number  gives  the  number  of  grams  of  water 
which  a  gram  of  the  combustible  can  evaporate. 

*See  Chemical  Technology,  Vol.   I. 


EXPERIMENTAL   ENGINEERING.  [§  355. 

354.  The   Berthier  Calorimeter.* — This   calorimeter  is 
based  on  the  reduction  of  oxide  of  lead  by  the  carbon  and 
hydrogen  of  the  coal,  the  amount  of  lead  reduced  affording  a 
measure  of  the  oxygen  expended,  whence  the  heating  power 
may  be  calculated  by  Welter's  law,  Article  345.     One  part  of 
pure  carbon  being    capable  of  reducing  34^-  times  its  weight 
in  lead. 

The  operation  is  performed  by  mixing  intimately  the 
weighed  sample  (10  grams)  with  a  large  excess  of  pure  litharge 
(400  grains).  The  mixture,  placed  in  a  crucible  sufficiently 
capacious  to  contain  three  times  its  bulk,  and  rendered  im- 
pervious to  the  gases  of  the  furnace  by  a  coating  of  fire-clay 
or  by  a  glaze,  is  covered  with  an  equal  quantity  of  pure 
litharge  (protoxide  of  lead).  The  crucible,  being  closed  with 
a  lid  and  placed  on  a  support  in  the  furnace,  is  slowly  heated  to 
redness,  and  when  the  gases  which  cause  the  mixture  to  swell 
considerably  have  escaped,  it  is  covered  with  fuel  and  strongly 
heated  for  about  ten  minutes,  in  order  to  collect  the  globules 
of  lead  in  a  single  button.  The  oxygen  from  the  litharge  com- 
bines with  and  burns  the  combustible  ingredients  of  the  fuel, 
leaving  for  every  equivalent  of  oxygen  consumed  an  equiva- 
lent of  reduced  metallic  lead. 

The  heating  power  is  calculated  as  follows :  I  part  of  pure  car- 
bon requires  2.666  parts  of  oxygen  by  weight,  which  taken  from 
litharge  leaves  34.5  parts  of  metallic  lead.  The  same  weight  of 
carbon  is  sufficient  to  heat  80  parts  of  water  from  32°  to  212°. 
Hence  every  unit  of  lead  reduced  by  any  kind  of  fuel  corre- 
sponds by  Welter's  law  with =  2.23  parts  of  water  raised 

from  the  freezing  to  the  boiling  point. 

355.  The   Berthelot   Calorimeter. — This  calorimeter,  as 
modified  by  Hempel,  consists  of  a  very  strong  vessel  with  a 
capacity  of  about  250  c.c.,  into  which  the  fuel  is  placed  after 
being  compressed  into  a  solid  form ;   the  combustion  is  per- 


*  Chemical  Technology,  Vol.  I.,  page  337. 


§  356-]  THE  HEATING    VALUE    OF  FUELS.  457 

formed  in  an  atmosphere  of  oxygen  gas  under  a  pressure  of  10 
to  12  atmospheres.* 

The  fuel  is  ignited  by  an  electric  spark,  and  the  heat  gen- 
erated is  known  by  measuring  the  rise  in  temperature  in  the  .sur- 
rounding water,  as  in  the  Favre  and  Silbermann  calorimeter. 

The  oxygen  gas  is  generated  in  a  tube  about  one  inch  in 
diameter  connected  to  the  calorimeter  by  an  intervening  tube 
about  J  inch  in  diameter.  To  this  latter  tube  is  attached  a 
pressure-gauge  to  indicate  the  pressure,  and  a  safety-gauge  to 
prevent  damage  from  explosion  or  excessive  -pressure.  A 
stop-cock  is  also  inserted  close  to  the  calorimeter.  For  gen- 
erating the  oxygen  the  tube  is  filled  with  40  grams  of  a  mix- 
ture of  equal  parts  of  manganese  dioxide  and  potassium 
chlorate.  It  is  then  heated  by  the  full  flame  of  a  Bunsen 
burner  applied  first  at  the  end  nearest  the  calorimeter  and 
gradually  moved  to  the  farther  end. 

To  use  the  instrument,  the  fuel,  connected  to  platinum 
wires  for  electrical  ignition,  is  introduced  and  suspended  in  the 
calorimeter,  the  top  of  which  is  firmly  screwed  on  and  the 
valve  closed.  Oxygen  gas  is  then  generated  until  the  pressure 
reaches  90  pounds,  and  exhausted  into  the  air  to  remove  other 
gases  from  the  calorimeter.  The  escape-valve  from  the  calo- 
rimeter is  closed  and  oxygen  gas  generated  until  the  pressure- 
gauge  shows  150  to  175  pounds  pressure  per  square  inch  ;  then 
the  connecting  stop-valve  is  closed  and  the  electric  current  ap- 
plied. After  the  heat  of  combustion  has  been  absorbed  the 
determination  is  made  as  with  the  Favre  and  Silbermann  calo- 
rimeter. 

355.  The  Bomb  Calorimeter.  —  This  instrument  was 
designed  by  the  French  chemist  M.  Berthelot,  and  consists 
of  a  strong  steel  vessel  provided  with  a  tightly  fitting  cover 
into  which  the  coal  is  placed  for  combustion.  For  the  pur- 
pose of  combustion  an  excess  of  oxygen  gas  is  supplied  under 
a  pressure  of  from  20  to  30  atmospheres.  The  fuel  is  sup- 
ported by  a  cage  of  platinum  connected  to  tHe  cover.  The 
fuel  is  fired  by  an  electric  current  passing  through  connecting 

*  See  Hempel's  Gas  Analysis,  translated  by  Dennis. 


458 


EXPERIMENTA  L  ENGINEERING. 


[§355. 


wires  and  generated  by  a  battery  of  ten  bichromate  cells.  To 
prevent  the  oxidation  of  the  instrument,  the  bomb  built  by 
Berthelot  was  lined  with  platinum.  The  heat  given  off 
during  the  process  of  combustion  was  absorbed  by  water  in  a 
vessel  surrounding  the  bomb.  During  the  process  of  com- 
bustion this  water  was  kept  in  motion  by  a  stirrer,  and  the 
heat  given  off  determined  by  its  rise  in  temperature. 

Various  modifications  of  coal-calorimeters  employing  the 
principle  of  Berthelot's  instrument  have  been  made  and  are 
in  extensive  use.  The  form  built  by  Mahler,  Fig.  212,  is 
perhaps  the  best  known,  which  differs  from  that  of  Berthelot 
only  in  the  form  of  the  stirring  apparatus  and  in  the  lining  of 
the  bomb,  which  is  of  porcelain  enamel,  instead  of  platinum. 
The  German  chemist  Hempel  has  also  designed  a  bomb 
calorimeter  in  which  the  bomb  is  made  of  steel,  the  interior 
of  which  is  protected  by  an  oxidized  surface  which  has  been 
found  to  give  practical  results. 

The  oxygen  for  use  in  the  calorimeters  can  be  obtained 
from  the  decomposition  of  water  by  electrical  means,  or  it  may 


FIG.  209.— PARTS  OF  THOMPSON'S  CALORIMETEK  IN  ACTION. 

be  made  by  heating  a  crucible  filled  with  equal  parts  of  man- 
ganese dioxide  and  potassium  chlorate-  Some  chlorine  will 
usually  pass  over,  which  may  be  removed  by  passing  through 


§  3550 


THE  HEATING    VALUE   OF  FUELS. 


459 


a  close  roll  of  brass  wire-gauze.  The  oxygen  may  be 
received  into  a  small  gasometer  and  compressed  by  the  action 
of  a  pump  to  the  required  density.  Oxygen  is  also  now 
manufactured  as  a  commercial  article  and  can  be  purchased  in 
cylinders  holding  4  or  5  cubic  feet  and  under  a  pressure  of  20 
atmospheres  in  nearly  all  the  large  cities.  Thus  it  may  be 
purchased  in  New  York  of  Eimer  &  Amend. 

In  the  Hempel  calorimeter,  as  shown    in    Fig.   210,   the 
crucible  for  making  the  oxygen  is  attached  directly  to  the 


FIG.  210.— HEMPEL'S  CALORIMETER  WITH  ENLARGED  CHARGING-PLUG. 

calorimeter  by  means  of  connecting  pipes.  In  this  case  the 
calorimeter  is  charged  before  connecting  the  crucible.  The 
crucible  is  filled  with  a  mixture  of  equal  parts  dioxide  of 
manganese  and  chlorate  of  potash,  and  the  oxygen  is  driven 
off  by  the  application  of  heat  with  the  Bunsen  burner;  the 
heat  being  first  applied  at  the  end  of  the  crucible  nearest  the 
calorimeter.  A  pressure-gauge  B  is  connected  to  the  pipe,  and 
when  the  required  pressure  is  reached  the  burner  is  removed, 
a  connecting  stop-cock  b  closed,  and  the  connections  to  the 


460 


EXPERIMENTAL  ENGINEERING. 


[§355- 


crucible  removed.  To  prevent  danger  from  accidents  during 
the  generation  of  the  oxygen,  the  crucible  and  gauge  should 
be  enclosed  in  a  large  wooden  vessel. 

The  value  of  the  fuel  burned  is  determined  from  the  rise 
in  temperature  of  the  water;  account  being  taken  of  the 
weight  of  water  and  also  the  weights  and  specific  heats  of  all 
parts  of  the  calorimeter.  Usually  during  combustion  some 
nitric  acid  is  formed  which  is  deposited  on  the  walls  of  the 
calorimeter.  The  heat  liberated  in  the  formation  of  nitric 
acid  should  be  taken  into  account,  but  as  this  is  seldom  greater 
than  ^  of  one  per  cent,  it  is  usually  less  than  the  unavoidable 


FIG.  211. — CHARGING  CALORIMETER  WITH  OXYGEN. 

errors  of  observation.  To  avoid  the  numerous  corrections 
and  the  tedious  calculations  which  result  therefrom,  the 
chemist  Hempel  adopted  the  plan  of  standardizing  his  instru- 
ments by  burning  definite  amounts  of  pure  carbon,  the -value 
o-f  which  he  took  as  known  from  the  best  investigations  by 
Berthelot.  To  obtain  pure  carbon  with  which  to  standardize 
the  instrument,  he  pulverized  and  carbonized  crystallized 
sugar  several  times  in  succession,  driving  off  at  a  high  heat  all 
volatile  matter.  This  process  of  calibration  gave  a  series  of 
factors,  which  multiplied  by  thermometer-readings  reduced 
the  results  to  heat-units.  The  following  example,  from 


UJ 


462 


EXPERIMENTAL   ENGINEERING. 


[I  355. 


"  Trait^  Pratique  de  Calorimetre  Chimique, "  by  M,  Berthe- 
lot,  illustrates  the  process  of  reduction  necessary  in  using  the 
bomb  calorimeter. 

The  weight  of  each  part  of  the  calorimeter  is  carefully 
ascertained  and  multiplied  by  the  specific  heat  of  the  material 
composing  the  part.  The  sum  of  these  various  products  gives 
the  water  equivalent  of  the  calorimeter  which  is  given  later. 

DETERMINATION  OF  THE  HEAT  IN  PURE  CARBON. 

Dried  at  a  temperature  of  from  120  to  130  degrees  C.  until  it  had  attained  a 
constant  weight  and  permitted  to  cool  in  a  closed  vessel  and  in  the  presence 
of  concentrated  sulphuric  acid.  (Observations  of  time  and  temperature,) 


Preliminary  Observations 
Before  Combustion. 

Observations  During 
Combustion. 

Observations  After 
Combustion. 

o  min.,  17.360  deg.  C. 

5 

min.,  18.500  deg.  C. 

9  min.,  18.810  deg.  C. 

I     "       17.360         " 

6 

18.782 

10 

18.802 

2     "       17.360 

7 

18.820 

ii 

18.795 

3     "       17-360 

8 

"       18.818 

12 

18.785 

4     "       17-360 

13 

18-775 

14              18.770 

Initial  cooling  per  minute,  zero  degrees;  final  cooling  per 
minute,  0.008  deg.  C.  Total  correction  for  cooling,  0.046 
deg.  C.  Variation  of  temperature,  not  corrected,  18.818  — 
17.360  —  1.438  deg.  C.  Corrected  =  1.484  deg.  C.  Value  in 
water  of  the  calorimeter  and  contents  —  2398. 4gr.  Weight  of 
nitric  acid  formed  —  0.0173  gr.  (Each  gram  is  equal  to  227 
calories..)  Each  gram  of  iron  burned  is  equal  to  1650  calories. 

Total  heat  observed =3558.5  calories. 

Disengaged  by  the  combustion  of  the 

iron-ware 22.4  cal. 

Disengaged  by  the  formation  of  nitric 

acid 3.9  cal. 

Heat  obtained  from  the  combustion  of  the 

carbon —  3532.9  calories. 

3532.2 


=       26.3 


Heat  for  one  gram 


0.4342 


=  8136.6 


§  356-]  rHE   HEATING    VALUE    OF  FUELS.  463 

The  latest  determinations  of  Berthelot  give  the  absolute 
heating  power  of  amorphous  carbon  as  8137.4  calories  = 
14629.5  B.  T.  U.  In  the  use  of  the  calorimeter,  the  coal 
is  to  be  first  powdered  and  then  reduced  by  pressure  to  a 
cylindrical  cake  or  lump  which  is  fired  by  the  heat  from  an 
electric  current.  Corrections  to  the  result  are  to  be  made 
for  the  heat  disengaged  by  the  oxidization  of  the  iron  and  by 
the  formation  of  nitric  acid  and  by  the  vapor  of  water 
remaining  in  the  atmosphere  of  the  bomb.  All  these  correc- 
tions are  very  small  and  may  be  avoided  by  using  the  process 
of  calibration  employed  by  Hempel. 

As  noticed  in  the  example  above  cited,  the  rise  in  tem- 
perature of  the  surrounding  water  is  very  small,  and  in  order 
to  obtain  accurate  results  this  water  must  be  thoroughly 
agitated  to  produce  a  uniform  temperature;  the  thermometer 
used  must  be  capable  of  reading  very  small  increments  of  a 
degree  and  must  be  read  by  a  strong  reading-glass  or  attached 
vernier.  The  accurate  determination  of  small  increments  of 
temperature  is  nearly  impossible  with  the  apparatus  to  be 
found  in  an  engineering  laboratory.  To  overcome  this  diffi- 
culty, the  author  has  designed  a  form  of  calorimeter  in  which 
the  increase  in  temperature  is  determined  by  the  expansion 
of  the  entire  amount  of  water  in  the  vessel  surrounding  the 
calorimeter.  The  value  of  the  scale  is  determined  by  calibra- 
tion. Two  forms  of  this  instrument  are  manufactured  by 
Schaeffer  and  Budenberg,  Brooklyn,  N.  Y.  In  one  form  the 
combustion  is  performed  in  a  steel  bomb  lined  with  enamel  in 
many  respects  similar  to  the  Mahler  calorimeter.  In  the 
other  the  combustion  is  performed  in  a  current  of  oxygen  gas 
under  low  pressure,  and  the  heat  of  combustion  is  absorbed 
by  water  in  the  surrounding  vessel,  the  products  of  combus- 
tion passing  through  a  coil  and  being  finally  discharged  into 
the  atmospheric  air. 

356.  Fuel-calorimeter  in  which  Heat  is  Measured  by 
E  xpansion  of  Water. — The  general  appearance  of  the  instru- 
ment is  shown  in  Fig.  212;  a  sectional  view  of  the  interior 


464  EXPERIMENTAL  ENGINEERING.  [§  3$6 

part  is  shown  in  Fig.  214,  from  which  it  is  seen  that,  ir 
principle,  the  instrument  is  a  large  thermometer,  in  the  bulb 
of  which  combustion  takes  place,  the  heat  being  absorbed  by 
the  liquid  which  is  within  the  bulb.  The  rise  in  temperature 
is  denoted  by  the  height  to  which  a  column  of  liquid  rises  in 
the  attached  glass  tube. 

In  construction,  Fig.  214,  the  instrument  consists  of  a 
chamber,  No.  15,  which  has  a  removable  bottom,  shown  in 
section  in  Fig.  213,  and  in  perspective  in  Fig.  214.  The 
chamber  is  supplied  with  oxygen  for  combustion  through 
tube  23,  24,  25,  the  products  of  combustion  being  discharged 
through  a  spiral  lube,  29,  28,  30. 

Surrounding  the  combustion-chamber  is  a  larger  closed 
chamber,  I,  Fig.  214,  filled  with  water,  and  connecting  with 
an  open  glass  tube,  9  and  10.  Above  the  water-chamber  I 
is  a  diaphragm,  12,  which  can  be  changed  in  position  by 
screw  14  so  as  to  adjust  the  zero  level  in  the  open  glass  tube 
at  any  desired  point.  A  glass  for  observing  the  process  of 
combustion  is  inserted  at  33,  in  top  of  the  combustion- 
chamber,  and  also  at  34,  in  top  of  the  water-chamber,  and  at 
36,  in  top  of  outer  case. 

This  instrument  readily  slips  into  an  outside  case,  which 
is  nickel-plated  and  polished  on  the  inside,  so  as  to  reduce 
radiation  as  much  as  possible.  The  instrument  is  supported 
on  strips  of  felting,  5  and  6,  Fig.  214.  A  funnel  for  filling 
is  provided  at  37,  which  can  also  be  used  for  emptying  if 
desired. 

The  plug  which  stops  up  the  bottom  of  the  combustion- 
chamber  carries  a  dish,  22,  in  which  the  fuel  for  combustion 
is  placed;  also  two  wires  passing  through  tubes  of  vulcanized 
fibre,  which  are  adjustable  in  a  vertical  direction,  and  con- 
nected with  a  thin  platinum  wire  at  the  ends.  These  wires 
are  connected  to  an  electric  current,  and  used  for  firing  the 
fuel.  On  the  top  part  of  the  plug  is  placed  a  silver  mirror, 
38,  to  deflect  any  radiant  heat.  Through  the  centre  of  this 
plug  passes  a  tube,  25,  through  which  the  oxygen  passes  to 


§  356.] 


THE   HEATING    VALUE   OF  FUELS. 


465 


supply  combustion.  The  plug  is  made  with  alternate  layers 
of  rubber  and  asbestos  fibre,  the  outside  only  being  of  metal, 
which,  being  in  contact  with  the  wall  of  the  water-chamber, 
can  transfer  little  or  no  heat  to  the  outside. 

The  discharge-gases  pass  through  a    long  coil  of  copper 


10 
9 


37 


FIG.  213.— FUEL-CALORIMETER.  FIG.  214.— ENLARGED  SECTION. 

pipe,  and  are  discharged  through  a  very  fine  orifice  in  a  cap 
at  30. 

The  instrument  has  been  so  designed  that  the  combustion 
can  take  place  in  oxygen  gas  having  considerable  pressure; 
and  in  the  form  of  a  bomb;  but  in  practice  we  have  found 
that  very  reliable  results  have  been  obtained  with  pressures 


466  EXPERIMENTAL  ENGINEERING.  [§  356. 

of  2  to  5  pounds  per  square  inch  in  an  instrument  of  the  form 
described,  and  this  has  been  commonly  used  in  investigations 
at  Sibley  College. 

For  the  purpose  of  making  determinations  of  fuel,  oxygen 
gas  has  been  made  and  stored  in  a  gasometer  holding  about 
15  cubic  feet,  from  which  it  was  drawn  as  required. 

Method  of  Using  the  Calorimeter.  —  i.  Select  an  accurate 
sample  by  a  system  of  quartering,  which  shall  commence  with 
a  very  great  amount,  if  possible,  and  finally  terminate  with  a 
very  small  fraction  of  a  pound. 

2.  Reduce  to  powder  by  grinding,  in  a  mortar  or  a  mill, 
sufficient    coal   for  several    samples.     A  coffee-mill  answers 
excellently  for  this  purpose. 

3.  Introduce  the  sample  into  a  small  asbestos  cup,  drive 
out  moisture  by  warming  it  over  a  Bunsen  burner  or  alcohol 
lamp.     Weigh  accurately  on  a  fine  chemical  balance-scale. 

4.  Introduce  the  sample  into  the  calorimeter:    (a)  start 
the  oxygen  gas  flowing;  (&)  fire  the  charge,  which  should  be 
done  by   pressing  on  a  key;  (c)  at  instant  coal   is  lighted, 
throw  off  the  current  and  note  the  reading  of  the  scale  and 
time.      During  combustion  keep  the  discharge  orifice  open, 
occasionally  trying  it  with  a  small  wire. 

5.  Watch   the  combustion,    which    will    usually   require 
about  ten  minutes  for  each  gram  of  coal,  and  when  completed 
note  the  scale  reading  and  the  time.     The  difference  between 
first  and  second  reading  is  the  actual  scale  reading. 

6.  To  correct  for  radiation  note  the  amount,  the  water  in 
the  column  has  fallen  for  the  same  time  as  required  for  com- 
bustion; add  this  to  the  actual  reading  to  get  the  corrected 
scale  reading. 

7.  Divide   the  value  as  shown  on  the  diagram   by   the 
weight  in  pounds  of  the  sample  burned.     The  result  will  be 
the  value  in  B.  T.  U.  of  one  pound  of  coal. 

8.  Remove  the  dish  in  which  the  combustion  took  place; 
weigh  it  carefully  with  and  without  contents.      If  the  com- 
bustion has  been  perfect,  the  difference  of  these  weights  gives 


§  356-]  THE  HEATING    VALUE   OF  FUELS.  467 

the  ash.     Wipe   the    combustion-chamber   dry  for   another 
determination. 

9.  To  prepare  for  another  determination,  remove  the 
calorimeter  from  the  outside  case  and  immerse  in  cold  water, 
care  being  taken  to  prevent  any  water  entering  oxygen-tubes 
or  combustion-chamber. 

This  method  is  preferable  to  emptying  the  calorimeter 
and  adding  fresh  water  each  time,  since  the  air,  which  is 
always  present  in  water,  will  affect  the  results  and  is  a  diffi- 
cult element  to  remove.  The  operation  of  cooling  takes  but 
a  few  minutes  and  is  easily  performed. 

In  order  that  the  instrument  may  give  accurate  values,  it 
is  necessary  that  all  air  be  removed  from  the  water,  and  that 
the  oxygen  be  supplied  at  a  constant  pressure.  The  pressure 
with  which  the  instrument  was  calibrated  is  given  with  the 
calibration  curve,  and  if  any  other  pressure  is  used  a  new  cali- 
bration should  be  made. 

Do  not  attempt  to  use  the  calorimeter  in  a  room  whose 
temperature  is  above  80  degrees  Fahr.,  as  the  calorimeter 
should  always  be  warmer  than  the  air  of  the  room. 

In  case  oxygen  is  purchased  in  a  condensed  form,  it  can 
be  reduced  to  any  desired  amount  by  passing  it  into  a  small 
gasometer  before  reading  the  calorimeter.  The  gasometer 
may  be  made  by  simply  inverting  one  pail  into  another  which 
is  partly  filled  with  water.  By  weighting  the  top  pail  any 
pressure  required  can  be  produced. 

If  oxygen  is  made  for  especial  use,  it  can  be  received  in 
a  gasometer,  made  as  described,  but  with  sufficient  capacity 
for  several  tests. 

Oxygen  can  be  made  by  heating  a  mixture  of  about  equal 
parts  of  dioxide  of  manganese  and  chlorate  of  potash  placed 
in  a  closed  retort. 

In  lighting  the  platinum  wire  we  use  1 6  Mesco  dry 
batteries  connected  in  four  series.  A  single  cell  of  a  storage 
battery,  the  current  of  which  is  ordinarily  used  for  incandes- 
cent lighting,  may  be  used  with  success. 


468  EXPERIMENTAL   ENGINEERING.  [§  356. 

EXAMPLE   SHOWING    HOW     TO     DETERMINE   THE    CALORIFIC 
POWER   OF    COAL. 

Weight  of  crucible 1.269  grams. 

11        "        "       andcoal , 3.017      il 

"        "        "       and  ash 1.567      " 

"         'combustibles «...    1.4$°      " 

-ash 297      " 

"        "  coal 1.747      " 

1.747  reduced  to  pounds  =  1.747  X  .002205  =  .003852  Ibs. 

First  scale-reading,     3.90  inches,  time  2  o'clock,  55  minutes. 
Second       "  14.70     "  "     3        "        20 

Third         "  14.30     "  "     3        "        45 

Actual  scale  reading 3.90  —  14.70  =  10.80  inches. 

For  radiation 14.30—14.70=       .40       " 

Corrected  scale-reading 11.2 

On  the  diagram  11.2  corresponds  to  46.25  B.  T.  U.'s  in 
sample. 

As  46.25  B.  T.  U.  are  .00385  Ibs.,  one  pound  will  be: 

46.25  -T-  .00385  =  12,000  heat-units. 

All  calorimeters  are  calibrated  before  shipment,  but  to 
enable  purchasers  to  make  a  new  calibration  in  case  a  new 
glass  tube  should  have  to  be  inserted  we  give  the  following 
instructions: 

1.  Make  a  pure  coke,  reduce  some  soft  coal  to  powder, 
fill  a  porcelain  or  clay  crucible  2/3  full,  cover  it  air-tight,  glow 
it  with  a  blast-lamp  or  in  a  forge-fire  for  one  hour.  .    If  cold, 
grind   it   in   a   mortar  to   a  very  fine   powder.      Repeat   this 
operation. 

2.  Remove  gland   and   hexagon  plug-screw  from  top  of 
calorimeter  and  fill  it  with  water.      Close  the  plug-screw  and 
connect  the  glass-tube  opening  by  some  rubber  hose  or  glass 
tube  with  a  smaller  vessel  filled  with  water.      Boil  the  water 
in  the  calorimeter  body ;  this  may  be  done  by  a  Bunsen  burner, 
protecting  the  calorimeter  by  a  thin  sheet  of  asbestos.      Place 


§35^.]  THE   HEATING   VALUE   OF  FUELS.  469 

the  instrument  in  such  a  position  that  the  glass-tube  opening 
may  be  its  highest  point  and  so  enable  all  air  and  steam  to 
pass  through  the  connection  to  the  smaller  vessel.  Also  keep 
the  water  in  the  smaller  vessel  boiling  until  the  calorimeter 
has  fully  cooled  off.  Remove  rubber  connection,  fill  the  glass 
tube  with  boiled  water  and  screw  it  tight.  Take  care  not  to 
allow  it  to  pass  so  far  into  the  calorimeter  that  air  will  be 
trapped. 

Put  about  two  inches  kerosene  oil  on  top  of  water-column 
to  prevent  air  from  coming  in  contact  with  the  water.  Should 
it  be  found  that  the  water  in  column  stands  too  high  after  the 
calorimeter  has  taken  the  temperature  of  the  room,  loosen 
the  plug  and  allow  water  to  leak  out  slowly  until  the  scale- 
reading  is  about  two  inches,  then  close  it  securely. 

3.  If  the  instrument  is  ready  for  calibration,  follow  in- 
structions given  under  method  of  using  the  calorimeter.  The 
difference  of  weight  between  the  weight  of  crucible  and 
carbon  (coke)  and  the  weight  of  crucible  and  ash  is  the 
weight  of  pure  carbon  burned. 

Dividing  14540  by  the  weight  of  burned  carbon,  we  obtain 
the  number  of  heat-units  in  the  sample. 

By  drawing  the  oblique  line  on  the  chart,  take  the  num- 
ber of  corrected  scale-reading  as  ordinates,  and  the  number 
of  B.  T.  U.'s  in  sample  as  abscissae,  make  a  point  on  crossing 
and  draw  a  line  to  zero. 

EXAMPLE   OF   CALIBRATION. 

Weight  of  crucible  and  coke  in  grams 3.002 

"        "        "  "    ash     "       "      1.064 

"        "  burned  pure  carbon 1*935 

1.935  grams  reduced  to  pound  =  .00426  Ibs. 
J-935  X. 002205  =  .00426  Ibs. 
14540  X  .00426  —  61.86  B.  T.  U.  in  sample. 
First  scale-reading,    3.33  inches,  time  n  o'clock,  15  minutes. 

Second      "  16.85       "          "      ll       "       4°  " 

Third        "  16.  "          "      12       "       10  " 


47°  EXPERIMENTAL  ENGINEERING.  [§  356, 

Actual  reading 16.85—    3-35  =  I3-5°  inches. 

For  radiation 16.00—16.85=      .85       " 

Corrected  scale-reading 14-35       " 

"  DIRECTIONS      FOR     PROXIMATE     ANALYSIS.* — COAL     AND 

COKE." 

The  sample  should  be  finely  pulverized  in  a  mortar,  and 
then  thoroughly  mixed. 

Moisture. — Place  the  weighed  sample  (about  I  gram)  in  a 
porcelain  crucible,  and  dry  in  an  air-bath  for  one  hour,  at  a 
temperature  between  105  and  no  degrees  C.  Weigh  as  soon 
as  cool.  Loss  is  moisture. 

Volatile  Matter. — Weigh  about  \\  grams  of  the  undried 
pulverized  coal,  place  it  in  a  platinum  crucible  and  cover 
tightly.  Heat  it  for  3^  minutes  over  Bunsen  burner  (bright 
red  heat),  and  then  immediately,  without  cooling,  for  3^ 
minutes  over  blast-lamp  (white  heat).  Cool  and  weigh. 
Loss,  less  the  moisture,  is  volatile  matter. 

Fixed  Carbon. — If  a  coke  be  formed  in  the  preceding  opera- 
tion, make  a  note  of  its  properties,  color,  firmness,  etc.,  then 
place  the  crucible,  with  cover  removed,  in  an  inclined  posi- 
tion, and  heat  over  Bunsen  burner  until  all  carbon  is  burned., 
i.e.,  to  constant  weight.  The  combustion  may  be  hastened 
by  stirring  the  charge  from  time  to  time  with  a  platinum  wire. 
Difference  between  this  and  last  weight  is  the  fixed  carbon. 

Ash. — Difference  between  last  weight  and  weight  of  cruci- 
ble is  the  ash. 

Total  Sulphur  in  Coal  and  Coke. — Prepare  a  fusing  mixture 
by  thoroughly  mixing  two  parts  calcined  magnesia  with  one 
part  anhydrous  sodium  carbonate.  Determine  the  sulphur 
in  the  mixture. 

Thoroughly  mix  I  gram  of  the  finely  pulverized  coal  with 
\\  grams  of  fusing  mixture.  Heat  over  an  alcohol  lamp,  in 
an  open  platinum  or  porcelain  crucible,  so  inclined  that  only 

*See  "Crooke's  Select  Methods,"  2d  Edition,  pp.  595-607. 


§  3 5 6.]  THE  HEATING    VALUE   OF  FUELS.  4/1 

its  lower  half  may  be  brought  to  a  red  heat.  The  crucible 
should  not  be  over  £  or  f  full,  and  the  heat  should  be  gentle 
at  first,  to  avoid  loss  upon  the  consequent  sudden  escape  of 
volatile  matter,  if  present  in  large  amount.  Raise  the  heat 
gradually  (it  must  not  at  any  time  be  high  enough  to  fuse  the 
mixture),  and  stir  the  contents  of  the  crucible  every  five 
minutes  with  a  platinum  wire.  The  oxidation  of  the  carbon 
is  complete  when  ash  becomes  yellowish  or  light  gray  (about 
one  hour).  Cool  crucible,  add  I  gram  pulverized  NH4NO,  to 
the  ash,  mix  thoroughly  by  stirring  with  a  glass  rod,  and  heat 
to  redness  for  five  to  ten  minutes,  the  crucible  being  covered 
with  its  lid. 

Cool,  digest  the  mass  in  water,  transfer  the  crucible  con- 
tents to  a  beaker,  rinse  out  the  crucible  with  dilute  warm 
HC1,  dilute  solution  in  beaker  to  about  150  c.c.,  acidulate 
with  HC1,  and  heat  almost  to  boiling  for  five  minutes.  Filter 
and  precipitate  the  sulphuric  acid  in  filtrate  by  BaCl3  in  usual 
manner. 

Phosphorus. — If  present,  it  will  be  found  in  the  ash. 
Ignite  about  10  grams  of  the  coal  in  a  large  platinum  crucible, 
and  determine  the  phosphorus  in  the  ash  in  the  usual  manner. 
(See  Fresenius,  p.  741.) 

Sulphur  and  phosphorus  are  not  usually  of  importance,  un- 
less the  coal  is  destined  for  certain  uses  where  these  ingredients 
would  be  harmful;  the  determination  requires  much  more 
time  than  that  of  all  other  processes  in  the  proximate  analysis. 

The  operation  recommended  for  a  mechanical  laboratory 
would  differ  principally  from  that  described,  first,  in  the  use 
of  larger  samples;  and  second,  in  the  use  of  porcelain  instead 
of  platinum  crucibles. 

In  the  determination  of  the  volatile  matter  the  conclusion 
of  the  operation  may  be  known  by  change  of  color  in  the 
flame.  During  the  operation  the  flame  would  be  yellow  or 
yellowish  so  long  as  any  volatile  matter  remained :  it  would 
then  die  down,  and  when  the  carbon  commenced  to  burn 
would  be  decidedly  blue.  The  operation  to  be  always  stopped 


4/2 


EXPERIMENTAL   ENGINEERING. 


[§  357- 


soon  after  the  blue  flame  appears.  The  crucible  recom- 
mended is  made  of  Royal  Meissen  porcelain,  and  provided 
with  cover.  It  has  a  capacity  of  half  an  ounce,  and  costs 
seventeen  cents.  During  the  operation  the  cover  is  fitted 
snugly  in  place,  and  the  gases  escape  around  the  edge,  and 
are  kept  burning. 

The  percentage  of  ash  is  determined  by  weighing  the 
residue  which  remains  after  combustion  in  the  calorimeter. 
The  burning  of  the  fixed  carbon  requires  a  long  time  when 
performed  in  the  air,  but  in  the  calorimeter  the  operation  is 
performed  very  quickly  and  very  accurately,  so  that  the  total 
time  required  to  determine  the  proximate  composition  and  also 
the  heat-values  of  a  sample  of  coal  need  not  exceed  twenty 
or  thirty  minutes,  for  a  person  familiar  with  the  operations. 

357.  Value  of  Coal  determined  by  a  Boiler-trial. — 
The  calorific  value  of  a  coal  is  sometimes  determined  by  the 
amount  of  water  evaporated  into  dry  steam  under  the  con- 
ditions of  use  in  a  steam-boiler.  This  method  is  fully  ex- 
plained in  the  latter  part  of  the  present  work  in  the  chapter 
on  the  methods  of  testing  steam-boilers.  The  calorific  values 
obtained  in  actual  boiler-trials  are  much  less  than  those  ob- 
tained in  the  calorimeters,  because  of  loss  of  heat  by  radiation 
into  the  air  and  by  discharge  of  hot  gases  into  the  chim- 
ney. The  results  obtained  by  such  a  trial  by  Prof.  W.  R. 
Johnson  at  the  Navy  Yard,  Washington,  in  1843,  with  a  small 
cylindrical  boiler,  were  as  follows : 


Coal  per  Hour. 

Water  evaporated 
per  Hour. 

Water 

evaporated 

Coal. 

from    ,- 

Sq.  Ft. 

Total. 

Per  Sq. 
Ft.  of 

Total. 

Per  Sq. 
Ft.  of 

212°  F.  per 
ib.  of  Coal. 

Grate. 

Grate. 

Anthracite  (7  samples).  .  . 

14.30 

94.94 

6.64 

12.37 

0.87 

9-63 

Bituminous     coals,      free 

burning  (IT  samples).  .  . 

14.14 

99.16 

7.01 

13-73 

0.97 

9.68 

Bituminous  coking  coals, 

Virginian  (  10  samples).. 

14.15 

105.02 

7.42 

12.  l6 

0.86 

8.48 

Average     

14.20 

99.71 

7.02 

12-75 

0.90 

9.26 

§  358.]  THE   HEATING    VALUE   OF  FUELS.  473 

358.  Object  of  Analysis  of  the  Products  of  Combustion. 

—The  products  resulting  from  the  combustion  of  ordinary  fuel 
contain  principally  a  mixture  of  air,  CO2 ,  and  some  combus- 
tible gases,  as  CO  and  H.  To  determine  whether  or  not  the 
combustion  is  perfect,  it  is  necessary  to  know  the  percentage 
that  the  combustible  gases  escaping  bear  to  the  total  products 
of  combustion.  It  is  also  important  to  know  whether  the  air 
supplied  is  sufficient  for  the  purposes  of  combustion,  and  also 
whether  it  is  in  excess  of  the  amount  actually  required.  As 
shown  in  Article  346,  page  448,  the  presence  of  an  excess  of 
air  over  that  required  has  the  effect  of  lowering  the  tempera- 
ture of  the  furnace  ;  steam  would  have  the  same  effect  even  in 
a  greater  degree,  as  can  readily  be  shown  by  calculation. 

From  a  careful  examination  of  the  products  of  combustion 
we  should  be  able  to  ascertain  its  character  and  make  the 
necessary  corrections  for  such  losses  as  may  be  due  to  imper- 
fect combustion. 

The  methods  to  be  employed  must  be  such  as  any  en- 
gineer can  fully  comprehend,  and  the  apparatus  portable 
and  convenient.  The  degree  of  accuracy  sought  need  not 
be  such  as  would  be  required  in  a  chemical  laboratory 
where  every  convenience  fpr  accurate  work  is  to  be  found. 
Indeed,  considering  the  approximations  to  be  made  in  its  ap- 
plication, it  is  very  doubtful  if  determinations  nearer  than  one 
per  cent  in  volume  are  required,  or  even  of  any  value.  Such 
determinations  are  obtained  readily  with  simple  instruments, 
and  serve  to  show  the  approximate  condition  of  the  gaseous 
products  of  combustion.  The  student  is  referred  to  "  Hand- 
book of  Technical  Gas  Analysis,"  by  Clemens  Winkler  (London, 
John  Van  Voorst),  and  to  "  Methods  of  Gas  Analysis,"  by  Dr. 
W.  Hempel,  translated  by  L.  M.  Dennis  (Macmillan  &  Co.) ; 
also  to  a  paper  on  tests  of  a  hot-blast  apparatus  by  J.  C.  Hoad- 
ley,  Vol.  VI.  Transactions  of  the  American  Society  of  Mechani- 
cal Engineers. 

In  a  thorough  examination  of  the  value  of  fuel,  the  ashes 
should  also  be  analyzed,  since  if  they  contain  any  combustible, 


474  EXPERIMENTAL   ENGINEERING.  [§  359. 

or  partly  burned  combustible,  the  heating  value  must  be  de- 
termined, and  proper  allowance  made  for  the  same. 

359.  General  Methods  of  Flue-gas  Analysis. — The 
gases  to  be  sought  for  are  CO,,  CO,  O,  and  H.  Unless  the 
temperature  is  very  high,  CO  is  found  only  in  very  small 
quantities,  and  rarely  exceeds  one  per  cent.  Prof.  L.  M. 
Dennis,  of  Cornell  University,  makes  the  statement  that  Dr. 
W.  Hempel,  of  Dresden,  whose  principal  work  has  been  the 
analysis  of  gases,  states  that  rarely  ever  is  more  than  a  trace  of 
carbonic  oxide  (CO)  to  be  found  in  the  products  resulting 
from  ordinary  combustion.  Considering  the  difficulty  of  ab- 
sorbing CO,  and  the  consequent  errors  that  are  likely  to  arise, 
it  may  be  in  general  better  to  neglect  it.  The  hydrogen,  H, 
present  is  also  a  very  small  quantity,  unless  the  temperature 
is  abnormally  low,  and  can  be  neglected  without  sensible  error. 

The  analysis  may  be  of  two  kinds,  gravimetrical  and 
volumetric.  The  former  is  seldom  used,  but  will  be  found 
described  in  an  article  by  J.  C.  Hoadley,  Transactions  of  the 
American  Society  of  Mechanical  Engineers,  Vol.  VI.,  page 
786.  In  this  case  the  various  gases  are  passed  through  solid 
absorbents,  and  the  several  constituents  successively  absorbed 
and  weighed.  The  method  of  analysis  usually  adopted  is  a 
volumetric  one,  and  consists  of  the  following  steps,  which  wiL 
be  described  in  detail  later  on. 

A.  The  sample  is  first  collected  and  then  introduced  into  a 
measuring-tube  ;    100  c.c.  of  the  gas  is  retained,  the  remainder 
wasted. 

B.  The  constituents  of  the  gas  are  then  absorbed  by  suc- 
cessive operations,  in  the  following  order  :  carbonic  acid  (CO3), 
free    oxygen    (O),   carbonic    oxide    (CO),   and    hydrogen  (H). 
The  absorption   is  accomplished   by  causing  the  gas  to  flow 
over  the  reagent  in  the  liquid  or  solid  form,  which  is  introduced 
into  the  gas   or  remains  permanently  in  a  separate  treating, 
tube.      It  is  then  made  to  flow  back  to  the  measuring-tube 

o 

and  the  loss  of  volume  measured.  The  loss  is  due  to  absorp. 
tion,  the  various  absorbents  used  being  as  follows : 


§  36°0  THE  HEATING    VALUE    OF  FUELS.  475 

For  carbonic  acid,  CO,,  either  potassium  hydroxide  (caustic 
potash  KOH),  or  barium  hydroxide. 

For  oxygen,  O,  either  (i)  a  strong  alkaline  solution  of 
pyrogallic  acid,  (2)  chromous  chloride,  (3)  phosphorus,  (4) 
metallic  copper. 

For  carbon  monoxide,  CO,  either  an  ammoniacal  or  a  hydro- 
chloric-acid solution  of  cuprous  chloride. 

For  hydrogen,  H,  an  explosion  or  rapid  combustion  in  the 
presence  of  oxygen,  or  absorption  by  metallic  potassium, 
sodium,  or  palladium.  The  reagent  usually  employed  as  an 
absorbent  is  the  one  first  mentioned  in  each  case. 

360.  Preparation  of  the  Reagents.— Absorbents  of  Oxy- 
gen.—  i.  Potassium  pyrogallate.  This  is  prepared  by  mixing 
together,  either  directly  in  the  absorption  pipette  or  in  the 
apparatus,  ,5  grams  of  pyrogallic  acid  dissolved  in  15  c.c.  of 
water,  and  120  grams  of  caustic  potash  (KOH)  dissolved  in  80 
c.c.  of  water.  Caustic  potash  purified  with  alcohol  should  not 
be  used  for  analysis.  The  absorption  of  the  gas  should  not  be 
carried  on  at  a  temperature  under  15°  C.  (55°  Fahr.)  ;  it  may 
be  completed  with  certainty  in  three  minutes  by  shaking  the 
gas  in  contact  with  the  solution. 

2.  Chromous  chloride  will  absorb  oxygen  alone  in  a  mixture 
of  oxygen  and  hydrogen  sulphide  ;  it  is  prepared  with  difficulty, 
and  not  much  used. 

3.  Phosphorus  is  one   of  the  most  convenient  absorbents: 
it  is  to  be  kept  in  the  solid  form  under  water  and  in  the  dark ; 
the  gas  is  to  be  passed  over  the  reagent,  displacing  the  water, 
and  kept  in  contact  with  it  for  about  three  minutes.     The  end 
of  the  absorption  is  shown  by  a  disappearance  of  a  light  glow, 
which  characterizes  the  process  of  absorption.     The  phosphorus 
will  remain  in  serviceable  condition  for  a  long  time. 

4.  Copper,  at  a  red  heat  or  in  the  form  of  little  rolls  of  wire- 
gauze  immersed  in  a  solution  of  ammonia  and  ammonium  car- 
bonate, is  a  very  active  absorbent  for  oxygen. 

Absorbents  of  Carbonic  Acid  (CO3). — i.  Caustic  potash. 
This  solution  may  be  used  in  varying  strengths,  depending  on 
the  method  of  gas  analysis.  With  the  Elliot  apparatus,  a  solu- 


4/6  EXPERIMENTAL   ENGINEERING.  [§  360. 

tion  of  3  to  5  per  cent  of  KOH  in  distilled  water  is  sufficiently 
strong,  the  gas  being  kept  in  contact  with  it  for  several  min- 
utes. When  a  separate  treating-tube  is  used  for  each  reagent, 
a  solution  of  one  part  of  commercial  caustic  potash  to  two 
parts  of  water  is  employed.  The  absorption  is  accomplished 
very  quickly  in  the  latter  case,  and  often  by  passing  the  gas  but 
once  through  the  treating-tube.  The  process  is  more  quickly 
and  thoroughly  performed  by  introducing  into  the  treating- 
tubes  as  many  rolls  of  fine  iron-wire  gauze  as  it  will  hold. 

2.  Barium  hydroxide  in  solution  is  the  best  absorbent  in 
case  the  quantity  of  CO2  is  very  small ;  in  this  case  titration 
with  oxalic  acid  will  be  required. 

Absorbents  of  Carbon  Monoxide  (CO). — i.  (a)  Hydrochlo- 
ric-acid solution  of  cuprous  chloride  is  prepared  by  dissolving  10.3 
grams  of  copper  oxide  in  100  to  200  c.c.  of  concentrated  hydro- 
chloric acid,  and  then  allowing  the  solution  to  stand  in  a  flask 
of. suitable  size,  filled  as  full  as  possible  with  copper  wire,  until 
the  cupric  chloride  is  reduced  to  cuprous  chloride,  and  the 
solution  is  completely  colorless. 

(b)  Winkler  directs  that  86  grams  of  copper  scale  be  mixed 
with  17  grams  of  copper  powder,  prepared  by  reducing  copper 
oxide  with  hydrogen,  and  that  this  mixture  be  brought  slowly 
and  with  shaking  into  1086  grams  of  hydrochloric  acid  of 
1.124  specific  gravity.  A  spiral  of  copper  wire  is  then  placed 
in  the  solution,  and  the  bottle  closed  with  a  soft  rubber  stopper. 
It  is  dark  at  first,  then  becomes  colorless,  but  in  contact  with 
the  air  becomes  brown.  The  absorbing  power  is  4  c.c.  of  CO. 

The  a mmoniacial  solution  is  to  be  used  in  case  hydrogen  is 
to  be  absorbed  by  palladium.  This  is  prepared  from  the 
colorless  solution  (a)  as  follows :  Pour  the  clear  hydrochloric 
acid  solution  into  a  large  beaker-glass  containing  i£  to  2  litres 
of  water,  to  precipitate  the  cuprous  chloride.  After  the  pre- 
cipitate has  settled,  pour  off  the  dilute  acid  as  completely  as 
of  possible,  then  wash  the  cuprous  chloride  with  100  to  150  c.c. 
distilled  water,  and  add  ammonia  to  the  solution  until  the  liquid 
takes  a  pale-blue  color.  The  solutions  of  cupric  chloride  de- 
compose readily,  and  in  general  should  be  used  when  fresh,  or 


$  36 


THE   HEATING    VALUE   OF  FUELS. 


477 


preserved  under  a  layer  of  petroleum.  The  treating-tube  con- 
taining the  reagent  is  frequently  supplied  with  spirals  of  small 
copper  wire  which  tend  to  preserve  and  increase  the  absorb- 
ing capacity  of  this  reagent. 

361.  Method  of  obtaining  a  Sample  of  the  Gas. — In 
order  to  take  a  sample  of  the  ga*s  for  analysis  from  any  place, 
such  as  a  furnace,  flue,  or  chimney,  an  aspirating-tube  is  intro- 
duced into  the  flue :  this  consists  of  a  tube  open  at  both  ends, 
the  outside  end  being  provided  with  a  stop-cock  and  connected 
with  the  collecting  apparatus  by  an  india-rubber  tube.  There 


FIG.  215.— HOADLEY'S  FLUE-GAS  SAMPLER. 

is  probably  a  great  diversity  in  the  composition  of  gases  from 
various  parts  of  the  flue. 

For  obtaining  an  average  sample,  J.  C.  Hoadley  employed 
a  mixing-box  Bt*  provided  with  a  large  number  of  J-inch  pipes, 
ending  in  various  parts  of  the  cross-section  of  the  flue  A.  An 
elevation  of  the  mixing-box  is  shown  at  B' .  From  the  mix- 
ing-box four  tubes  CC  lead  downward  from  various  parts  to  a 
mixing-chamber  D,  from  which  a  pipe  E  leads  to  the  collecting 
apparatus.  Two  of  these  mixing-boxes  were  used,  one  placed 
in  the  flue  a  short  distance  above  the  other,  and  an  agreement 
of  the  samples  obtained  from  each  was  regarded  as  proof  of  the 
substantial  accuracy  of  the  sample. 

*  Trans.  Am.  Soc.  M.  E.,  Vol.  VI. 


4/8  EXPERIMENTAL   ENGINEERING.  [§  361. 

It  is  hardly  probable  that  a  tube  furnished  with  various 
branches  or  a  long  slit  will  give  a  fair  sample,  since  the  velocity 
of  gases  in  the  aspirating-tube  is  such  that  most  of  the  gas 
will  be  collected  at  the  openings  nearest  the  collecting  appa- 
ratus ;  the  author  has  often  employed  a  branch-tube  with  holes 
opening  in  different  portions  of  the  chimney.  The  material 
for  the  aspirating-tube  is  preferably  porcelain  or  glass,  but 
iron  has  no  especial  absorptive  action  on  the  gases  usually  to 
be  found  in  the  flue,  and  may  be  used  with  satisfaction.  A  long 
length  of  rubber  tubing  may,  however,  sensibly  affect  the 
results. 

The  gas  should  be  collected  as  closely  as  possible  to 
the  furnace,  since  it  is  liable  to  be  diluted  to  a  considerable 
extent  by  infiltration  of  air  through  the  brick-work  beyond 
the  furnace. 

In  order  to  induce  the  gas  to  flow  outward  and  into  the 
collecting  apparatus,  pressure  in  the  collecting  vessel,  termed 
an  aspirator,  must  be  reduced  below  that  in  the  flue.  This  is 
accomplished  by  using  for  an  aspirator  two  large  bottles  con- 
nected together  by  rubber  tubing  near  the  bottom,  or  better 
still,  two  galvanized  iron  tanks,  about  6  inches  diameter  and 
2  feet  high,  connected  near  the  bottom  by  a  rubber  tube,  in 
which  is  a  stop-cock;  one  of  the  bottles  or  tanks  has  a  closed 
top  and  a  connection  for  rubber  tubing  provided  with  stop- 
cock at  the  top ;  the  other  bottle  or  tank  is  open  to  the  atmos- 
phere. To  use  the  aspirator,  the  vessel  with  the  closed  top  is 
filled  with  water  by  elevating  the  other  vessel ;  it  is  then  con- 
nected to  the  aspirating-tube,  the  open  vessel  being  held  so 
high  that  it  will  remain  nearly  empty.  After  the  connection  is 
made,  and  the  stop-cocks  opened,  the  empty  vessel  is  brought 
below  the  level  of  the  full  one,  and  the  water  passing  from 
the  one  connected  to  the  aspirating-tube  lessens  the  pres- 
sure to  such  an  extent  that  it  will  be  filled  with  gas.  This 
process  should  be  repeated  several  times  in  order  to  in- 
sure the  thorough  removal  of  all  air  from  the  aspirating- 
tubes.  The  liquid  used  for  this  purpose  is  generally  water, 
which  is  an  absorbent  to  a  considerable  extent  of  the  gases 


§  363-J  THE   HEATING    VALUE    OF  FUELS.  4/9 

contained  in  the  flues.  To  lessen  its  absorbent  power,  the 
water  used  should  be  shaken  intimately  with  the  gas  in  order 
to  saturate  it  before  the  sample  for  analysis  is  taken.  When 
mercury  is  used  as  the  liquid  this  precaution  is  not  necessary. 

A  small  instrument,  on  the  principle  of  an  injector,  in  which 
a  small  stream  of  water  or  mercury  is  constantly  delivered,  is 
an  efficient  aspirator,  and  is  extremely  convenient  for  continu- 
ous analysis. 

362.  General  Forms  of  Apparatus  employed  for  Volu- 
metric Gas  Analysis. — The  apparatus  employed  for  volumetric 
gas  analysis  consists  of  a  measuring-tube,  in  which  the  volume 
of  gas  can  be  drawn  and  accurately  measured  at  a  given  press- 
ure, and  a  treating  tube  into  which  the  gases  are  introduced 
and  then  brought  in  contact  with  the  various  reagents  already 
described.     The  apparatus  employed  may  be  divided  into  two 
classes:    (i)  those  in  which  there  is  but  one  treating-tube,  the 
different  reagents  being  successively  introduced  into  the  same 
tube ;  (2)  those  in  which  there  are  as  many  treating-tubes  as 
there  are  reagents  to  be  employed,  the  reagents  being  used  in 
a  concentrated  form,  and  the  gases  brought  into  contact  with 
the  required  reagent  by  passing  them  into  the  special  treating 
tube. 

In  either  case  the  steps  are,  as  explained  in  Article  358:  (a) 
Obtain  loo  c.c.  by  measurement;  (b)  to  absorb  the  CO2,  bring 
the  gas  in  contact  with  KOH,  and  measure  the  reduction  of 
volume  so  caused  ;  this  is  equivalent  to  the  percentage  of  CO2 ; 

(c)  bring  the  gas  in  contact  with  pyrogallic  acid  and  KOH,  and 
absorb  the  free  oxygen.     Measure  the  reduction  of  volume  so 
caused  ;  this  is  equivalent  to  the  percentage  of  free  oxygen ; 

(d)  determine  the  other  constituents  in  a  similar  manner. 

In  performing  these  various  operations  it  is  essential  that 
the  tubes  be  kept  clean  and  that  the  reagents  be  kept  entirely 
separate  from  each  other.  This  is  accomplished  by  washing  or 
causing  some  water  to  pass  up  and  down  the  tubes  or  pipettes 
several  times  after  each  operation. 

363.  Elliot's  Apparatus. — This  is  one  of  the  most  simple 
outfits  for  gas  analysis,  and  consists  of  a  treating-tube  AB  and 


480 


EXPERIMENTAL   ENGINEERING. 


[§  363. 


C'y 


FIG.  216. — ELLIOT'S 
APPARATUS. 


a  measuring-tube  A'B',  Fig.  216,  connected  by  a  capillary  tube 
at  the  top,  in  which  is  a  stop-cock,  G.  The  tubes  shown  in  Fig. 
163  are  set  in  a  frame-work  having  an  upper  and  a  lower  shelf, 
on  which  the  bottles  L  and  K  can  be  placed.  In  using  the 
apparatus,  it  is  first  washed,  which  is  done  by 
filling  the  bottles  with  water,  opening  the 
stop-cocks  F  and  G,  and  alternately  raising 
and  lowering  the  bottles  K  and  L.  The 
bottles  are  then  filleU  with  clean  distilled 
water,  raised  to  the  positions  shown,  and  the 
stop-cocks  G  and  F  closed.  The  gas  is  then 
introduced  by  connecting  the  discharge  from 
the  aspirator  to  the  stem  of  the  three-way- 
cock  F,  and  turning  it  so  that  its  hollow  stem 
is  in  connection  with  the  interior  of  the  tube 
AB ;  lowering  the  bottle  L,  the  water  will  flow  out  from  the 
tube  AB  and  the  gas  will  flow  in.  When  the  tube  AB  is  full 
of  gas  the  cock  F  is  closed,  the  aspirator  is  disconnected,  and 
the  gas  is  measured.  The  gas  must  be  measured  at  atmos- 
pheric pressure.  That  may  be  done  by  holding  the  bottle  in 
such  a  position  that  the  surface  of  the  water  in  the  bottle  shall 
be  of  the  same  height  as  that  in  the  tube,  A  distinct  meniscus 
will  be  formed  by  the  surface  of  the  water  in  the  tube  ;  the 
reading  must  in  each  case  be  made  to  the  bottom  of  the 
meniscus.  To  measure  the  gas,  which  will  be  considerably  in 
excess  of  that  needed,  the  cock  G  is  opened,  the  bottle  K  de- 
pressed, the  bottle  L  elevated  ;  the  gas  will  then  pass  over  into 
the  measuring-tube  A ' B' ;  the  bottle  K  is  then  held  so  that  the 
surface  of  the  water  shall  be  at  the  same  level  as  in  the  measuring- 
tube,  and  the  bottle  L  manipulated  until  exactly  100  c.  c.  are 
in  the  measuring-tube  ;  then  the  cock  G  is  closed,  the  cock  F 
opened,  the  bottle  L  raised,  and  the  remaining  gas  wasted, 
causing  a  little  water  to  flow  out  each  time  to  clean  the  con- 
necting tubes.  The  measuring-tube  A' B'  is  surrounded  with  a 
jacket  of  water  to  maintain  the  gas  at  the  uniform  temperature 
of  the  room.  After  measuring  the  sample  it  is  then  run  over 
into  the  treating-tube  AB,  and  the  reagent  introduced  through 


THE   HE  A  7" ING    VALUE    OF  FUELS. 


48l 


the  funnel  above  F  by  letting  it  drip  very  slowly  into  the  tube 
AB.  After  there  is  no  farther  absorption  in  the  tube  AB,  the 
cock  F  is  closed  and  the  gas  again  passed  over  to  the  measur- 
ing-tube^^, and  its  loss  of  volume  measured.  This  operation 
is  repeated  until  all  the  reagents  have  been  used  ;  in  each  case, 
when  the  gas  is  run  back  from  the  measuring-tube,  pass  over 
a  little  water  to  wash  out  the  connections  ;  exercise  great  care 
that  in  manipulating  the  cocks  K  or  G  no  gas  be  allowed  to 
escape  or  air  to  enter. 

364.  Wilson's  Apparatus.* — This  apparatus  is  illustrated 
in  Fig.  217.     It  is  used  in  essentially  the  same  manner  as  the 
Elliot  apparatus,  mercury  being  used  as  the  displacing  liquid 
in  place  of  water.     It  consists  of 

a  treating-tube  d,  a  measuring- 
tube  a,  connected  at  the  top  by  a 
capillary  tube  f.  The  measuring- 
tube  ends  in  a  vessel  filled  with 
mercury,  and  in  this  case  the  press- 
ure on  the  tubes  can  be  regulated 
by  lowering  and  raising  the  single 
bottle  filled  with  mercury,  and  the 
gas  can  be  manipulated  as  in  the 
Elliot  apparatus,  using  one  bottle 
instead  of  two.  Reagents  are  in- 
troduced into  the  funnel  e,  and 
come  in  contact  with  the  gas  in 
the  treating-tube  d. 

The  collecting-tube  used  with 
this  apparatus  is  shown  at  B,  and 
consists  of  a  vessel  filled  with  mer- 
cury. One  side  is  connected  to 
the  aspirator-tube;  some  of  the 
mercury  is  allowed  to  run  out 
through  a  cock,  and  the  space  is  filled  by  the  gas.  Sufficient 
mercury  is  retained  to  form  a  seal. 

365.  Fisher's  Modification  of  Orsat's  Apparatus. — This 

*  Thurston's  Engine  and  Boiler  Trials,  p.  107. 


FIG.  217. — APPARATUS  FOR  GAS  ANALYSIS. 


482 


EXPERIMENTAL   ENGINEERING. 


[§  365. 


apparatus,  shown  in  Fig.  218,  belongs  to  the  class  in  which 
each  reagent  is  introduced  in  a  concentrated  form  into  a  special 
treating-tube.  The  apparatus  consists  of  a  measuring-tube 
surrounded  by  a  water-jacket,  into  which  the  gas  can  be  intro- 
duced substantially  as  explained  for  the  Elliot  apparatus.  Each 


FIG.  218. — ORSAT'S  GAS-ANALYSIS  APPARATUS. 

reagent  is  introduced   in  a  concentrated  form  into  a  pair  of 
burettes  connected  at  the  bottom  by  a  U-shaped  tube. 

In  making  an  analysis  the  gas  is  first  drawn  into  the 
measuring-tube  and  100  c.c.  retained  ;  the  cock  in  the  tube 
leading  to  one  of  the  treating-tubes  is  then  opened,  the  bottle 
raised,  and  the  gas  driven  over  into  the  treating-tube.  This 


§366.]  THE  HEATING    VALUE   OF  FUELS.  483 

operation  is  facilitated  by  connecting  a  soft  rubber  bag  to 
the  opposite  side  of  the  treating-tube,  by  means  of  which 
alternate  pressure  and  suction  can  be  applied,  and  the  reagent 
protected  from  the  atmosphere.  After  the  absorption  is  com- 
plete, which  will  take  from  one  to  three  minutes  in  each  tube, 
the  gas  is  returned  to  the  measuring-tube  by  lowering  the 
bottle  and  exerting  pressure  on  the  attached  rubber  bag.  The 
rubbei  bag  is  not  shown  in  Fig.  218,  and  is  not  required,  pro- 
vided the  treating-tube  is  completely  filled  with  the  reagent 
on  the  side  toward  the  measuring-tube. 

The  treating-tubes  are  filled  in  order  from  the  measuring, 
tube  with  the  following  reagents:  (i)  with  33  per  cent  solution 
of  KOH  ;  (2)  with  a  solution  of  pyrogallic  acid  and  KOH, 
or  with  sticks  of  phosphorus  (see  Article  -^60) ;  (3)  with  a 
hydrochloric-acid  or  an  ammoniacal  solution  of  cuprous  chloride 
in  contact  with  copper  wire  (see  Article^9). 

In  the  first  treating-tube  is  absorbed  CO2,  in  the  second  O, 
ard  in  the  third  CO. 

A  modification  of  the  Orsat  apparatus  has  a  fourth  tube  in 
wnich  hydrogen  can  be  exploded  ;  the  reduction  in  volume,  due 
to  the  explosion,  gives  the  amount  of  hydrogen  present. 

An  apparatus  for  flue-gas  analysis  has  been  designed  by 
the  author  in  whjch  the  treating-tubes  are  arranged  as  in  the 
Orsat,  but  they  are  of  such  a  form  as  to  permit  the  use  of  solid 
reagents  for  absorbing  oxygen,  and  are  much  less  liable  to 
rupture.  It  is  used  exactly  as  described  for  the  Orsat,  but  is 
much  more  convenient  and  is  somewhat  more  accurate. 

366.  Hempel's  Apparatus  for  Gas  Analysis.* — This  ap- 
paratus, shown  in  Figs.  219  to  224,  is  especially  designed  for 
the  accurate  analysis  of  the  constituents  of  various  gases ;  for 
laboratory  use  it  presents  many  advantages  over  the  other 
apparatus  described.  The  apparatus  consists  of  the  following 
parts:  I.  The  measuring  burette,  shown  in  Fig.  220,  which  is 
constructed  and  used  as  follows :  It  is  furnished  with  an  iron 


*  See   Hempel's  Gas  Analysis,  by  L.   M.   Dennis.     Catalogue  of   Eimer  & 
Amend,  New  York. 


EXPERIMENTAL   ENGINEERING. 


[§  366, 


base,  which  is  connected  by  a  rubber  tube  to  an  open  tube  a 
(see  Fig.  219)  with  a  similar  base.  The  stop-cock  d  is  opened, 
the  tube  a  elevated,  and  water  or  mercury,  whichever  may  be 


FIG.  219. 


FIG. 


used,  flows  from  a  over  to  b.  Gas  is  introduced  as  follows : 
The  measuring-tube  b  is  filled  with  liquid,  the  cocks  d  and  c 
closed,  and  connection  made  at  e  to  the  vessel  containing  the 

o 

gas  to  be  measured  ;  the  cocks  d  and  c  are  then  opened,  the 


§  366.] 


THE   HEATING    VALUE   OF  FUELS. 


485 


tube  a  lowered  ;  the  liquid  will  then  flow  from  the  measuring- 
tube  b  to  a,  and  the  gas  will  fill  the  measuring-tube.  To  meas- 
ure the  volume  of  gas,  hold  the  tube  a  as  shown  in  Fig.  219,  so 
that  the  water-level  shall  be  the  same  in  both  tubes^  thus 
bringing  the  gas  under  atmospheric  pressure.  Read  the  vol- 


FlG. 


FlG.   222. 


FIGS.  223-224.— HEMPBL'S  ABSORPTION  BURETTES. 

ume  directly  by  the  graduation  corresponding  to  the  lower 
edge  of  the  meniscus. 

The  absorption-pipettes  are  different  in  form  from  those  used 
in  the  Orsat  apparatus,  and  are  connected  only  as  required  to 
the  measuring-burette,  but  are  used  in  essentially  the  same 
way.  Several  forms  of  these  are  employed  as  shown  in  Figs. 
221  to  224.  The  forms  shown  in  Fig.  222  and  Fig.  224  are 


486  EXPERIMENTAL   ENGINEERING.  [§  367 

ordinarily  used  for  reagents  in  solution.  In  such  a  case  the 
measuring-tube  is  connected  at  e,  Fig.  222,  the  reagent  occupy- 
ing the  bulbs  a  and  b.  The  top  of  the  measuring-burette 
^,  Fig.  219,  is  connected  to  the  absorption-pipette,  and  the 
gas  moved  alternately  forward  and  backward  as  required  by 
raising  or  lowering  the  tube  a.  In  case  reagents  in  the  solid 
form  are  to  be  used,  the  absorption-pipette  is  made  of  the  form 
shown  in  Fig.  223,  in  case  regents  which  decompose  very  easily 
are  used  a  pipette  of  the  form  shown  in  Fig.  221  is  employed. 
The  general  methods  employed  are  the  same  as  those  pre- 
viously described. 

367.  Deductions  and  Computations  from  Flue-gas 
Analysis.  —  The  determinations  give  the  percentage  of  volume 
of  COa  ,  O,  and  CO  existing  in  the  products  of  combustion. 
Of  these  constituents  the  carbon  is  derived  entirely  from  the 
fuel  and  the  oxygen  in  great  part  from  the  atmosphere.  Every 
part  of  oxygen  drawn  in  from  the  atmosphere  brings  with  it 
nitrogen,  which  passes  through  the  furnace  unchanged.  The 
nitrogen  is  calculated  as  follows  :  The  proportion  of  nitrogen 
to  oxygen  existing  in  the  atmosphere  is  79  to  21  by  volume; 
call  this  ratio  S\  denote  the  percentage  of  volume  of  the  gases 
existing  in  the  sample  as  follows:  CO2  by  K'>  oxygen  by  Of, 
CO  by  U'  ,  nitrogen  by  N'.  Then  we  shall  have 

jK^-\-O'  +  U'  +  N'=  100  per  cent,   .     .     .     (i) 
from  which 

N'  =  I00  _  (K'  +  0'+  U'\     ....     (2) 

If  the  oxygen  were  all  derived  from  the  atmosphere,  both 
the  amount  of  nitrogen  N'  and  of  carbonic  oxide  U'  could  be 
computed,  since  in  such  a  case  the  volume  occupied  by  the 
free  oxygen  before  combining  would  equal 


Hence  the  nitrogen 

(3) 


§367.]  THE  HEATING    VALUE  OF  FUELS.  487 

Substituting  this  latter  value  in  equation  (i), 

K'  +  (y+u'  +  s(K'  +  a  +**/')  =  ioo, 

from  which 

.    (4) 


Since  there  is  to  be  found  from  2  to  5  per  cent  of  oxygen 
in  the  fuel,  equation  (4)  will  generally  give  negative  values  for 
the  CO,  and  should  not  be  used.  - 

The  composition  of  the  flue-gases  is  an  index  of  the  com- 
pleteness of  the  combustion.  The  flue-gases  should  contain 
only  nitrogen,  oxygen,  steam,  and  carbon  dioxide,  if  the  com- 
bustion is  perfect.  Since  the  amount  of  CO  and  of  hydrogen 
compounds  are  always  small,  the  excess  of  air  can  be  com- 
puted very  nearly  from  the  amount  of  CO,.  Thus,  were  the 
products  of  combustion  free  oxygen,  nitrogen,  and  carbon 
dioxide,  only,  the  volume  of  oxygen  and  carbon  dioxide 
would  replace  that  of  oxygen  in  the  air,  or  would  equal  about 
20.  8  per  cent.  On  account  of  slight  losses,  it  is  more  nearly 
20  in  actual  cases.  The  percentage  of  excess  of  air  would 
then  be  20  less  the  per  cent  of  carbon  dioxide  divided  by  the 
percentage  of  carbon  dioxide, 

20  -  k' 

y=—e~  .......  (5) 

Siegert  gives  an  approximate  formula  for  the  percentage  of 
heat  lost, 

T  —  t 
Vl  =  0.65     rn     =  in  centigrade  units,  (6) 


in  which       T=  temperature  of  the  flue; 

/  =  temperature  of  air  entering  furnace, 
CO,  =  percentage  of  CO2. 

The  principal  object  of  the  flue-gas  analysis  may  be  con- 
sidered  as  accomplished  when  the  percentage  of  uncombined 


488  EXPERIMENTAL   ENGINEERING.  [ 

oxygen  and  of  COa  is  determined,  since  in  every  case  the 
amount  of  the  ether  gases  present  will  be  very  small.  From 
these  we  can  find  the  ratio  of  the  total  oxygen  supplied  to 
that  used.  This  ratio,  which  is  called  the  dilution  coefficient  X, 
shows  the  volume  of  air  supplied  to  that  required  to  furnish 
the  oxygen  for  the  combustion. 

It  may  be  computed  by  comparing  the  total  volume  of 
gases  with  that  required  to  unite  with  the  combined  oxygen, 
from  which 


N' 


rj — J,  nearly.       .     .     (7) 


The  analysis  and  the  computations  considered  relate  to 
volumes  of  the  various  gases.  They  may  be  reduced  to  pro- 
portional weights  by  multiplying  the  volume  of  each  gas  by  its 
molecular  weight  and  dividing  by  the  total  weights.  Knowing 
the  proportional  weights  for  each  gas  and  the  total  carbon 
consumed,  the  total  air  passing  through  the  furnace  can  be 
computed.  Thus  for  the  perfect  combustion  of  a  pound  of 
carbon  will  be  required  2.67  pounds  of  oxygen,  for  which  will 
be  required  11.7  pounds  of  air.  If  the  ratio  of  air  used  to  that 
required  be  X,  then  the  weight  of  air  per  pound  of  fuel  equal 
n. 7 X.  One  pound  of  air  at  32°  Fahr.  occupies  12.5  cubic  feet. 
Knowing  which,  the  volume  of  air  per  pound  of  coal  can  be 
computed  as  equal 

12.5  X  11.7^  —  146.2^. 

The  maximum  temperature  Tm ,  that  can  possibly  be  attained 
in  the  furnace,  is  to  be  calculated  as  in  Article  346,  page  449. 


T    _  I45QQ  

-  (3.67X0.216)  +  (8.88)(o.24)  +  (X-  i)(i2.6)(o.238) 

14500     -  5000 

=  2.91  +  2.84(Jr-  i)  =  -JT  aPPr°*"»*tely.      •     •     (8) 


§  $68.]  THE  HEATING    VALUE   OF  FUELS.  489 

Having  the  maximum  temperature  of  the  furnace  and  the 
temperature  of  the  escaping  gases,  the  efficiency,  E,  of  the 
boiler  and  grate  may  be  calculated  by  the  formula 

TJ  —  T' 
E  =  -^Y~f      , (9) 

•*  m 

in  which  Tm'  is  the  excess  of  temperature  of  the  furnace  and 
Tr  the  excess  of  temperature  of  the  escaping  gases  above  that 
of  the  entering  air.  This  hypothesis  would  be  strictly  true 
were  there  no  loss  of  heat  and  were  the  weight  of  entering  and 
discharge  gases  the  same.  The  error  in  the  calculation  is  not 
usually  a  serious  one. 

Rankine,  in  his  work  on  the  steam-engine,  pages  287  and 
288,  gives  formulae  for  computing  velocity  of  flow  in  flues, 
the  head  required  to  produce  a  given  reading  of  the  draught- 
gauge,  and  the  required  height  of  chimney. 

These  formulae  are  developed  from  the  experimental  work 
of  Pecl£t,  and  while  they  do  not  agree  well  with  modern 
practice,  still  give  interesting  results  for  comparison.  The 
practical  application  is  shown  in  the  following  example  of  an 
analysis  made  at  Cornell  University,  the  coal  burned  being  that 
obtained  after  deducting  ashes  and  clinkers. 

368.  Form  for  Data  and  Computations  in  Flue-gas 
Analysis. — Test  made  Nov.  3,  1890. 

Determinations  made  by  F.  Land,  H.  B.  Clarke,  and  O.  G.  Heilman. 
Location  of  plant,  Ithaca,  N.  Y. 
Owners,  Cornell  University. 

Area  of  grate,  sq.  ft l8l 

Area  of  chimney,  sq.  ft.  (symbol  A) » 12.5 

Height  of  chimney,  in  feet  (symbol  H'} 100 

Length  of  heated  flue  (symbol  /),  feet .  , «. , , 130 

Inside  perimeter  of  chimney,  feet . . . 14 

Niimbet  of  boilers . .  .  , 3 

Size  of  boilers  :  one  of  61  H.  P.,  two  of  250  H.  P. . 
Kind  of  boilers  :  Water-tube,  made  by  Babcock  &  Wilcox. 
Character  of  draught,  forced  by  steam-blowers. 


490 


ENGINEERING. 


[§368, 


4 

CO 

yj     O      O     CO     O      0*            J 
O     o        o        o        *^      ix    vO       O*     O      OJ             * 

O       0         d       "                        M                                 00 

M      t->.     TJ-     vn 

CO 

^            M         Tt    C 
•                •            '     fl) 
H           CO     CO    y 

N 

vO              C 

<t 

0 

eterminatic 

N 

r^ 

yj      OO        O>      M       O       Tf           O 
O     O      N     rt               MM              oo 

CO 

^                 *J 

•          •    4J 

H             O          O^   (J 

M            O. 

r^ 

04              0 

3 

0 

Q 

- 

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rf                            „;      0    in    0     O     ^         t 

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O     r>»     ^    vo 

CO 

^                   <-. 

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H             1^        O  O 

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in         o 

n 
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H 

*: 

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S       W 

CO 

0 

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t^ 

+    i 

!^       « 

-«s 
4 

L 
^ 
^ 

a. 

1 

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OO 

ci 

4           ^( 
*•           ^ 

8    ::::::::: 

I    I    Mil    i   • 

^wr^'isJj^S&^G         | 
|11    S  1   Il|l:l      1 

•§  1  1  •  1  "s  w  ;  |  1  |     £ 

Proportional  weight  
Per  cent  free  O.  by  Weight.  .  . 

Per  cent  total  O.  by  weight.  .  . 
Per  cent  total  carbon  bv  weie^h 

> 

§  368.] 


THE   HEATING    VALUE   OF  FUELS. 


491 


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CHAPTER   XV. 
METHODS   OF   TESTING   STEAM-BOILERS. 

369.  Object  of  Testing  Steam-boilers. — The  object  of 
the  test  must  be  clearly  perceived  in  the  outset ;  it  may  be  to 
determine  the  efficiency  of  a  given  boiler  under  given  condi- 
tions; the  comparative  value  of  various  fuels,  or  of  different 
boilers  working  under  the  same  conditions;  or  the  quantity  of 
coal  consumed  and  water  used  in  providing  steam  for  a  given 
engine.  The  results  of  the  test  are  usually  expressed  in  pounds 
of  v/ater  evaporated  for  one  pound  of  the  fuel  used. 

The  conditions  of  temperature  and  pressure  between  which 
boilers  work  vary  within  wide  limits,  the  amount  of  heat  ab- 
sorbed per  pound  of  steam  produced  is  not  constant,  and  a 
standard  of  reference  is  necessary.  Thus  to  convert  a  pound 
of  steam  from  feed-water  at  a  temperature  of  70  degrees  Fahr. 
into  steam  at  70  pounds  absolute  pressure  per  square  inch  will 
require,  per  pound  of  steam,  (1174.3  —  70  +  32)  =  1 136.3 
B.  T.  U. ;  but  to  convert  a  pound  of  water  at  a  temperature  of 
212°  into  steam  at  atmospheric  pressure  will  require  only  967 
B.  T.  U.  To  compare  the  work  done  with  a  standard  con- 
dition it  is  customary  to  express  the  results  of  the  test  as 
equivalent  to  the  evaporation  per  pound  of  fuel  from  water 
at  212°  Fahr.  to  steam  at  atmospheric  pressure,  or,  in  other 
words,  "  from  and  at  212°." 

The  fuel  also  varies  greatly  in  its  evaporative  power,  as 
shown  in  the  preceding  chapter,  and,  moreover,  a  certain  proper- 
tion  is  likely  to  drop  through  the  grates  unconsumed,  so  that 

;       '    .   :  492 


§  371-]         METHODS   OF    TESTING   STEAM-BOILERS.  493 

it  is  customary  to  reduce  the  results  still  further,  and  to  find 
the  evaporation  per  pound  of  the  combustible  part. 

370.  Definitions.  —  The  following  terms  are  frequently 
used  : 

Actual  evaporation.  This  is  the  evaporation  per'  pound  of 
fuel  or  of  combustible  under  the  actual  conditions  of  the  test, 
uncorrected  for  temperature  of  feed-water  and  for  moisture. 

Equivalent  evaporation  from  and  at  212°  is  the  amount  of 
water  that  would  have  been  evaporated  had  the  temperature 
of  feed-water  been  212°,  the  steam  dry  and  at  atmospheric 
pressure.  If  x  represent  the  quality  of  steam,  e  the  factor  of 
evaporation,  the  equivalent  evaporation  is  equal  to  the  actual 
multiplied  by  xe. 

Factor  of  evaporation  is  the  ratio  that  the  total  heat,  \,  in 
one  pound  of  steam  at  the  given  pressure  and  reckoned  from 
the  temperature,  •  /,  of  feed-water,  bears  to  the  latent  heat 
of  evaporation  at  212°,  r.  That  is, 


-  = 


A  table  of  the  factors  of  evaporation  is  given  in  the  Appendix. 

The  ash  is  the  actual  incombustible  part  of  the  coal ;  it  is 
the  residue  which  falls  through  the  grates,  less  any  combustible 
particles. 

The  combustible  is  the  fuel  less  the  residue  which  falls 
through  the  grates ;  it  is  the  weight  of  that  portion  actually 
burned.  In  the  absence  of  any  determinations  whatever,  the 
combustible  is  frequently  assumed  as  ^  of  that  of  the  coal. 

The  quality  of  the  steam  is  the  percentage  by  weight  of 
dry  saturated  steam  in  a  mixture  of  steam  and  water.  It  is  to 
be  found  by  a  throttling  or  separating  calorimeter  attached 
very  near  the  boiler  (see  Articles  334  to  338). 

371.  The  Efficiency  of  a  Boiler.— The  efficiency  is  the 
ratio  of  the  heat  utilized  to  that  supplied.  The  heat  supplied 
is  measured  by  the  coal  consumed,  multiplied  by  the  heat 
value  per  pound. 

OF  THE 

UNIVERSITY 

Of 


494  EXPERIMENTAL   ENGINEERING.  [§  372 

There  are  in  use  two  methods  of  defining  and  calculating 
the  efficiency  of  a  boiler.  They  are: 

rrr  .  f   .     ,     .,          Heat  absorbed  per  Ib.  combustible 

1.  Efficiency  of  the  boiler  =  -—  — -f — — -  — • 

Heating  value  of  I  Ib.  combustible 

2.  Efficiency  of  the  boiler  and  grate 

_  Heat  absorbed  per  Ib.  coal 
Heating  value  of  i  Ib.  coal 

The  first  of  these  is  sometimes  called  the  efficiency  based 
on  combustible,  and  the  second  the  efficiency  based  on  coal. 
The  first  is  recommended  as  a  standard  of  comparison  for  all 
tests,  and  this  is  the  one  which  is  understood  to  be  referred 
to  when  the  word  "  efficiency  "  alone  is 'used  without  qualifica- 
tion. The  second,  however,  should  be  included  in  a  report 
of  a  test,  together  with  the  first,  whenever  the  object  of  the 
test  is  to  determine  the  efficiency  of  the  boiler  and  furnace 
together  with  the  grate  (or  mechanical  stoker),  or  to  com- 
pare different  furnaces,  grates,  fuels,  or  methods  of  firing. 

In  calculating  the  efficiency  where  the  coal  contains  an  ap- 
preciable amount  of  surface  moisture,  allowance  is  to  be  made 
for  the  heat  lost  in  evaporating  this  moisture  by  adding  to  the 
heat  absorbed  by  the  boiler  the  heat  of  evaporation  thus  lost. 

372.  The    Heat-balance. — An    approximate    "  heat-bal- 
ance, or  statement  of  the  distribution  of  the  heating  value  of 
the   coal   among  the  several  items  of  heat  utilized  and  heat 
lost  should  be  included  in  the  report  of  a  test  when  analyses 
of  the  fuel  and  of  the  chimney-gases  have  been  made.      This 
should  show  both  in  B.T.U.  and  in  per-cent  the  total  heat 
received,  that  absorbed  by  the  boiler,  discharged  in  the  flue 
with   the   products   of   combustion,   that   lost   in  evaporating 
moisture  in  the  combustible,  that  due  to  incomplete  combus- 
tion of  carbon  or  hydrogen,  and  that  not  accounted  for. 

373.  Horse-power  of  a  Boiler. — The  horse-power  of   a 
boiler  is  a  conventional  definition  of  capacity,  since  the  boiler 
of  itself  does  no  work.      As  the  weight  of  steam  required  for 
different  engines  varies  within  wide  limits,  an  arbitrary  rating 
was  adopted  by  the  judges  of  the  Centennial  Exhibition  in 


375-] 


METHODS  OF   TESTING   STEAM-BOILERS. 


495 


1876  as  a  standard  nominal  horse-power  for  boilers.  This 
standard,  which  is  now  generally  used,  fixed  one  horse-power 
as  equivalent  to  30  pounds  of  water  evaporated  into  dry  steam 
per  hour  from  feed-water  at  100°  Fahr.,  and  under  a  pressure  of 
seventy  pounds  per  square  inch  above  the  atmosphere.  This  is 
equal  to  an  evaporation  of  34.488  pounds  from  and  at  212°  F. 
The  "  unit  of  evaporation  "  being  966.7  B.  T.  U.,  the  commer- 
cial horse-power  is  34.488  X  966.7  =  33,391  B.  T.  U. 

374.  Graphical  Log. — The  results  of  a  boiler-test  can  be 
represented  graphically  by  considering  intervals  of  time  as 
proportional  to  the  abscissae,  and  ordinates  as  proportional  to 
the  various  pressures  and  temperatures  measured,  as  shown  in 
Fig.  225,  from  Thurston's  Engine  and  Boiler  Trials. 


9216.1) 


10.30 10.60  11.10  11.30  11.00   12.10  12.30    12.50    1.10     1.30     1.50     2.10     2.30     2.00     3.10     3^0     3.50    4.10     4.30    4.50 

FIG.  223. 


375.  Method  of  Making  a  Boiler-test— A  standard 
method  of  making  a  boiler-test  was  adopted  by  the  American 
Society  of  Mechanical  Engineers  in  1884;  this  was  revised  in 
1899.  The  first  report  is  published  in  the  Transactions,  Vol. 
VI,  the  latter  in  Vol.  XXI,  with  discussion  on  the  same  as 
appendices. 


496  EXPERIMENTAL   ENGINEERING.  [§  375 

EULES  FOE  CONDUCTING  BOILEE  TEIALS. 

CODE  OF  1899. 

I.  Determine  at  the,  outset  the  specific  object  of  the  proposed 
trial,  whether  it  be  to  ascertain  the  capacity  of  the  boiler,  its 
efficiency  as  a  steam  generator,  its  efficiency  and  its  defects  under 
usual  working  conditions,  the  economy  of  some  particular  kind 
of  fuel,  or  the  effect  of  changes  of  design,  proportion,  or  opera- 
tion ;  and  prepare  for  the  trial  accordingly.     (Appendix  II.) 

II.  Examine  the  boiler,  both  outside  and  inside ;  ascertain  the 
dimensions  of  grates,  heating  surfaces,  and  all  important  parts ; 
and  make  a  full  record,  describing  the  same,  and  illustrating 
special  features  by  sketches.     The  area  of  heating  surface  is  to 
be  computed  from  the  surfaces  of  shells,  tubes,  furnaces,  and  fire- 
boxes in  contact  with  the  fire  or  hot  gases.     The  outside  diam- 
eter of  water-tubes  and  the  inside  diameter  of  fire-tubes   are 
to  be  used  in  the  computation.     All  surfaces  below  the  mean 
water  level  which  have  water  on  one  side  and  products  of  com- 
bustion  on  the   other  are  to  be  considered  as  water-heating 
surface,  and  all  surfaces   above  the   mean  water  level   which 
have  steam  on  one  side  and  products  of  combustion  on  the 
other  are  to  be  considered  as  superheating  surface. 

III.  Notice  the  general  condition  of  the  boiler  and  its  equipment, 
and  record  such  facts  in  relation  thereto  as  bear  upon  the  objects 
in  view. 

If  the  object  of  the  trial  is  to  ascertain  the  maximum  economy 
or  capacity  of  the  boiler  as  a  steam  generator,  the  boiler  and  all 
its  appurtenances  should  be  put  in  first-class  condition.  Clean 
the  heating  surface  inside  and  outside,  remove  clinkers  from 
the  grates  and  from  the  sides  of  the  furnace.  Eemove  all  dust, 
soot,  and  ashes  from  the  chambers,  smoke  connections,  and 
flues.  Close  air  leaks  in  the  masonry  and  poorly  fitted  clean- 
ing doors.  See  that  the  damper  will  open  wide  and  close  tight. 
Test  for  air  leaks  by  firing  a  few  shovels  of  smoky  fuel  and  im- 
mediately closing  the  damper,  observing  the  escape  of  smoke 
through  the  crevices,  or  by  passing  the  flame  of  a  candle  over 
cracks  in  the  brickwork. 

IV.  Determine  the  character  of  the  coal  to  be  used.     For  tests 
of  the  efficiency  or  capacity  of  the  boiler  for  comparison  with 
other  boilers  the  coal  should,  if  possible,  be  of  some  kind  which 
is  commercially  regarded   as   a   standard      For  Ne\y  England 


§  375-]  TESTING   STEAM-BOILERS.  497 

and  that  portion  of  the  country  east  of  the  Allegheny  Moun- 
tains, good  anthracite  egg  coal,  containing  not  over  10  per  cent, 
of  ash,  and  semi-bituminous  Clearfield  (Pa.),  Cumberland  (Md.), 
and  Pocahontas  (Va.)  coals  are  thus  regarded.  West  of  the 
Allegheny  Mountains,  Pocahontas  (Va.)  and  New  River  (W.  Va.) 
semi-bituminous,  and  Toughiogheny  or  Pittsburg  bituminous 
coals  are  recognized  as  standards.*  There  is  no  special  grade 
of  coal  mined  in  the  Western  States  which  is  widely  recognized 
as  of  superior  quality  or  considered  as  a  standard  coal  for 
boiler  testing.  Big  Muddy  lump,  an  Illinois  coal  mined  in 
Jackson  County,  111.,  is  suggested  as  being  of  sufficiently  high 
grade  to  answer  these  requirements  in  districts  where  it  is  more 
conveniently  obtainable  than  the  other  coals  mentioned  above. 

For  tests  made  to  determine  the  performance  of  a  boiler  with 
a  particular  kind  of  coal,  such  as  may  be  specified  in  a  contract 
for  the  sale  of  a  boiler,  the  coal  used  should  not  be  higher  in 
ash  and  in  moisture  than  that  specified,  since  increase  in  ash 
and  moisture  above  a  stated  amount  is  apt  to  cause  a  falling  off 
of  both  capacity  and  economy  in  greater  proportion  than  the 
proportion  of  such  increase. 

V.  Establish  the  correctness  of  all  apparatus  used  in  the  test  for 
weighing  and  measuring.     These  are  : 

1.  Scales  for  weighing  coal,  ashes,  and  water. 

2.  Tanks,  or  water  meters  for  measuring  water.     Water  me- 
ters, as  a  rule,  should  only  be  used  as  a  check  on  other  measure- 
ments.    For  accurate  work,  the  water  should  be  weighed  or 
measured  in  a  tank.     (See  Chapter  VII.) 

'3.  Thermometers  and  pyrometers  for  taking  temperatures  of 
air,  steam,  feed-water,  waste  gases,  etc.  (Chapter  XII.) 

4.  Pressure-gauges,  draught-gauges,  etc.  (Chapter  XI,  pages 
345  to  369.) 

The  kind  and  location  of  the  various  pieces  of  testing  appara- 
tus must  be  left  to  the  judgment  of  the  person  conducting  the 
test ;  always  keeping  in  mind  the  main  object,  i.e.,  to  obtain 
authentic  data. 

VI.  See  that  the  boiler  is  thoroughly  heated  before  the  trial  to 
its  usual  working  temperature.     If  the  boiler  is  new  and  of  a 

*  These  coals  are  selected  because  they  are  about  the  only  coals  which  possess 
the  essentials  of  excellence  of  quality,  adaptability  to  various  kinds  of  furnaces, 
grates,  boilers,  and  methods  of  firing,  and  wide  distribution  and  general  accessi- 
bility in  the  markets.  See  various  appendices  in  Vol.  XXI,  Transactions 
A.  S.  M.  E. 


498  EXPERIMENTAL  ENGINEERING.  [§  3/5- 

form  provided  with  a  brick  setting,  it  should  be  in  regular  use 
at  least  a  week  before  the  trial,  so  as  to  dry  and  heat  the  walls. 
If  it  has  been  laid  off  and  become  cold,  it  should  be  worked 
before  the  trial  until  the  walls  are  well  heated. 

VII.  The  boiler  and  connections  should  be  proved  to  be  free  from 
leaks  before  beginning  a  test,  and  all  water  connections,  includ- 
ing blow  and  extra  feed  pipes,  should  be  disconnected,  stopped 
with  blank  flanges,  or  bled  through  special  openings  beyond  the 
valves,  except  the  particular  pipe  through  which  water  is  to  be 
fed  to  the  boiler  during  the  trial.  During  the  test  the  blow-oflf 
and  feed  pipes  should  remain  exposed  to  view. 

If  an  injector  is  used,  it  should  receive  steam  directly  through 
a  felted  pipe  from  the  boiler  being  tested.* 

If  the  water  is  inetered  after  it  passes  the  injector,  its  tem- 
perature should  be  taken  at  the  point  where  it  leaves  the  injector. 
If  the  quantity  is  determined  before  it  goes  to  the  injector  the 
temperature  should  be  determined  on  the  suction  side  of  the 
injector,  and  if  no  change  of  temperature  occurs  other  than  that 
due  to  the  injector,  the  temperature  thus  determined  is  properly 
that  of  the  feed- water.  When  the  temperature  changes  between 
the  injector  and  the  boiler,  as  by  the  use  of  a  heater  or  by  radi- 
ation, the  temperature  at  which  the  water  enters  and  leaves  the 
injector  and  that  at  which  it  enters  the  boiler  should  all  be 
taken.  In  that  case  the  weight  to  be  used  is  that  of  the  water 
leaving  the  injector,  computed  from  the  heat  units  if  not 
directly  measured,  and  the  temperature,  that  of  the  water 
entering  the  boiler. 

Let  w  —  weight  of  water  entering  the  injector. 

x  =      "         "  steam      " 

A,  =  heat  units  per  pound  of  water  entering  injector. 

A2  =     "        "       "        "        "  steam       "  " 

A3  =     "        "       <l         "        "  water  leaving         « 
Then,  w  +  x  =  weight  of  water  leaving  injector. 

A.  —  A. 
x  =  w  z-5 ^- 


*  In  feeding  a  boiler  undergoing  test  with  an  injector  taking  steam  from  another 
hoiler,  or  from  the  main  steam  pipe  from  several  boilers,  the  evaporative  results 
may  be  modified  by  a  difference  in  the  quality  of  the  steam  from  such  source 
compared  with  that  supplied  by  the  boiler  being  tested,  and  in  some  cases  the 
connection  to  the  injector  may  act  as  a  drip  for  the  main  steam  pipe.  If  it  is 
known  that  the  steam  from  the  main  pipe  is  of  the  same  pressure  and  quality  as 
that  furnished  by  the  boiler  undergoing  the  test,  the  steam  may  be  taken  from 
such  main  pipe. 


§  375-]  TESTING   STEAM-BOILERS.  499 

See  that  the  steam  main  is  so  arranged  that  water  of  con- 
densation cannot  run  back  into  the  boiler. 

VIII.  Duration  of  tlie  Test. — For  tests  made  to  ascertain  either 
the  maximum  economy  or  the  maximum  capacity  of  a  boiler,  irre- 
spective of  the  particular  class  of  service  for  which  it  is  regularly 
used,  the  duration  should  be  at -least  10  hours  of  continuous  run- 
ning.    If  the  rate  of  combustion  exceeds  25  pounds  of  coal  per 
square  foot  of  grate  surface  per  hour,  it  may  be  stopped  when  a  to- 
tal of  250  pounds  of  coal  has  been  burned  per  square  foot  of  grate. 

In  cases  where  the  service  requires  continuous  running  for 
the  whole  24  hours  of  the  day,  with  shifts  of  firemen  a  number 
of  times  during  that  period,  it  is  well  to  continue  the  test  for  at 
least  24  hours. 

When  it  is  desired  to  ascertain  the  performance  under  the 
working  conditions  of  practical  running,  whether  the  boiler  be 
regularly  in  use  24  hours  a  day  or  only  a  certain  number  of 
hours  out  of  each  24,  the  fires  being  banked  the  balance  of  the 
time,  the  duration  should  not  be  less  than  24  hours. 

IX.  Starting  and  Stopping  a  Test. — The  conditions  of  the  boiler 
and  furnace  in  all  respects  should  be,  as  nearly  as  possible,  the 
same  at  the  end  as  at  the  beginning  of  the  test.     The  steam 
pressure  should  be  the  same  ;  the  water  level  the  same  ;  the  fire 
upon  the  grates  should  be  the  same  in  quantity  and  condition ; 
and  the  walls,  flues,  etc.,  should  be  of  the  same  temperature. 
Two  methods  of  obtaining  the  desired  equality  of  conditions  of 
the  fire  may  be  used,  viz.  :  those  which  were  called  in  the  Code 
of  1885  "  the  standard  method  "  and  "the  alternate  method," 
the   latter  being  employed  where  it  is  inconvenient  to  make 
ruse  of  the  standard  method.* 

X.  Standard  Method  of  Starting  and  Stopping  a  Test. — Steam 
being  raised    to    the   working    pressure,   remove    rapidly   all 
the  fire  from  the  grate,  close  the  damper,  clean  the  ash   pit, 
:and   as   quickly   as   possible    start   a    new  fire    with    weighed 
wood   and   coal,  noting  the  time  and  the  water  level  f   while 

*  The  Committee  concludes  that  it  is  best  to  retain  the  designations  "stand- 
ard" and  "  alternate,"  since  they  have  become  widely  known  and  established  in 
the  minds  of  engineers  and  in  the  reprints  of  the  Code  of  1885.  Many  engineers 
prefer  the  ' '  alternate  "  to  the  "  standard  "  method  on  account  of  its  being  less 
liable  to  error  due  to  cooling  of  the  boiler  at  the  beginning  and  end  of  a  test. 

f  The  gauge-glass  should  not  be  blown  out  within  an  hour  before  the  water 
level  is  taken  at  the  beginning  and  end  of  a  test,  otherwise  an  error  in  the  read- 
ing of  the  water  level  may  be  caused  by  a  change  in  the  temperature  and  density 
•of  the  water  in  the  pipe  leading  from  the  bottom  of  the  glass  into  the  boiler. 


500  EXPERIMENTAL   ENGINEERING.  [§  375 

the   water  is  in   a  quiescent    state,  just  before   lighting    th( 
fire. 

At  the  end  of  the  test  remove  the  whole  fire,  which  has 
been  burned  low,  clean  the  grates  and  ash  pit,  and  note  the 
water  level  when  the  water  is  in  a  quiescent  state,  and 
record  the  time  of  hauling  the  fire.  The  water  level  should 
be  as  nearly  as  possible  the  same  as  at  the  beginning  of  .the 
test.  If  it  is  not  the  same,  a  correction  should  be  made  bj 
computation,  and  not  "by  operating  the  puikp  after  the  test  is 
completed. 

XI.  Alternate  Method  of  Starting  and   Slipping  a   Test. — The 
boiler  being  thoroughly  heated  by  a  preliminary  run,  the  fires 
are  to  be  burned  low  and  well  cleaned.     Note  the  amount  oi 
coal  left  on  the  grate  as  nearly  as  it  can  be  estimated  ;  note  the 
pressure  of  steam  and  the  water  level.     Note    the   time,  and 
record  it  as  the  starting  time.      Fresh    coal  which    has  beer 
weighed  should  now  be  fired.     The  ash  pits  should  be  thor- 
oughly cleaned  at  once  after  starting.     Before  the  end  of  the 
test  the  fires  should  be  burned  low,  just  as  before  the  start,  and 
the  fires  cleaned  in  such  a  manner  as  to  leave  a  bed  of  coal  OB 
the  grates  of  the  same  depth,  and  in  the  same  condition,  as  at 
the  start.     When  this  stage  is  reached,  note  the  time  and  record 
it  as  the  stopping  time.     The  water  level  and  steam  pressures 
should  previously  be  brought  as  nearly  as  possible  to  the  same 
point  as  at  the  start.     If  the  water  level  is  not  the  same  as  at 
the  start,  a  correction  should  be  made  by  computation,  and  not 
by  operating  the  pump  after  the  test  is  completed. 

XII.  Uniformity  of  Conditions. — In  all  trials  made  to  ascertain 
maximum  economy  or  capacity,  the  conditions  should  be  main- 
tained uniformly  constant.     Arrangements  should  be  made  to 
dispose  of  the  steam  so  that  the  rate  of  evaporation  may  be 
kept  the  same  from  beginning   to  end.      This  may  be  accom- 
plished in  a  single   boiler  by  carrying  the  steam  through    a 
waste  steam  pipe,  the  discharge  from  which  can  be  regulated  as 
desired.     In  a  battery  of  boilers,  in  which  only  one  is  tested, 
the  draft  may  be  regulated  on  the  remaining  boilers,  leaving  the 
test  boiler  to  work  under  a  constant  rate  of  production. 

Uniformity  of  conditions  should  prevail  as  to  the  pressure  of 
steam,  the  height  of  water,  the  rate  of  evaporation,  the  thickness 
of  fire,  the  times  of  firing  and  quantity  of  coal  fired  at  one  time, 
and  as  to  the  intervals  between  the  times  of  cleaning  the  fires. 


§  375-]  TESTING   STEAM-BOILERS.  SO  I 

The  method  of  firing  to  be  carried  on  in  such  tests  should  be 
dictated  by  the  expert  or  person  in  responsible  charge  of  the 
test,  and  the  method  adopted  should  be  adhered  to  by  the  fire- 
man throughout  the  test. 

XIII.  Keeping  the  Records. — Take  note  of   every  event  con* 
n3cted  with  the  progress  of  the  trial,  however  unimportant  it 
may  appear.      Record  the  time  of  every  occurrence  and  the 
time  of  taking  every  weight  and  every  observation. 

The  coal  should  be  weighed  and  delivered  to  the  fireman  in 
equal  proportions,  each  sufficient  for  not  more  than  one  hour's 
run,  and  a  fresh  portion  should  not  be  delivered  until  the  pre- 
vious one  has  all  been  fired.  The  time  required  to  consume 
each  portion  should  be  noted,  the  time  being  recorded  at  the 
instant  of  firing  the  last  of  each  portion.  It  is  desirable  that  at 
the  same  time  the  amount  of  water  fed  into  the  boiler  should  be 
accurately  noted  and  recorded,  including  the  height  of  the 
water  in  the  boiler,  and  the  average  pressure  of  steam  and  tem- 
perature of  feed  during  the  time.  By  thus  recording  the 
amount  of  water  evaporated  by  successive  portions  of  coal,  the 
test  may  be  divided  into  several  periods  if  desired,  and  the  de- 
gree of  uniformity  of  combustion,  evaporation,  and  economy 
analyzed  for  each  period.  In  addition  to  these  records  of  the 
coal  and  the  feed  water,  half  hourly  observations  should  be  made 
of  the  temperature  of  the  feed  water,  of  the  flue  gases,  of  the 
external  air  in  the  boiler-room,  of  the  temperature  of  the  fur- 
nace when  a  furnace  pyrometer  is  used,  also  of  the  pressure  of 
steam,  and  of  the  readings  of  the  instruments  for  determining 
the  moisture  in  the  steam.  A  log  should  be  kept  on  properly 
prepared  blanks  containing  columns  for  record  of  the  various 
observations. 

When  the  "  standard  method "  of  starting  and  stopping  the 
test  is  used,  the  hourly  rate  of  combustion  and  of  evaporation 
and  the  horse-power  should  be  computed  from  the  records  taken 
during  the  time  when  the  fires  are  in  active  condition.  This 
time  is  somewhat  less  than  the  actual  time  which  elapses  be- 
tween the  beginning  and  end  of  the  run.  The  loss  of  time  due 
to  kindling  the  fire  at  the  beginning  and  burning  it  out  at  the 
«nd  makes  this  course  necessary. 

XIV.  Quality  of  Steam. — The  percentage  of  moisture  in  the 
steam  should  be  determined  by  the  use  of  either  a  throttling  or 


502  EXPERIMENTAL    ENGINEERING,  \\  3 7$, 

a  separating  steam  calorimeter.  The  sampling  nozzle  should 
be  placed  in  the  vertical  steam  pipe  rising  from  the  boiler.  It 
should  be  made  of  J-inch  pipe,  and  should  extend  across  the 
diameter  of  the  steam  pipe  to  within  half  an  inch  of  the  oppo- 
site side,  being  closed  at  the  end  and  perforated  with  not  less 
than  twenty  J-inch  holes  equally  distributed  along  and  around 
its  cylindrical  surface,  but  none  of  these  holes  should  be  nearer 
than  J  inch  to  the  inner  side  of  the  steam  pipe.  The  calorim 
eter  and  the  pipe  leading  to  it  should  be  well  covered  with 
felting.  Whenever  the  indications  of  the  throttling  or  separat- 
ing calorimeter  show  that  the  percentage  of  moisture  is  irregu- 
lar, or  occasionally  in  excess  of  three  per  cent.,  the  results  should 
be  checked  by  a  steam  separator  placed  in  the  steam  pipe  as 
close  to  the  boiler  as  convenient,  with  a  calorimeter  in  the  steam 
pipe  just  beyond  the  outlet  from  the  separator.  The  drip  from 
the  separator  should  be  caught  and  weighed,  and  the  percent- 
age of  moisture  computed  therefrom  added  to  that  shown  by 
the  calorimeter.  (See  Chapter  XIII,  page  438.)  ) 

Superheating  should  be  determined  by  means  of  a  thermome- 
ter placed  in  a  mercury  well  inserted  in  the  steam  pipe.  The 
degree  of  superheating  should  be  taken  as  the  difference  be- 
tween the  reading  of  the  thermometer  for  superheated  steam 
and  the  readings  of  the  same  thermometer  for  saturated  steam 
at  the  same  pressure  as  determined  by  a  special  experiment, 
and  not  by  reference  to  steam  tables. 

For  calculations  relating  to  quality  of  steam  and  corrections 
for  quality  of  steam,  see  Chapter  XIII,  pages  393  and  435. 

XV.  Sampling  the  Coal  and  Determining  its  Moisture. — As 
each  barrow  load  or  fresh  portion  of  coal  is  taken  from  the  coal 
pile,  a  representative  shovelful  is  selected  from  it  and  placed  in 
a  barrel  or  box  in  a  cool  place  and  kept  until  the  end  of  the 
trial.  The  samples  are  then  mixed  and  broken  into  pieces  not 
exceeding  one  inch  in  diameter,  and  reduced  by  the  process  of 
repeated  quartering  and  crushing  until  a  final  sample  weighing 
about  five  pounds  is  obtained,  and  the  size  of  the  larger  pieces 
is  such  that  they  will  pass  through  a  sieve  with  J-inch  meshes. 
From  this  sample  two  one-quart,  air-tight  glass  preserving  jars, 
or  other  air-tight  vessels  which  will  prevent  the  escape  of  moist- 
ure from  the  sample,  are  to  be  promptly  filled,  and  these  sam- 
ples are  to  be  kept  for  subsequent  determinations  of  moisture 
and  of  heating  value  and  for  chemical  analyses.  During  the 


§  375-]  TESTING   STEAM-BOILERS.  503 

process  of  quartering,  when  the  sample  has  been  reduced  to 
about  100  pounds,  a  quarter  to  a  half  of  it  may  be  taken  for  an 
approximate  determination  of  moisture.  This  may  be  made  by 
placing  it  in  a  shallow  iron  pan,  not  over  three  inches  deep, 
carefully  weighing  it,  and  setting  the  pan  in  the  hottest  place 
that  can  be  found  on  the  brickwork  of  the  boiler  setting  or  flues, 
keeping  it  there  for  at  least  12  hours,  and  then  weighing  it. 
The  determination  of  moisture  thus  made  is  believed  to  be  ap- 
proximately accurate  for  anthracite  and  semi-bituminous  coals, 
and  also  for  Pittsburg  or  Youghiogheny  coal ;  but  it  cannot  be 
relied  upon  for  coals  mined  west  of  Pittsburg,  or  for  other  coals 
containing  inherent  moisture.  For  these  latter  coals  it  is  impor- 
tant that  a  more  accurate  method  be  adopted.  The  method 
recommended  by  the  Committee  for  all  accurate  tests,  whatever 
the  character  of  the  coal,  is  described  as  follows  : 

Take  one  of  the  samples  contained  in  the  glass  jars,  and 
subject  it  to  a  thorough  air-drying,  by  spreading  it  in  a  thin  layer 
and  exposing  it  for  several  hours  to  the  atmosphere  of  a  warm 
room,  weighing  it  before  and  after,  thereby  determining  the  quan- 
tity of  surface  moisture  it  contains.  Then  crush  the  whole  of  it  by 
running  it  through  an  ordinary  coffee  mill  adjusted  so  as  to  pro- 
duce somewhat  coarse  grains  (less  than  TVinch),  thoroughly  mix 
the  crushed  sample,  select  from  it  a  portion  of  from  10  to  50 
grams,  weigh  it  in  a  balance  which  will  easily  show  a  variation 
as  small  as  1  part  in  1,000,  and  dry  it  in  an  air  or  sand  bath  at 
a  temperature  between  240  and  280  degrees  Fahr.  for  one  hour. 
Weigh  it  and  record  the  loss,  then  heat  and  weigh  it  again 
repeatedly,  at  intervals  of  an  hour  or  less,  until  the  minimum 
weight  has  been  reached  and  the  weight  begins  to  increase  by 
oxidation  of  a  portion  of  the  coal.  The  difference  between  the 
original  and  the  minimum  weight  is  taken  as  the  moisture  in  the 
air-dried  coal.  This  moisture  test  should  preferably  be  made 
on  duplicate  samples,  and  the  results  should  agree  within  0.3 
to  0.4  of  one  per  cent.,  the  mean  of  the  two  determinations  being 
taken  as  the  correct  result.  The  sum  of  the  percentage  of 
moisture  thus  found  and  the  percentage  of  surface  moisture 
previously  determined  is  the  total  moisture. 

XYI.  Treatment  of  Ashes  and  Refuse. — The  ashes  and  refuse 
are  to  be  weighed  in  a  dry  state.  If  it  is  found  desirable  to 
show  the  principal  characteristics  of  the  ash,  a  sample  should 
be  subjected  to  a  proximate  analysis  and  the  actual  amount 


504  EXPERIMENTAL   ENGINEERING  [§  3/5. 

of  incombustible  material  determined.  For  elaborate  trials  a 
complete  analysis  of  the  ash  and  refuse  should  be  made. 

XVII.  Calorific  Tests  and  Analysis  of  Coal. — The  quality  of  the 
fuel  should  be  determined  either  by  heat  test  or  by  analysis,  or 
by  both. 

The  rational  method  of  determining  the  total  heat  of  combus- 
tion is  to  burn  the  sample  of  coal  in  an  atmosphere  of  oxygen 
gas,  the  coal  to  be  sampled  as  directed  in  Article  XY.  of  this 
code.  (See  Chapter  XIV.) 

The  chemical  analysis  of  the  coal  should  be  made  only  by  an 
expert  chemist.  The  total  heat  of  combustion  computed  from 
the  results  of  the  ultimate  analysis  may  be  obtained  by  the 
use  of  Dulong's  formula  (with  constants  modified  by  recent 

determinations),  viz.:  14,600  G  +  62,000  (#— g)    +  4000  8, 

in  which  Ct  H,  0,  and  S  refer  to  the  proportions  of  carbon,  hy- 
drogen, oxygen,  and  sulphur  respectively,  as  determined  by  the 
ultimate  analysis.* 

It  is  desirable  that  a  proximate  analysis  should  be  made, 
thereby  determining  the  relative  proportions  of  volatile  matter 
and  fixed  carbon.  These  proportions  furnish  an  indication  of 
the  leading  characteristics  of  the  fuel,  and  serve  to  fix  the 
class  to  which  it  belongs.  (Page  470.)  As  an  additional 
indication  of  the  characteristics  of  the  fuel,  the  specific  gravity 
should  be  determined. 

XVIII.  Analysis  of  Flue  Gases. — The  analysis  of  the  flue  gases 
is  an  especially  valuable  method  of  determining  the  relative 
value  of  different  methods  of  firing,  or  of  different  kinds  of  fur- 
naces.    In  making  these  analyses  great  care  should  be  taken  to 
procure  average  samples — since  the  composition  is  apt  to  vary 
at  different  points  of  the  flue  pages  475  to  492).         The  com- 
position is  also  apt  to  vary  from  minute  to  minute,  -and  for  this 
reason  the  drawings  of  gas  should  last  a  considerable  period  of 
time.    Where  complete  determinations  are  desired,  the  analyses 
should  be  intrusted  to  an  expert  chemist.     For  approximate 
determinations  the  Orsat  t  or  the  Hempel  J  apparatus  may  be 
used  by  the  engineer.     (See  pages  481  and  483.) 

*  Favre  and  Silberraan  give  14,544  B.T.U.  per  pound  carbon  ;  Berthelot  14, 64V 
B.T.U.  Favre  and  Silberman  give  J32, 032  B.T.U.  per  pound  hydrogen  ;  Thomsen 
61,816  B.T.TJ. 

f  See  R.  S.  Hale's  paper  on  "  Flue  Gas  Analysis,"  Transactions,  voj  xviii.,  p.  901. 

$  See  Hempel's  "  Methods  of  Gas  Analysis  "  (Macmillan  &  Co.). 


§  375-]  TESTING   STEAM-BOILERS.  505 

For  the  continuous  indication  of  the  amount  of  carbonic  acid 
present  in  the  flue  gases,  an  instrument  may  be  employed  which 
shows  the  weight  of  the  sample  of  gas  passing  through  it. 

XIX.  Smoke    Observations. — It   is   desirable   to   have   a   uni- 
form system  of  determining  and  recording  the  quantity  of  smoke 
produced  where  bituminous  coal  is  used.      The  system  com- 
monly employed  is  to  express  the  degree  of  smokiness  by  means 
of  percentages  dependent  upon  the  judgment  of  the  observer. 
The  Committee  does  not  place  much  value  upon  a  percentage 
method,  because  it  depends  so  largely  upon  the  personal  ele- 
ment, but  if  this  method  is  used,  it  is  desirable  that,  so  far  as 
possible,  a  definition  be  given  in  explicit  terms  as  to  the  basis 
and  method  employed  in  arriving  at  the  percentage.     The  actual 
measurement  of  a  sample  of  soot  and  smoke  by  some  form  of 
meter  is  to  be  preferred.  (See  Appendices  XXXIV.  and  XXXV.) 

XX.  Miscellaneous. — In  tests  for   purposes   of  scientific  re- 
search, in  which  the  determination  of  all  the  variables  entering 
into  the  test  is  desired,  certain  observations  should  be  made 
which  are  in  general  unnecessary  for  ordinary  tests.     These  are 
the   measurement  of  the  air  supply,  the  determination  of  its 
contained  moisture,  the  determination  of  the  amount  of  heat 
lost  by  radiation,  of  the  amount  of  infiltration  of  air  through 
the  setting,  and  (by  condensation  of  all  the  steam  made  by  the 
boiler)  of  the  total  heat  imparted  to  the  water. 

As  these  determinations  are  rarely  undertaken,  it  is  not 
deemed  advisable  to  give  directions  for  making  them. 

XXI.  Calculations  of  Efficiency. — Two  methods  of  defining  and 
calculating  the  efficiency  of  a  boiler  are  recommended.    They  are  : 

-in.**!  •  *ru    -U   •!          Heat  absorbed  per  Ib.  combustible 

1.  Efficiency  of  the  boiler  =  ^-^ — ^ —  *  .  ,.  ... . — 

Calorific  value  of  1  Ib.  combustible 

o    T?#?  •  t  j.-u    u  -i          A  Heat  absorbed  per  Ib.  coal 

2.  Efficiency  of  the  boiler  and  grate  =  >*-^ — ^—  *  -.  „ 

Calorific  value  of  1  Ib.  coal 

The  first  of  these  is  sometimes  called  the  efficiency  based  on 
combustible,  and  the  second  the  efficiency  based  on  coal.  The 
first  is  recommended  as  a  standard  of  comparison  for  all  tests, 
and  this  is  the  one  which  is  understood  to  be  referred  to  when 
the  word  "  efficiency  "  alone  is  used  without  qualification.  The 
second,  however,  should  be  included  in  a  report  of  a  test,  to- 
gether with  the  first,  whenever  the  object  of  the  test  is  to  deter- 
mine the  efficiency  of  the  boiler  and  furnace  together  with  the 


5o6 


EXPERIMENTAL  ENGINEERING. 


[§  37 


grate  (or  mechanical  stoker),  or  to  compare  different  furnace 
grates,  fuels,  or  methods  of  firing. 

The  heat  absorbed  per  pound  of  combustible  (or  per  poui 
coal)  is  to  be  calculated  by  multiplying  the  equivalent  evapor 
tion  from  and  at  212  degrees  per  pound  combustible  (or  coal)  \ 
965.7. 

XXII.  The  Heat  Balance.—  An  approximate  "  heat  balance,"  < 
statement  of  the  distribution  of  the  heating  value  of  the  co 
among  the  several  items  of  heat  utilized  and  heat  lost  may  \ 
included  in  the  report  of  a  test  when  analyses  of  the  fuel  and  < 
the  chimney  gases  have  been  made.  It  should  be  reported  : 
the  following  form : 

HEAT  BALANCE,  OR  DISTRIBUTION  OF  THE  HEATING  VALUE  OF  THE  COMBUSTIBL 
Total  Heat  Value  of  1  Ib.  of  Combustible. .  .  .B.  T.  U. 


B.  T.  U. 

Per  Ce 

1.     Heat  absorbed  by  the  boiler  =  evaporation  from  and  at  212 
degrees  per  pound  of  combustible  x  965.7. 
2.     Loss  due  to  moisture  in  coal  =  per  cent,  of  moisture  referred 
to  combustible  -=-  100  x  [(212  -  t]  +  966  +  0.48  (T  - 
212)]  (t  —  •  temperature  of  air  in  the  boiler-room,  T  = 
that  of  the  flue  gases) 
3.     Loss  due  to  moisture  formed  by  the  burning  of  hydrogen 
=  per  cent,  of  hydrogen  to  combustible  -7-100  x  9  x 
[  (212  -  t)  4-  966  +  0.48  (T  -  212)]. 
4.*  Loss  due  to  heat  carried  away  in  the  dry  chimney  gases  = 
weight  of  gasper  pound  of  combustible  x  0.24  x  (T  —  t). 

COa     +    CO 

per  cent.  C  in  combustible       1  n  1  w 

100 
6.     Lose  due  to  unconsumed  hydrogen   and  hydrocarbons,   to 
heating  the  moisture  in  the  air,  to  radiation,  and  unac- 
counted for.     (Some  of  these  losses  may  be  separately 
itemized  if  data  are  obtained  from  which  they  may  be 
calculated  ) 

Totals  

100  01 

Dry  gas  per  pound  carbon 


)^  Jn  which  CQ^  CQ^  Q  &nd  N  ftre  ( 


*The  weight  of  gas  per  pound  of  carbon  burned  maybe  calculated  from  the  gas  analyses 
follows  : 

11  COa  +  8  O  +  7  (CO  + 

3  (COj  +  CO) 

percentages  by  volume  of  the  several  gases.  As  the  sampling  and  analyses  of  the  gases  in  t 
present  state  of  the  art  are  liable  to  considerable  errors,  the  result  of  this  calculation  is  nsua 
only  an  approximate  one.  The  heat  balance  itself  is  also  only  approximate  for  this  reason,  ns  w 
as  for  the  fact  that  it  is  not  possible  to  determine  accurately  the  percentage  of  unburned  hydrog 


gas  perpou 


or  hydrocarbons  in  the  flue  gases. 

The  weight  of  dry  gas  per  pound  of  combustible  is  found  by  multiplying  the  dry 
of  carbon  by  the  percentage  of  carbon  in  the  combustible,  and  dividing  by  100. 

t  CO2  and  CO  are  respectively  the  percentage  by  volume  of  carbonic  acid  and  carbonic  oxide 
the  flue  gases.  The  quantity  10,150  ;=  Number  of  heat  units  generated  by  burning  to  carboi 
acid  one  pound  of  carbon  contained  in  carbonic  oxide. 

XXIII.  Report  of  the  Trial. — The  data  and  results  should  1 
reported  in  the  manner  given  in  either  one  of  the  two  followir 


§375-]  TESTING   STEAM-BOILERS. 


SO/ 


tables,  omitting  lines  where  the  tests  have  not  been  made  as 
elaborately  as  provided  for  in  such  tables.  Additional  lines  may 
be  added  for  data  relating  to  the  specific  object  of  the  test.  The 
extra  lines  should  be  classified  under  the  headings  provided  in 
the  tables,  and  numbered  as  per  preceding  line,  with  sub  letters 
a,  b,  etc.  The  Short  Form  of  Report,  Table  No.  2,  is  recom- 
mended for  commercial  tests  and  as  a  convenient  form  of 
abridging  the  longer  form  for  publication  when  saving  of  space 
is  desirable,  f  For  elaborate  trials,  it  is  recommended  that  the 
full  log  of  the  trial  be  shown  graphically,  by  means  of  a  chart* 
(See  page  495.) 

TABLE  NO.  1. 
DATA  AND  RESULTS  OF  EVAPORATIVE  TEST, 

Arranged  in  accordance  with  the  Complete  Form  advised  by  the  Boiler  Test* 
Committee  of  the  American  Society  of  Mechanical  Engineers.     Code  of  1899. 

Made  by. of boiler  at to- 

determine 

t 

Principal  conditions  governing  the  trial 


Kind  of  fuel* 

Kind  of  furnace  .... 
State  of  the  weather. 


Method  of  starting  and  stopping  the  test  ("  standard"  or  "  alternate,"  Art.  X. 
and  XI. ,  Code) 

1.  Date  of  trial 

2.  Duration  of  trial houn. 

Dimensions  and  Proportions. 

(A  complete  description  of  the  boiler,  and  drawings  of  the  same  if  of  unusual 
type,  should  be  given  on  an  annexed  sheet.     (See  Appendix  X.) 

3.  Grate  surface  ....... .width length area sq.  ft. 

4.  Height  of  furnace , ins. 

5.  Approximate  width  of  air  spaces  in  grate in. 

6.  Proportion  of  air  space  to  whole  grate  surface per  cent. 

7.  Water-heating  surface sq.  ft. 

8.  Superheating  surface 

9.  Ratio  of  water-heating  surface  to  grate  surface —  to  1. 

10.  Ratio  of  minimum  draft  area  to  grate  surface 1  to  — 

*  The  items  printed  in  italics  correspond  to  the  items  in  the  "  Short  Form  of  Code.11 
t  Also  see  short  form  on  page  513,  used  in  Cornell  University. 


EXPERIMENTAL    ENGINEERING.  [§  375- 

Average  Pressure*. 

11.  Steam  pressure  by  gauge Ibs.  per  sq.in* 

12.  Force  of  draft  between  damper  and  boiler ins.  of  water 

13.  Force  of  draft  in  furnace "  " 

14.  Force  of  draft  or  blast  in  ashpit " 

Average  Temperatures. 

15.  Of  external  air deg. 

16.  Of  fireroora " 

17.  Of  steam " 

18.  Of  feed  water  entering  heater " 

19.  Of  feed  water  entering  economizer " 

20.  Of  feed  water  entering  boiler ...• 

21 .  Of  escaping  gases  from  boiler 

22.  Of  escaping  gases  from  economizer 


Fuel. 

23.  Size  and  condition 

24.  Weight  of  wood  used  in  lighting  fire Ibs. 

25.  Weight  of  coal  as  fired*  ,....  " 

26.  Percentage  of  moisture  in  coal  \ per  cent. 

27.  Total  weight  of  dry  coal  consumed Ibs. 

28.  Total  ash  and  refuse • " 

29.  Quality  of  ash  and  refuse 

30.  Total  combustible  consumed Ibs. 

31.  Percentage  of  ash  and  refuse  in  dry  coal per  cent. 


Proximate  Analysis  of  Coal. 

(App.  XII.) 

Of  Coal.      Of  Combustible. 

32.  Fixed  carbon percent.        percent. 

33.  Volatile  matter "                    " 

34.  Moisture <f 

55.  Ash  . ,  "                 


100  per  cent.     100  per  cent. 
36.  Sulphur,  separately  determined "  " 


*  Including  equivalent  of  wood  used  in  lighting  the  fire,  not  including  unburnt  coal  withdrawn 
from  furnace  at  times  of  cleaning  and  at  end  of  test.  One  pound  of  wood  is  taken  to  be  equal  to 
0.4  pound  of  coal,  or,  jin  case  greater  accuracy  is  desired,  as  having  a  heat  value  equivalent  to  the 
evaporation  of  6  pounds  of  water  from  and  at  212  degrees  per  pound.  (6  x  965.7  =  5,794  B.  T.  U.) 
The  term  "as  fired  "  means  it.  its  actual  condition,  including  moisture. 

t  This  is  the  total  moisture  in  the  coal  as  found  by  drying  it  artificially,  as  described  in  Art, 
XV.  of  Code. 


§  375-1  TESTING    STEAM-BOILERS.  509 


Ultimate  Analysis  of  Dry  Coal. 
(Art.  XVII.,  Code.) 


Of  Coal.  Of  Combustible. 

37.  Carbon  (C) , per  cent.  per  cent. 

38.  Hydrogen  (H) "  " 

39.  Oxygen(O) "  " 

40.  Nitrogen  (N) "  " 

41.  Sulphur  (S) "  «' 

42.  Ash  . ,  "  


100  per  cent.    100  per  cent. 

43.  Moisture  in  sample  of  coal  as  received "  " 

Analysis  of  Ash  and  Refute. 

44.  Carbon percent 

45.  Earthy  matter " 

Fuel  per  Hour. 

46.  Dry  coal  consumed  per  hour Its. 

47.  Combustible  consumed  per  hour  , : " 

48.  Dry  coal  per  square  foot  of  grate  surface  per  hour " 

49.  Combustible  per  square  foot  of  water-heating  surface  per  hoar.  " 

Calorific  Value  of  Fuel. 
(Art.  XVII.,  Code.) 

50.  Calorific  value  by  oxygen  calorimeter,  per  Ib.  of  dry  coal B.T.U. 

51.  Calorific  value  by  oxygen  calorimeter t  per  Ib.  of  combustible " 

52.  Calorific  value  by  analysis,  per  Ib.  of  dry  coal  * •• 

53.  Calorific  value  by  analysis,  per  Ib.  of  combustible. M 

Quality  of  Steam. 
(App.  XV.  to  XIX.) 

54.  Percentage  of  moisture  in  steam percent. 

55.  Number  of  degrees  of  superheating deg. 

56.  Quality  of  steam  (dry  steam  =  unity).     (For  exact  determina- 

tion of  the  factor  of  correction  for  quality  of  steam  see  Ap- 
pendix XVIII.) '. 

Water. 
(App.  I,  IV.,  VII.,  VIII.) 

57.  Totalweightof  water  fed  to  Jboiler^ Ibs. 

58.  Equivalent  water  fed  to  boiler  from  and  at  212  degrees . .  " 

59.  Water  actually  evaporated,  corrected  for  quality  of  steam " 

*  See  formula  for  calorific  value  under  Article  XVII.  of  Code. 

t  Corrected  for  inequality  of  water  level  and  of  steam  pressure  at  beginning  and  end  of  test. 


510  EXPERIMENTAL   ENGINEERING.  [§  375« 

60.  Factor  of  evaporation  * RNL 

61.  Equivalent  water  evaporated  into  dry  steam  from  and  at  212 

degrees,  f     (Item  59  x  Item  60.) 

Water  per  Hour. 

€2.   Water  evaporated  per  hour,  corrected  for  quality  of  steam 

63.  Equivalent  evaporation  per  hour  from  and  at  212  degrees  \ 

64.  Equivalent  evaporation  per  hour  from  and  at  212  degrees  per 

square  foot  of  water-lieating  surface  f 

Horse-Power. 

65.  Horse-power  developed.     (34£.  Ibs.  of  water  evaporated  per  hour 

into  dry  steam  from  and  at  212  degrees,  equals  one  horse- 
power) $ H.  P. 

66.  Builders'  rated  horse-power 

67.  Percentage  of  builders'  rated  horse-power  developed per  cent. 

Economic  Results. 

68.  Water  apparently  evaporated  under  actual  conditions  per  pound 

of  coal  as  fired.     (Item  57 "-*•  Item  25.) Ibs. 

69.  Equivalent  evaporation  from  and  at  212  degrees  per  pound  of 

coal  as  fired.  \    (Item  61  -f-  Item  25.) " 

70.  Equivalent  evaporation  from  and  at  212  degrees  per  pound  of  dry 

coal.\    (Item  61  -4-  Item  27.) " 

71.  Equivalent  evaporation  from  and  at  212  degrees  per  pound  of 

combustible,  f     (Item  61  -5-  Item  30.) •• 

(If  the  equivalent  evaporation,  Items  69,  70,  and  71,  is  not  cor- 
rected for  the  quality  of  steam,  the  fact  should  be  stated). 


(Art.  XXL,  Code.) 

72.  Efficiency  of  the  boiler  ;  heat  absorbed  by  the  boiler  per  Ib.  of  com," 

bustible  divided  by  the  heat  value  of  one  Ib.  of combustible  §. . . .        percent. 

73.  Efficiency  of  boiler,  including  the  grate ;  heat  absorbed  by  the 

boiler,  per  Ib.  of  dry  coal,  divided  by  the  heat  value  of  one  Ib.  of 

dry  coal  ». " 

*  Factor  of  evaporation  =  -^~L,  in  which  H  and  h  are  respectively  the  total  heat  in  steam  of 

«7OO.  t 

the  average  observed  pressure,  and  in  water  of  the  average  observed  temperature  of  the  feed. 

t  The  symbol  "  IT.  E."  meaning  "Units  of  Evaporation,"  may  be  conveniently  substituted  for 
the  expression  "Equivalent  water  evaporated  into  dry  steam  from  and  at  212  degrees,"  its  defini- 
tion being  given  in  a  foot-note. 

t  Held  to  be  the  equivalent  of  30  Ibs.  of  water  per  hour  evaporated  from  100  degrees  Fahr.  into 
dry  steam  at  70  Ibs.  gauge  pressure.  (See  page  494.) 

$  In  all  cases  where  the  word  combustible  is  used,  it  means  the  coal  without  moisture  and  ash, 
bat  including  all  other  constituents.  It  is  the  same  as  what  is  called  in  Europe  "  coal  dry  and  free 
from  ash." 


§  375-]  TESTING   STEAM-BOILERS.  $11 

Cost  of  Evaporation. 

74.  Cost  of  coal  per  ton  of Ibs.  delivered  in  boiler  room $' 

75.  Cost  of  fuel  for  evaporating  1,000  Ibs.  of  water  under  observed 

conditions $ 

76.  Cost  of  fuel  used  for  evaporating  1,000  Ibs.  of  water  from  and  at 

212  degrees $ 

Smoke  Observations. 
(App.  XXXIV.  and  XXXV.) 

77.  Percentage  of  smoke  as  observed per  cent 

78.  Weight  of  soot  per  hour  obtained  from  smoke  meter ounces. 

79.  Volume  of  soot  per  hour  obtained  from  smoke  meter cub.  in. 

Methods  of  Firing. 

80.  Kind  of  firing  (spreading,  alternate,  or  coking). 

81.  Average  thickness  of  fire 

82.  Average  intervals  between  firings  for  each  furnace  during  time 

when  fires  are  in  normal  condition 

83.  Average  interval  between  times  of  levelling  or  breaking  up. . . . 

Analyses  of  the  Dry  Bases. 

84.  Carbon  dioxide  (CO2) percent. 

85.  Oxygen  (0) " 

86.  Carbon  monoxide  (CO) " 

67.  Hydrogen  and  hydrocarbons " 

88.  Nitrogen  (by  difference)  (N) " 

100  per  cent. 
TABLE  NO.  2. 

DATA  AND  RESULTS  OF  EVAPORATIVE  TEST, 

Arranged  in  accordance  with  the  Short  Form  advised  by  the  Boiler  Test  Com- 
mittee of  the  American  Society  of  Mechanical  Engineers.     Code  of  1899. 

Made  by on boiler,  at to 

determine 

Kind  of  fuel 

Kind  of  furnace 

Method  of  starting  and  stopping  the  test  ('*  standard"  or  "  alternate,"  Art.  X. 

and  XL,  Code) 

Grate  surface sq.  ft. 

Water-heating  surface " 

Superheating  surface " 

Total  Quantities. 

1.  Date  of  trial 

2.  Duration  of  trial hours. 

3.  Weight  of  coal  as  fired* Ibs. 

4.  Percentage  of  moisture  in  coal  * per  cent. 

5.  Total  weight  of  dry  coal  consumed Ibs. 

6.  Total  ash  and  refuse " 

7.  Percentage  of  ash  and  refuse  in  dry  coal per  cent. 

*  See  foot-notes  of  Complete  Form. 


$12  EXPERIMENTAL   ENGINEERING.  [§375 

8.  Total  weight  of  water  fed  to  the  boiler  *...<, Ibe. 

9.  Water  actually  evaporated,  corrected  for  moisture  or  super- 

heat in  steam 

10.  Equivalent  water  evaporated  into  dry  steam  from  and  at  212 

!*       i- 

Hourly  Quantities. 

11.  Dry  coal  consumed  per  hour Ibs. 

12.  Dry  coal  per  square  foot  of  grate  surface  per  hour 

13.  Water  evaporated  per  hour  corrected  for  quality  of  steam. ...  " 

14.  Equivalent  evaporation  per  hour  from  and  at  212 degrees*. . .  " 

15.  Equivalent  evaporation  per  hour  from  and  at  212  degrees  per 

square  foot  of  water-heating  surface  * '* 

Average  Pressures,  Temperatures,  etc. 

16.  Steam  pressure  by  gauge Ibs.  per  sq.  in, 

17.  Temperature  of  feed  water  entering  boiler deg. 

18.  Temperature  of  escaping  gases  from  boiler " 

19.  Force  of  draft  between  damper  and  boiier ins.  of  water, 

20.  Percentage  of  moisture  in  steam,  or  number  of  degrees  of 

superheating per  cent,  ordeg. 

Horse-Power. 

21.  Horse-power  developed  (Item  14  -*-  34£)  * H.  P. 

22.  Builders'  rated  horse-power 

23.  Percentage  of  builders'  rated  horse-power  developed per  cent. 

Economic  Results. 

24.  Water   apparently  evaporated   under    actual    conditions  per 

pound  of  coal  as  fired.     (Item  8  •*-  Item  3) Ibs. 

25.  Equivalent  evaporation  from  and  at  212  degrees  per  pound  of 

coal  as  fired.*     (Item  10 -r- Item  3) " 

26.  Equivalent  evaporation  from  and  at  212  degrees  per  pound  of 

dry  coal.*    (Item  10 -*- Item  5) '* 

27.  Equivalent  evaporation  from  and  at  212  degrees  per  pound  of 

combustible.*    [Item  10  -T-  (Item  5  —  Item  6)J " 

(If  Items  25,  26,  and  27  are  not  corrected  for  quality  of  steam, 
the  fact  should  be  stated.) 

Efficiency. 

28.  Calorific  value  of  the  dry  coal  per  pound B.  T.  U. 

29.  Calorific  value  of  the  combustible  per  pound 

30.  Efficiency  of  boiler  (based  on  combustible)  * per  cent. 

81.  Efficiency  of  boiler,  including  grate  (based  on  dry  coal) 

Cost  of  Evaporation. 

32.  Cost  of  coal  per  ton  of Ibs.  delivered  in  boiler-room $ 

83.  Cost  of  coal  required  for  evaporating  1,000  pounds  of  water 

from  and  at  212  degrees $ 


*See  foot-notes  of  Complete  Form. 


§  376-1         METHODS   OF   TESTING    STEAM-BOILERS.  $1$ 


376.  CONDENSED   REPORT   OF   BOILER-TEST. 

(Sibley  College,  Cornell  University.) 
LOG  OF  BOILER-TRIAL. 


M*de  at. 

Date 

Fireman, 


..189.. 

REPORT  OF   BOILER-TEST. 


Made  by. . 
Kind  of  Boiler. 


N.  Y., 

Manufactured  by. . 


..189.. 


Duration  of  Trial Hours. 


.ft., 


Sq.  ft. 


Grate-surf.,  length 

width ft 

Water-heating  surface " 

Superheating  surface " 

Area  for  draught  (calorimeter).      " 

Area,  chimney 

Height,  chimney Ft. 

Ratio  heating  to  grate  surface 

Ratio  air-space  to  grate-surface 

Barometer  Inches  mercury. 

Steam-gauge Pounds. 

Draught-gauge Inches  water. 

Absolute  steam-pressure Pounds. 

External  air Degrees  F. 

Boiler-room " 

Flue 

Furnace  

Feed-water " 

Steam " 

Total  coal  consumed Pounds. 

Moisture  in  coal Per  cent. 

Dry  coal  consu  med Pounds. 

Total  refuse,  dry " 

Total  refuse,  dry Percent. 

Total  combustible Pounds. 

Dry  coal  per  hour 

Combustible  per  hour 

Dry  coal  per  square  foot  of 

grate 

Combustible  per  square  foot 

of  grate 

Dry  coal  per  square  foot  of 

grate Heating-surface. 

Combustible  per  squaYe  foot  of 

grate Heating-surface. 

Quality  of  steam  Percent. 

Superheat Degrees. 

Total  weight  water  used ...  Pounds, 
(by  meter)...  Cu.  ft. 

Total  evap.,  dry  steam Pounds. 

Factor  of  evaporation 

Total  from  and  at  212°. ..    .   Pounds. 


Amount  used Pounds. 

Evaporated,  dry  steam " 

2£  Evap.  from  and  at  212° " 

Per  Pound  of  Fuel. 

Actual Pounds. 

Equiv.  from  and  at  212° " 

Per  Pound  of  Combustible. 

Actual Pounds. 

Equiv.  from  and  at  212° " 

Per  Sq.  Ft.  Heating-surface  per  Hr. 

Actual Pounds. 

Equiv.  from  and  at  212° " 

From  100°  F.  to  70  Pounds  by  Gauge. 

Per  Pound  of  Fuel  Pounds. 

Per  Pound  of  Combustible. . .       •* 
Per  f-pound  of  Fuel " 

Per  Square  Foot  of  Grate. 

Actual,  from  feed-water  tem- 
perature   Pounds. 

Equiv.  from  and  at  212° " 


Per  Sq.  Ft.  of  Water-heating  Surface. 

Actual Pounds. 

Equiv.  from  and  at  212° " 

Per  Sf.  Ft.  of  Least  Draught-area. 

Actual Pounds. 

Equiv.  from  and  at  212° " 

*  On  basis  34^  Ibs.  equiv.  evap. 

per  hour H.  P. 

Builders'  rating " 

Ratio  of  commercial  to  builders'  rat- 


ing. 


Heat  generated  per  hour. . .  B.  T.  U. 

Heat  absorbed  per  hour " 

Efficiency  of  boiler.    Per  cent. 

Efficiency  of  furnace " 


NOTE. — Actual  evaporation  signifies  the  evaporation  from  feed-water  temperature  to  dry 
steam  at  gaupe-pressure.     It  is  apparent  evaporation  corrected  for  calorimeter-determination. 
*  Standard  Commercial  H.  P. 


514  EXPERIMENTAL    ENGINEERING.  [§  37/. 

377.  Abbreviated  Directions  for  Boiler-testing. — Ap- 
paratus.— As  in  standard  tests  :  tanks  and  scales  for  weighing 
water ;  meter  for  measuring  water ;  apparatus  for  flue-gas 
analysis  ;  barometer  and  pyrometer. 

Directions. — Calibrate  all  apparatus,  meters,  scales,  ther- 
mometers, and  gauges ;  arrange  throttling  or  separator  calo- 
rimeter to  obtain  quality  of  steam  delivered.  Note  condition 
of  Boiler  and  Furnace  Rules,  VII-IX.  Start  and  close  the 
test  either  by  standard  or  alternative  method,  Rules  X  and  XL 
-During  test  proceed  as  in  Rules  XIII  and  XIV.  Continue 
the  test  as  long  as  time  will  permit,  at  least  four  hours,  taking 
simultaneous  observations  each  15  minutes  at  a  signal  given 
by  a  whistle  ;  keep  record  so  that  coal  and  water  consumption 
<:an  be  computed  for  each  hour. 

Put  100  pounds  of  coal  in  a  box  and  dry  in  a  hot  place  for 
24  hours ;  if  ashes  are  damp  from  use  of  a  steam-blower,  dry  a 
sample  of  100  pounds  in  same  manner.  In  general,  ashes  may 
be  removed  at  once  and  weighed. 

Report  and  Computation. — Make  report  on  standard  forms 
submitted  and  compute  the  required  quantities.  Submit  with 
report  a  graphical  log,  in  which  time  is  taken  as  abscissa,  and 
the  various  observed  quantities  as  ordinates. 

Revised  Code  for  Boiler-testing. — At  the  meeting  of  the 
American  Society  of  Mechanical  Engineers  in  December, 
1899,  a  revised  code  for  boiler-testing  was  presented  before 
the  society  by  a  special  committee  appointed  for  that  pur- 
pose. The  new  code  is  given  in  the  Appendix  to  this  volume  ; 
it  differs  from  the  old  one  principally  in  the  use  of  improved 
methods. 


CHAPTER   XVI. 
THE   STEAM-ENGINE   INDICATOR. 

378.  Uses  of  the  Steam-engine  Indicator. — The  steam- 
engine  indicator  is  an  instrument  for  drawing  a  diagram  on 
paper  which  shall  accurately  represent  the  various  changes  of 
pressure  on  one  side  of  the  piston  of  the  steam-engine  during 
both  the  forward  and  return  stroke. 


FIG   226. — THE  INDICATOR-DIAGRAM. 

The  general  form  of  the  indicator-diagram  is  shown  in  Fig. 
226;  the  ordinates  of  the  diagram,  measured  from  the  line 
GG,  are  proportional  to  the  pressure  per  square  inch  above  the 
atmosphere ;  measured  from  the  line  ////,  are  proportional  to 
the  absolute  pressure  per  square  inch  acting  on  the  piston. 
The  abscissa  corresponding  to  any  ordinate  is  proportional  to 
the  distance  moved  by  the  piston.  ABODE  is  the  line  drawn 
during  the  forward  stroke  of  the  engine,  EFA  that  drawn  dur- 
ing the  return  stroke.  The  ordinates  to  the  line  ABCDE  rep- 
resent the  pressures  acting  to  move  the  piston  forward  ;  those 
to  the  line  EFA  represent  the  pressures  acting  to  retard  or 

515 


516  EXPERIMENTAL   ENGINEERING.  [§379- 

stop  the  motion  of  the  piston  on  its  back  stroke.  The  ordi- 
nates  intercepted  between  the  lines  represent  the  effective 
pressure  acting  to  urge  the  piston  forward.  Since  the  abscissae 
of  the  diagram  are  proportional  to  the  space  passed  through 
by  the  piston,  and  the  intercepted  ordinate  to  the  effective 
pressure  acting  on  the  piston,  the  area  of  the  diagram  must  be 
proportional  to  the  work  done  by  the  steam  on  one  side  of  the 
piston,  acting  on  a  unit  of  area  and  during  both  forward  and 
return  stroke.  (See  Article  21,  page  21.) 

From  this  diagram  can  be  obtained,  by  processes  to  be  ex- 
plained later:  I.  The  quantity  of  power  developed  in  the 
cylinder,  and  the  quantity  lost  in  various  ways, — by  wire-draw- 
ing, by  back  pressure,  by  premature  release,  by  mal-adjustment 
of  valves,  leakage,  etc. 

2.  The  redistribution  of  horizontal  pressures  at  the  crank- 
pin,  through  the  momentum  and  inertia  of  the  reciprocating 
parts,  and  the  angular  distribution  of  the  tangential  component 
of  the  horizontal  pressure ;  in  other  words,  the  rotative  effect 
around  the  path  of  the  crank. 

3.  Taken  in  combination  with  measurements  of  feed-water 
or  of  the  exhaust  steam,  with  the  amount  and  temperatures  of 
condensing  water,   the    indicator   furnishes   opportunities   for 
measuring    the   heat    losses  which    occur   at    different   points 
during  the  stroke. 

4.  The    indicator-diagram  also   shows  the   position  of  the 
piston    at    times  when   the  valve-motion  opens  or  closes  the 
steam  and  exhaust  ports  of  the  engine.     It  also  furnishes  in- 
formation regarding  the  general  condition  of  the  engine,  and 
the  arrangement  of  the  valves,  adequacy  of  the  ports  and  pas- 
sages, and  of  the  steam  or  the  exhaust  pipes. 

379.  Indicated  and  Dynamometric  Power. — The  steam, 
engine  indicator  is  used  in  all  steam-engine  tests  to  measure 
the  force  of  the  steam  acting  on  a  unit  of  area  of  the  piston.  A 
dynamometer  of  the  absorbing  or  transmission  type  (see  pages 
235  to  2 50) is  used  to  measure  the  work  delivered  by  the  steam- 
engine.  The  work  of  the  engine  is  usually  expressed  in  horse- 
power; one  horse-power  being  equivalent  to  33,000  foot-pounds 


§  3«o.] 


THE    STEAM-ENGINE   INDICATOR. 


per  minute.  The  work  shown  by  the  steam-engine  indicator- 
diagram  is  termed  the  Indicated  horse-power  (I.H.P.);  that  shown 
by  the  dynamometer,  Dynamometric  horse-power  (D.H.P.). 

The  mean  effective  pressure  per  unit  of  area  acting  on  the 
piston  is  obtained  from  the  indicator-diagram  ;  this  quantity, 
multiplied  by  the  area  of  the  piston  and  the  distance  travelled 
t>y  the  piston  in  feet  per  minute,  will  give  the  work  in  foot- 
pounds.  Thus  let  /  equal  the  mean  effective  pressure,  /  the 
length  of  stroke  of  the  engine  in  feet,  n  the  number  of  revolu- 
tions, a  the  area  of  the  piston  in  square  inches.  Then  the 
work  done  per  minute  by  the  steam  acting  on  one  side  of  the 
piston,  in  horse-power,  is 

plan  -;-  33,000. 

380.  Early  Forms  of  the  Steam-engine  Indicator. — 
Watt  and  Me  Naught. — The  steam-engine  indicator  was  in- 
vented by  James  Watt,  and  was  extensive-  sj 
ly  used  by  him  in  perfecting  his  engine. 
The  indicator  of  Watt,*  as  used  in  1814, 
consisted  of  a  small  steam-cylinder  AA, 
as  shown  in  Fig.  227,  in  which  a  piston 
was  moved  by  the  steam-pressure,  against 
the  resistance  of  a  spring  FC.  The  end 
of  the  piston-rod  carried  a  pencil,  which 
was  made  to  press  against  a  sheet  of 
paper  DD,  moved  backward  and  forward 
in  conformity  to  the  motion  of  the  piston. 
By  this  method  a  diagram  was  produced 
similar  to  that  shown  in  Fig.  227. 

McNaught's  indicator,  which  succeeded 
that  of  Watt  and  was  in  general  use  until 
about  1860,  differed  from  the  form  used 
by  Watt  principally  in  the  use  of  a  verti- 
cal cylinder  instead  of  the  sliding  panel, 
which  was  turned  backward  and  forward 
on  a  vertical  axis,  in  conformity  to  the  motion  of  the  piston. 


FIG.  227.— THE  WATT 
INDICATOR. 


*  See  Thurston's  Engine  and  Boiler  Trials,  page  130. 


5i8 


EXPERIMENTAL   ENGINEERING. 


381.  The  Richards  Indicator.*— The  Richards  indicator 
was  invented  by  Professor  C.  B.  Richards  about  1860;  it  con- 
tains every  essential  constructive  feature  found  in  recent  indi- 
cators, and  may  be  considered  the  prototype  from  which  all 
other  indicators  differ  simply  in  details  of  workmanship,  form, 
and  size  of  parts. 

The  construction  of  this  indicator  is  well  shown  in  Fig.  22&,. 


PIG.  228. — THE  RICHARDS  INDICATOR. 

from  which  it  is  seen  to  consist  of  a  steam-cylinder  AA,  in 
which  is  a  piston  B,  connected  by  a  rigid  rod  with  the  cap  F. 
The  movement  of  the  piston  is  resisted  by  the  spring  CD  in 
such  a  manner  that  its  motion  in  either  direction  is  proportional 
to  the  pressure.  The  motion  of  the  piston-rod  is  transferred 
to  a  pencil  at  K,  by  links  which  are  so  arranged  that  the  pencil 

*  See  the  Richards  Indicator,  by  C.  B.  Porter;  New  York,  D.  Van  Nostrand. 


g  382.] 


THE   STEAM-ENGINE   INDICATOR. 


519. 


moves  parallel  to  the  piston  B,  but  through  a  considerably 
greater  range.  The  indicator-spring  can  be  taken  out  by 
unscrewing  the  cap  E,  removing  the  top  of  the  instrument  and 
unscrewing  the  piston  By  and  another  spring  with  a  different 
tension  can  be  substituted.  The  drum  OR  is  made  of  light 
metal,  mounted  on  a  vertical  axis,  and  provided  with  a  spring 
arranged  to  resist  rotation.  The  drum  is  connected  to  the  cross- 
head  or  reducing  motion  by  a  cord,  and  is  given  a  motion  in  one 
direction  by  the  tension  transmitted  through  the  cord  and  in  a 
reverse  direction  by  the  indicator  drum-spring.  The  paper  on 
which  the  diagram  is  to  be  drawn  is  wrapped  smoothly  around 
the  drum  OQ,  being  held  in  place  by  the  clips  PQ.  The  indicator 
is  connected  to  the  steam-cylinder  by  a  pipe  leading  to  the 
clearance-space  of  the  engine ;  a  cock,  T,  being  screwed  into  this 
pipe,  and  the  indicator  connected  to  the  cock  by  the  coupling  U. 
382.  The  Thompson  Indicator. — This  indicator  is  shown 
in  Figs.  229  and  230.  It  differs  from  the  Richards  indicator 


FIG.  2*9.— THE  THOMPSON  INDICATOR. 


FIG.  230.— SECTION  OF  THOMPSON 
INDICATOR. 


principally  in  the  form  of  the  parallel  motion,  form  of  indicator- 
spring,  and  details  of  workmanship.     The  parts  of  the  instrti- 


520  EXPERIMENTAL   ENGINEERING.  [§  383. 

ment  are  much  lighter,  and  it  is  better  adapted  for  use  on  high- 
speed  engines. 

The  use  is  essentially  the  same  as  the  Richards  ;  the  method 
of  changing  springs  should  be  thoroughly  understood,  and  is  as 
follows :  Unscrew  the  milled-edged  cap  at  the  top  of  steam- 
cylinder;  then  take  out  piston,  with  arm  and  connections;  dis- 
connect pencil-lever  and  piston  by  unscrewing  the  small  milled- 
headed  screw  which  connects  them  ;  remove  the  spring  from  the 
piston,  substitute  the  one  desired,  and  put  together  in  same 
manner,  being  careful,  of  course,  to  screw  the  spring  up  firmly 
against  ca'p  and  well  down  to  the  piston-head.  The  method  of 
changing  springs  is  simple,  easy,  and  convenient,  and  does  not 
require  the  use  of  any  wrench  or  pin  of  any  kind. 

383.  The  Tabor  Indicator. — The  Tabor  indicator,  shown 
in  Figs.  231  and  232,  in  the  form  now  manufactured  differs 
from  other  indicators  principally  in  producing  the  parallel 


FIG.  231. — THE  TABOR  INDICATOR. 


motion  of  the  pencil  by  a  pin  moving  in  a  peculiarly-shaped 
slot.  It  also  differs  in  details  of  construction  and  in  form 
of  the  indicator-spring;  the  pencil-point  being  arranged  to 
move  not  only  parallel  to  the  piston,  but  uniformly  five  times 
a*  fast  as  the  piston  at  every  part  of  the  range. 


§  384-] 


THE   STEAM-ENGINE  INDICATOR. 


521 


The  method  of  changing  springs  in  the  Tabor  indicator  is  as 
follows  :  Remove  the  cover  of  the 
cylinder,  remove  the  screw  beneath 
the  piston,  unscrew  the  piston  from 
the  spring  and  the  spring  from 
the  cover,  and  replace  the  spring 
desired.  When  the  lower  end 
of  the  piston-rod  is  introduced 
into  the  square  hole  in  the  centre 
of  the  piston,  care  must  be  taken 
chat  it  sets  fairly  in  the  hole  be- 
fore the  screw  is  applied.  Unless 
such  care  is  observed,  the  corners 
may  catch  and  cause  derangement. 
The  tension  on  the  drum-spring 

FIG.  232. — SECTION  OF  TABOR  INDICATOR. 

may  be  varied   by  removing  the 

paper  drum,  loosening  the  thumb-screw  which  encircles  the 
central  shaft,  lifting  the  drum-carriage  so  as  to  clear  the  stop, 
and  then  winding  the  carriage  in  the  direction  desired. 

384.  The  Crosby  Indicator. — The  Crosby  indicator  as  at 
present  constructed  is  shown  in  Figs.  233  and  234.  It  differs 
from  those  already  described  in  the  form  of  piston-  and  drum- 
springs  and  in  the  arrangement  for  producing  accurate  parallel 
motion. 

The  special  directions  for  this  instrument  are  given  by  the 
manufacturers  as  follows  : 

To  -remove  the  piston,  spring,  etc.,  unscrew  the  cap,  then,  by 
the  sleeve,  lift  all  the  connected  parts  free.  This  gives  full 
access  to  the  parts  to  clean  and  oil  them. 

To  detach  the  spring,  unscrew  the  cap  from  spring-head, 
then  unscrew  piston-rod  from  swivel-head,  then,  with  the  hol- 
low slotted  wrench,  unscrew  the  piston-rod  from  the  piston. 
To  attach  a  spring,  simply  reverse  this  process.  Before  setting 
the  foot  of  the  spring  unscrew  G  slightly,  then,  after  the  piston- 
rod  has  been  firmly  screwed  down  to  its  shoulder,  set  G  up 
firmly  against  the  bead,  and  thereby  take  up  all  lost  motion. 

It  is  often  desirable  to  change  the  position  of  the  atmospheric 


522 


EXPERIMENTAL   ENGINEERING. 


[§  384. 


line  on  the  paper.  This  can  easily  be  done  by  unscrewing  the 
cap  from  the  cylinder  and  raising  the  sleeve  BB  which  carries 
the  pencil-movement.  Then  turn  the  cap  to  the  right  or  left, 


FIG.  233.— THE  CROSBY  INDICATOR. 

and  the  piston-rod  will  be  screwed  off  or  on  the  swivel  E,  and 
the  position  of  the  atmospheric  line  will  be  raised  or  lowered. 

Never  remove  the  pins  or  screws  from  the  joints  K,  /,  L,  M, 
but  keep  them  well  oiled  with  refined  porpoise-jaw  oil,  which 
is  furnished  with  each  instrument. 

The  tension  on  the  drum-spring  should  be  increased  or 
diminished  according  to  the  speed  at  which  the  instrument  is 
used,  by  means  of  the  thumb-nut  on  top  of  the  drum-spindle. 

Use  a  spring  of  such  a  number  that  the  diagram  will  not  be 


385-] 


THE  STEAM-ENGINE   INDICATOR. 


523 


over  one  and  three-quarter  inches  high;  as,  for  instance,  a  No. 
40  spring  should  not  be  used  for  pressures  above  70  Ibs. 


FIG.  234. — SECTION  OP  THE  CROSBY  INDICATOR. 

385.  Indicators  with  External  Springs.— The  Bachelder 
indicator,  shown  in  Fig.  235,  has  a  flat  spring  that  is  flexed  over 
a  movable  fulcrum  by  the  steam  pressure  acting  on  the  piston. 
The  scale  of  the  spring  is  changed,  through  a  limited  range,  by 
moving  the  fulcrum.  This  form  is  desirable  when  the  spring 
is  subjected  to  high  temperatures;  it  is  only  open  to  the  objec- 
tion that  the  scale  may  be  somewhat  unreliable  due  to  an  acci- 
dental motion  of  the  fulcrum. 

An  indicator  with  the  spring  entirely  outside  and  above  the 
indicator  cylinder  is  shown  in  Fig.  236.  For  indicating  gas- 


524 


EXPERIMENTAL   ENGINEERING. 


[§  386. 


engines  when  the  spring  is  exposed  to  a  high  temperature  this 
form  is  desirable.     That  shown  is  a  form  of  the  Tabor. 


FIG.  235.— THE  BACHELDER   INDICATOR. 


FIG.  236. — INDICATOR  WITH   EXTERNAL 
SPRING. 


386.    Sundry  Types  of  Indicators. — Many  of  the  makers 
of  indicators  provide  reducing- wheels  which  may  be  adapted  to 


FIG.   237. — INDICATOR  WITH    REDUCING-WHEEL. 

varying  lengths  of  strokes  either  by  changing  gear-wheels  in 
the  train  of  gears,  or  by  varying  the  diameter  of  the  wheels  driven 
by  the  cord  from  the  cross-head.  An  indicator  provided  with 
one  form  of  reducing- wheels  is  shown  in  Fig.  237. 


§ 


THE   STEAM-ENGINE   INDICATOR. 


525 


In  Figs.  238  and  2380  are  shown  indicators  with  pencil-moving 
mechanism  of  different  character  from  those  described.     In  one 


FIG.  238. — THE  STRAIGHT-LINE  INDICATOR.          FIG.  2380. — THE  PERFECTION  INDICATOR. 


case  the  pencil  is  directed  in  a  straight  line  by  a  slotted  guide- 
bar,  in  the  other  case  it  is  made  to  move  in  a  right  line  by  a  species 
of  parallel  motion  links. 

387.  Optical  Indicators. — The  ordinary  steam-engine  indi- 
cator is  not  adapted  for  a  very  high  speed  of  rotation,  because 
the  inertia  of  the  moving  parts  distorts  the  diagram.  By  arranging 
a  mirror,  which  may  be  illuminated  so  as  to  be  deflected  in 
one  direction  by  changes  of  pressure  in  the  cylinder,  and  in  a 
direction  at  right  angles  by  the  motion  of  the  piston,  the  indi- 
cator diagram  will  be  traced  by  a  beam  of  light  thrown  on  a 
ground-glass  screen  or  on  a  sensitive  plate  in  a  camera.  The 
form  of  the  diagram  may  be  studied  by  observing  it  on  the  ground 
plate,  or  it  may  be  photographed  and  preserved. 

One  form  of  this  instrument  is  made  by  J.  Carpentier  of 
Paris,  and  is  called  the  Mano graphic.'  Another  form  is  made  by 
the  Elsassische  Elektricitats-Werke,  Strassburg,  and  is  called 
the  optical  indicator. 

A  perspective  view  and  section  of  the  Manographie  is  shown 
in  Figs.  239  and  2390.  A  small  mirror  is  located  at  A  in  the 


526 


EXPERJM&N  TA  L   ENGINEERING. 


[§  388= 


back  part  of  the  camera  E.     It  is  deflected  in  one  direction  by 

a  small  crank  operated  in  unison  with  the  engine  piston  by  the 

revolving  shaft  P,  to 
which  it  is  connected  by 
the  flexible  shaft  R,  Fig. 
239;  it  is  deflected  in  a 
direction  at  right  angles 
against  the  resistance  of 
a  spring  by  the  pressure 
from  the  engine  cylinder 
acting  through  a  pipe  T 
FIG.  239.  uP°n  a  diaphragm  di- 

rectly back  of  the  mirror. 
Tne  mirror  is  illuminated  by  light  from  a  lamp  at  G  which 

is  reflected  by  the  prism  shown  at  H.     The  indicator  diagram 

is  traced  on  the  screen  D 

by  the  ray  of  light,  and 

may  be  photographed  by 

the  use    of    a    sensitive 

plate.      This    apparatus 

has     been     successfully 

used   to    take    indicator 

diagrams  of  gas-engines 

when  moving  at  the  rate 

of  2000  revolutions   per  FIG.  2390. 

minute. 

388.  Parts  of  the  Steam-engine  Indicator. — The  parts  of 

the  steam-engine  indicator  are  essentially  as  follows: 

1.  The  Steam-cylinder. — This  contains  the  piston,  the  indi- 
cator-spring,   and   attachments   for   the   pencil   mechanism. 

2.  The  Piston. — This  is  usually  solid,  with  grooves  or  holes 
in  its  outer  edge;    it  must  move  easily  in  the  cylinder.     When 
in  use  it  must  be  lubricated  with  cylinder-oil  of  best  quality. 

3.  The  Pencil  Mechanism. — This  receives  the  motion  from 
the   piston-rod,   increases  its   amplitude,   and   transfers  it   to   a 
pencil  by  means  of  guides  or  parallel- motion  links,  so  that  the 


§  388.]  THE   STEAM-ENGINE  INDICATOR.  $2? 

pencil  moves  in  a  right  line  and  usually  four  to  six  times  the 
distance  of  the  piston.  The  height  of  the  atmospheric  line,  or 
line  of  no  pressure,  on  the  drum,  can  often  be  adjusted  by 
means  of  a  threaded  sleeve  fitting  on  the  piston-rod.  In  the 
arc  indicator  the  pencil  swings  in  an  arc  of  a  circle. 

4.  The  Indicator- spring. — This  is  usually  a  helical  spring; 
when,  in  use  it  has  one  end  screwed  to  the  upper  head  of  the 
cylinder,  and  the  other  screwed  to  the  piston.  To  insure  accu- 
rate results  the  spring  must  be  accurate,  and  there  must  be  no 
play  or  lost  motion  between  the  piston  and  the  cylinder-head, 
and  the  spring  must  receive  and  deliver  the  force  axially.  The 
number  of  pounds  pressure  on  the  square  inch  required  to  move 
the  pencil  one  inch  is  stamped  on  the  spring,  and  the  springs 
are  designated  by  that  number.  It  is  essential  to  know  the 
error,  if  any,  in  this  number.  A  spring  can  be  readily  removed 
and  another  substituted  when  desired  ;  the  maximum  compres- 
sion probably  should  not  exceed  one  third  of  an  inch. 

The  spring  is  in  many  respects  the  most  important  part  of 
the  indicator,  as  the  form  of  the  diagram  is  directly  affected 
by  any  error.  The  following  cuts  show  some  of  the  principal 


FIG.  240. — CROSBY  SPRING.  FIG.  241. — TABOR  SPRING. 

forms  adopted  by  a  few  of  the  makers,  and  it  may  perhaps  be 
sufficient  to  state  that  within  the  range  of  action  of  the  indi- 
cator any  of  these  forms  can  be  made  practically  perfect. 


528 


EXPERIMENTAL   ENGINEERING. 


[§  389. 


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§  39°-]  THE   STEAM-ENGINE   INDICATOR.  529 

The  Bachelder  indicator  (see  Fig.  238)  is  made  with  a  flat 
spring,  and  to  a  certain  extent  the  tension  is  regulated  by 
changing  its  fulcrum. 

5.  The  Paper-drum,  to  which  the  card  is  attached,  consists 
of  a  brass  cylinder  attached  to  a  spindle  which  is  connected 
to  the  drum-spring,  the  action  of  which  has  been  described. 
The  drum  can  be  removed  readily,    and  the   tension  on  the 
spring  changed  at  pleasure.     Two  clips  or  fingers  serve  to  hold 
the  paper  in  position. 

6.  The  Cord  used,  although   not  a  part  of  the  indicator, 
must  be  selected  with  great  care;  it  must  be  of  a  character 
not  to   be    stretched   by  the   forces   acting  on   the   indicator. 
Steel  wire  is  sometimes  used  for  this  purpose.     Any  variation 
in  length  of  the  connecting  cord  affects  the  abscissa  in  the 
diagram. 

7.  The  Reducing-motions,  also  not  a  part  of  the  indicator, 
must  give  an  exact  reproduction,  on  a  smaller  scale,  of  the 
motion  of  the  piston  ;  otherwise  the  length  of  the  indicator- 
diagram  will  either  not  be  accurately  reduced,  or  the  events 
will  not  be  properly  timed. 

389.  The  table  opposite  gives  the  actual  dimensions  of  the 
principal  indicators  described,  as  obtained  by  careful  measure- 
ment of  those  owned  by  Sibley  College. 

390.  Reducing-motions  for  Indicators. — The   maximum 
motion  of  the  indicator-drum  is  usually  less  than  four  inches  ; 
consequently  it  can  seldom  be  connected  directly  to  the  cross- 
head  of  the  engine,  but  must  be  connected  to  some  apparatus 
which  has  a  motion  less  in  amplitude  but  corresponding  exactly 
in  all  its  phases  to  that  of  the  cross-head.     This  apparatus  is 
termed   a  reducing-motion.     Since   the  horizontal  components 
of  the  indicator-diagram  and  consequently  its  area  and  form 
depend  upon  the  motion  of  the  piston,  it  is  evident  that  the 
accuracy  of  the  diagram   depends   upon   the   accuracy  of  the 
reducing-motion.     Various  combinations  of  levers  and  pulleys 
have  been  used  *  for  reducing-motions,  a  few  of  which  will  be 


*  See  Thurston's  Engine  and  Boiler  Trials. 


530 


EXPERIMENTAL   ENGINEERING. 


[§  390- 


described.  Several  simple  forms  of  reducing-motion  are 
given  here  as  suggestions,  but  it  is  expected  that  the  student 
will  devise  other  motions  if  required,  and  ascertain  the  amount 
of  error,  if  any,  in  the  motion  used. 


H 


FlG,    242.— THE  SIMPLE  PENDULUM  REDUCING-MOTION. 

The  cheaper  and  more  easily  arranged  reducing-motion? 
consist  usually  of  some  form  of  swinging  lever  or  pendulum 
(see  Fig.  242)  pivoted  at  one  point,  and  connected  at  its 
lower  end  to  the  cross-head  by  a  lever.  The  indicator-cord 
is  attached  to  the  swinging  lever  at  some  point  having  the 
proper  motion.  These  motions  never  give  an  exact  reproduc- 


390.] 


THE    STEAM-ENGINE  INDICATOR. 


531 


tion  of  the  motion  of  the  piston ;  but  if  the  pendulum  and 
cross-head  are  simultaneously  at  the  centre  of  the  stroke,  the 
error  is  very  small. 


FIG.  243.— THE  BRUMBO  PULLEY. 

A  form  of  the  pendulum-motion,  called  the  Brumbo  pulley, 
is  frequently  used  as  shown  in  Fig.  243.  The  pendulum  is  some- 
times modified,  so  that  its  lower  end  is  pivoted  directly  to  a 


FIG.  244  —THE  PANTOGRAPH. 


point  in  the  cross-head,  its  upper  half  moving  vertically  in  a 
swinging  tube.  The  cord  is  attached  to  an  arc  on  this  tube  as 
in  Fig.  242. 


532 


EXPERIMEN  TA  L   ENGINEERING. 


[§  39'. 


The  pantograph,  or  lazy-tongs,  as  shown  in  Fig.  244  with 
plan  of  method  of  attachment  shown  in  Fig.  245,  is  a  perfect 
reducing  motion,  but  because  of  its  numerous  joints  it  is  not 
adapted  to  high-speed  engines. 


FIG.  245.— METHOD  OK  ATTACHING  THE  PANTOGRAPH. 

A  form  of  pantograph  with  four  joints  only,  shown  in  Fig. 
246,  is  much  better  adapted  to  high-speed  engines  than  the  one 
with  more  numerous  joints  shown  above. 


FIG.  246. — METHOD  OF  USING  THE  PANTOGRAPH. 

Reducing-wheels. — Reducing  wheels,  which  consist  of  a 
large  and  a  small  pulley  (see  Fig.  247)  attached  to  the  same 
axis,  are  extensively  used  by  engineers.  The  method  of  attach- 
ing this  reducing-motion  to  an  engine  is  shown  in  Fig.  248. 

391.  The  Indicator-cord.— The  indicator-cord  should  be  as 
nearly  as  possible  inextensible,  since  any  stretch  of  the  cord 
causes  a  corresponding  error  in  the  motion  of  the  indicator- 
arum.  As  it  is  nearly  impossible  to  secure  a  cord  that  will  not 


§  39I-] 


THE   STEAM-ENGINE  INDICATOR. 


533 


stretch,  it  should  be  made  as  short  as  possible,  and  a  fine  wire  of 
steel  or  iron  or  of  hard-drawn  brass  should  be  used  if  practicable, 


FlG.     247.— SCHABFFEK    AND    BuDENBERG    REDUCING-MOTION. 


FIG.  248.— WEBSTER  AND  PERKS  REDUCING-MOTION. 

The  indicator-cord  supplied  by  makers  of  indicators  is  a  braided 
hard  cotton  cord,  stretching  but  little  under  the  required  stress. 


534  EXPERIMENTAL   ENGINEERING.  [§  392- 

* 
If  a  "  rig"  is  to  be  permanently  erected,  it  is  recommended  that 

the  motion  be  taken  from  a  sliding  bar  attached  to  the  cross- 
head  and  extending  to  or  beyond  the  indicators.  The  angle 
of  the  cord  with  the  path  of  motion  of  the  cross-head  should 
be  as  nearly  constant  as  possible,  since  any  variation  in  this 
angle  will  cause  a  distortion  in  the  motion  of  the  drum. 

In  Figs.  243,  246,  and  248  will  be  seen  devices  to  over- 
come the  effect  of  angularity  of  the  indicator-cord. 

The  indicator-cord  is  usually  hooked  and  unhooked  into  a 
loop  in  a  cord  fastened  to  the  reducing-motion.  A  very  con- 
venient form  for  such  a  loop,  and  one  that  can  readily  be  ad- 
justed, is  shown  in  Fig.  249.  The  indicator-cord  is  usually 


FIG.  249.— THE  LOOP. 

provided  with  a  hook  fastened  as  shown  in  Fig.  182,  which  is 
hooked  when  diagrams  are  needed  into  the  loop  attached  to 
the  reducing-motion. 

The  author  would  strongly  urge  that  the  indicator-cord  be 
arranged  so  as  to  avoid  the  necessity  of  frequent  hooking  and 
unhooking,  thus  throwing  severe  and  unnecessary  strains  on 
the  indicator-drum  and  cord :  this  can  be  done  by  connecting 
a  point  on  the  cord  near  the  indicator  with  a  spiral  spring 
fastened  to  a  fixed  point  in  the  line  of  the  cord  produced.  This 
spring  should  be  strong  enough  to  keep  the  slack  out  of  the  cord. 
When  it  is  desired  to  stop  the  motion,  the  drum-cord  is  pulled 
toward  the  reducing-motion  to  the  extent  of  its  travel,  and 
held  or  tied  until  another  diagram  is  needed.  Some  of  the 
indicator-drums  are  provided  with  ratchets  or  detents  that 
serve  the  same  purpose.  When  several  indicators  are  in 
use  and  simultaneous  diagrams  are  required,  a  detent-motion 
worked  by  an  electric  current  will  prove  very  satisfactory. 
In  case  of  compound  engines  when  numerous  indicators  are  re- 
quired these  suggestions  become  of  even  greater  importance. 

392.  Standardization  of  the  Indicator. — The  accuracy  of 


§393-]  THE   STEAM-ENGINE   INDICATOR.  535 

the  indicator-diagram  depends  upon  the  following  features,  all 
of  which  should  be  the  subject  of  careful  examination : 

(1)  Uniformity  of  the  indicator-spring. 

(2)  Accuracy  of  the  drum-motion. 

(3)  Parallelism  of  the  piston-movement  to  the  cylinder. 

(4)  Parallelism  of  the  pencil-movement  to  the  axis  of  the 
drum. 

(5)  Friction  of  the  piston  and  pencil-movements. 

(6)  Lost  motion. 

The  calibration  of  these  parts  should  be  made  as  nearly  as 
possible  under  the  conditions  of  actual  use  and  as  described 
in  the  following  articles. 

393.  Calibration  of  the  Indicator-spring.— The  accuracy 
of  the  indicator-spring  is  only  to  be  determined  by  comparison 
with  standardized  apparatus.  This  may  be  done  as  follows  : 

Firstly  :  with  the  open  mercury  column.  This  can  be  done 
with  steam  only,  as  the  leakage  of  water  past  the  loosely-fitting 
piston  would  render  it  impossible  to  maintain  the  pressure. 
Insert  the  spring;  see  that  the* indicator  is  oiled  and  in  good 
condition.  Attach  the  indicator  as  previously  explained  for 
the  calibration  of  steam-gauges,  page  366;  put  paper  on  the 
drum;  turn  on  steam-pressure  until  the  instrument  is  warm; 
turn  off  the  steam,  and  pressing  the  pencil  lightly  against  the 
paper,  turn  the  drum  by  hand,  thus  drawing  the  atmospheric 
line.  Apply  pressure  by  increments  equal  to  one  fifth  that 
marked  on  the  spring;  keeping  the  motion  continually  upward, 
stopping  only  long  enough  to  draw  the  line  for  the  required 
pressure.  Take  ten  increments  first  up  then  down  ;  the  average 
position  of  any  line  will  give  the  ordinate  corresponding  to 
that  pressure ;  the  difference  between  any  two  lines  (see  Fig. 
250)  will  be  twice  the  friction  of  indicator-piston  at  that  point. 

Second  :  with  the  standard  scales.  This  method  was  devised 
by  Professor  M.  E.  Cooley,  of  Ann  Arbor.  In  this  case  the 
indicator  is  supported  on  a  bracket  above  the  platform  of  the 
scales.  Force  is  applied  to  the  indicator-piston  by  means  of  a 
rod  which  can  be  raised  or  lowered  by  turning  a  hand-wheel; 
this  rod  terminates  above  in  a  cap  nicely  fitted  to  the  under 


536 


EXPERIMEN TA  L   ENGINEERING. 


[§  393- 


side  of  the  piston,  and  below  it  rests  on  a  pedestal  standing  on 
the  platform  of  the  scales.  Any  force  applied  to  compress  the 
spring  is  registered  on  the  scale-beam.  The  reading  of  the 
scale-b£am  is  that  force  acting  on  one-half  square  inch,  as  the 
piston  is  usually  one-half  square  inch  in  area  ;  this  is  to  be  multi- 
plied by  2  to  correspond  with  the  reading  given  by  the  indica- 
tor-spring. The  indicator  can  be  heated  by  wrapping  rubber 
tubing  around  the  cylinder  and  passing  steam  through  the  tube. 


Up. 


'•TTp. 


Down. 


Down. 


FlG     25O. — iNDlCATOK-SPRING    CALIBRATION. 

FORM    FOR   CALIBRATION    OF    INDICATOR  SPRING. 

By  comparison  with 

Make  of  indicator 

Mark  and  No.  of  spring 

Date. . 


Observers  : 


No. 

.  Gauge. 

Actual 
Pressure. 

Ordinates. 

Actual 
Pressure. 

Error. 
Per  cent. 

Inches 

Lbs. 

Inches. 

Pounds. 

Up. 

Down. 

Mean. 

§  394.] 


THE   STEAM-ENGINE  INDICATOR. 


537 


The  indicator-springs  should  be  calibrated  as  nearly  as  possi- 
ble under  the  conditions  of  actual  use.  The  springs  are  elon- 
gated by  increase  in  temperature  and  weakened  because  of  that 
fact,  so  that  the  calibration  of  the  spring  cold  will  give  results 
which  differ  by  approximately  3  per  cent,  from  the  calibration  when 
the  spring  is  at  a  temperature  approximating  212°,  as  has  been 
proved  by  extended  experiments.* 

Various  forms  of  apparatus  have  been  devised  for  the  testing 
of  indicator-springs  both  cold  and  hot.  A  simple  device  is  shown 


FIG.  251.— INDICATOR-SPRING  TESTING  DEVICE. 


in  Fig.  251  consisting  of  a  cylinder,  A,  supported  on  a  bracket 
above  a  pair  of  scales  and  fitted  with  a  piston  having  an  area  of 
cross-section  exactly  the  same  as  the  indicator-piston.  A  rod 
from  this  piston  extends  downward  on  to  a  platform  scale,  as 
shown  in  the  figure.  The  indicator  is  connected  by  suitable 


Experiments,  Marks  and  Barraclough,  Vol.  XV,  Transactions    A.  S.  M.  E. 


538 


EXPERIMENTAL   ENGINEERING. 


[§  395- 


piping  to  the  upper  end  of  the  cylinder.  The  steam  for  the  pur- 
pose of  calibration  is  adjusted  in  pressure  by  a  valve,  E,  before 
it  enters  the  drum,  B.  The  pressure  in  the  steam  in  the  drum 
is  shown  on  the  attached  gauge.  This  steam-pressure  exerts 
an  upward  pressure  on  the  indicator-piston  and  a  downward 
pressure  on  the  piston  in  the  cylinder,  A,  which  latter,  cor- 
rected for  dead  weight,  is  measured  on  the  weighing-scales 
shown. 

A    modification    of    this   apparatus    is   shown    in  Fig.    252, 
which  consists  of  a  vessel,  A,  into  which  steam  can  be  admitted 


FIG.  252. — INDICATOR-SPRING  TESTING  APPARATUS. 


at  any  desired  pressure.  The  pressure  in  the  vessel  acts  on 
the  piston,  K,  which  is  \  square  inch  in  area  and  may  be 
measured  by  the  attached  scale-beam.  The  same  pressure 
reacts  on  the  indicator-piston.  By  taking  simultaneous  read- 
ings of  the  pressure  on  the  piston,  K,  and  on  the  indicator- 
piston,  the  calibration  may  be  performed  substantially  as 
described. 

This  apparatus  has  proved  satisfactory  after  an  extensive 
use.  It  can  be  purchased  of  Schaeffer  &  Budenberg  of  Brooklyn 
N.  Y. 


§395-]  THE    STEAM-ENGINE   INDICATOR.  539 

394.  Test  for  Parallelism  of  the  Pencil-movement  to  the 
Axis  of  the  Drum. — This  is  tested  by  removing  the  spring 
from  the  indicator,  rotating  the  drum,  and  drawing  an  atmos- 
pheric line  ;  then  hold  the  drum  stationary  in  various  positions 
and  press  the  piston  of  the  indicator  upward  throughout  its 
full  stroke,  while  the  pencil  is  in  contact  with  the  paper.     The 
lines  thus  drawn  should  be  parallel  to  each  other  and  perpen- 
dicular to  the  atmospheric  line. 

Parallelism  of  the  piston-movement  to  the  cylinder  axis  is 
shown  when  the  increments  for  equal  pressure  are  the  same  in  all 
positions  of  the  diagram.  It  is  important  that  the  piston  is  not 
cramped  or  pushed  over  by  the  spring,  in  any  part  of  its  stroke. 

Friction  of  the  piston  and  pencil-movement  can  be  determined 
in  the  calibration  of  the  indicator-spring  as  explained.  When 
the  spring  is  removed  from  the  indicator,  the  parts  should 
work  easily  and  freely  but  without  lost  motion. 

395.  Accuracy  of  the  Drum-motion. — The  accuracy  of  the 
drum-motion    depends  on-  the    form   of   the  drum-spring,  the 
mass  moved,  the  length  of  the  diagram,  and  the  elasticity  of 
the  connecting  cord. 

Indicator-drums  would  revolve  in  a  harmonic  motion  if 
the  inertia  of  the  mass  could  be  neglected.  The  speed  of  ro- 
tation is  greatest  near  the  half-stroke  of  the  piston  ;  therefore, 
if  the  drum-spring  tension  can  be  adjusted  so  as  to  exactly 
counterbalance  the  effect  of  the  inertia  of  the  moving  parts, 
the  theoretical  harmonic  motion  will  be  nearly  realized. 

In  most  indicator  drum-springs  the  tension  increases  directly 
in  proportion  to  the  extension.  Since  the  speed  of  the  drum 
is  greatest  at  half  stroke,  at  this  point  the  drum  will  run 
ahead  of  its  theoretic  motion  if  the  spring  tension  is  not  suffi- 
cient to  counteract  the  effect  of  the  inertia  of  the  moving  parts. 
Therefore  if  the  tension  of  the  drum-spring  is  adjusted  to 
exactly  balance  the  effect  of  inertia  at  half-stroke,  the  card 
should  be  as  nearly  as  possible  theoretically  correct.  To  ob- 
tain the  value  of  this  tension,  use  is  made  of  the  formulae  for 
the  harmonic  motion  of  a  body  as  follows.  Let 


540 


EXPERIMENTAL   ENGINEERING. 


[§395 


t  =  time  of  £  length  of  card  =  J  of  a  revolution  ; 
s  =  i  length  of  card  ; 

/  —  — j=  ;  (see  Church's  Mechanics.) 

2  v  a 

P  —  pM  =  T,  where  T  is  the  tension  in  the  spring  at  J  the 
length  of  the  card. 


p  =  -  sa  ; 


M=  —  =  mass  of  rotating  parts  ; 

o 


t*  = 


\Msl 


«=-f 

T_ 

a~~  Ws 


T  = 


The  foot,  pound,  second  system  is  used  in  the  formulae, 
The  results  are  shown  in  the  following  table. 

TABLE  FOR  TENSION  ON  INDICATOR  DRUM  OF  i.o  LB. 
1     'WEIGHT. 


Revolutions 
per 
Minute. 

Pounds  of 
Force  to  pull 
Drum  1.75  in. 

Revolutions 
Minute. 

Pounds  of 
Force  to  pull 
Drum  1.75  in. 

50 

O,IO 

225 

2-5 

75 

0.25 

250 

3-15 

100 

0.50 

275 

3-8 

125 

0.8 

3OO 

4-55 

150 

i.i5 

350 

6.15 

175 

1-55 

375 

7.0 

200 

2.O 

400 

S.o 

The  total  error  introduced  by  inertia  can  be  determined  as 
follows :  Attaching  the  indicator  to  an  engine,  permit  it  to 
run  sufficiently  long  to  harden  the  cord  and  the  knots,  then 
stop  the  engine,  turn  it  over  by  hand  and  find  the  length  of  the 
diagram  with  the  speed  so  small  as  to  eliminate  the  inertia ; 
leaving  the  cords  connected,  run  the  engine  at  full  speed :  any 


?  395-]  THE   STEAM-ENGINE   INDICATOR.  541 

inertia  etitct  will  be  shown  by  an  increase  in  the  length  of  the 
diagram.  This  increase  inlength  may  be  partly  due  to  stretch 
in  the  indicator-cord  caused  by  inertia  of  the  rotating  parts,  as 
even  with  the  best  tension  on  the  springs,  determined  as  ex- 
plained, it  may  be  sensibly  lessened  by  the  use  of  wire.  A 
simple  arrangement,  consisting  of  a  pin  and  co_nnecting-rod 
leading  to  the  face-plate  of  a  lathe,  the  tool-rest  being  utilized 
as  a  guide,  may  be  used  instead  of  an  engine  for  obtaining 
complete  determination  of  this  error.  The  amount  of  error 
caused  by  over-travel  of  the  drum  has  been  found  by  experi- 
ment to  be  from  0.5  to  1.5  per  cent  at  250  revolutions,  with  the 
best  tension  on  the  drum  spring. 

Uniform  Tension  on  the  Indicator-cord. — It  is  often  impor- 
tant to  determine  whether  the  drum-spring  maintains  a  uniform 
tension  on  the  cord,  or  whether  it  alternately  exerts  a  greater 


FIG.  253. — BROWN  DRUM-SPRING  TESTING-DEVICE. 

or  less  stress;  this  may  be  determined  by  the  instrument  shown 
in  Fig.  253.  The  testing  instrument  consists  of  a  wooden 
plate,  A,  on  one  end  of  which  is  fastened  the  brass  frame,  BB, 
carrying  the  slide,  C,  with  its  cross-head,  D.  The  head  of 
the  spring,  R,  is  screwed  to  the  cross-head,  while  the  other 
'end  is  connected  with  the  bent  lever,  G,  carrying  the  pencil 
The  connecting-rod,  E,  which  moves  the  slide,  C,  receives 
its  motion  from  a  crank  not  shown  in  the  figure.  The 
swinging  leaf  F  holds  the  paper  on  which  the  diagram  is  to  be 
taken.  The  indicator  to  be  tested  is  clamped  to  the  plate  as 
shown,  and  the  drum-cord  connected  with  the  free  end  of  the 
spring.  The  crank  is  made  to  move  at  the  speed  at  which 
it  is  desired  to  test  the  drum-spring.  The  paper  is  then 
pressed  .up  to  the  pencil  and  the  diagram  taken.  If  the  tension 


542  EXPERIMENTAL   ENGINEERING.  |_§  396 

on  the  cord  is  constant,  the  lines  which  represent  the  forwarc 
and  return  strokes  will  be  parallel  to  the  motion  of  the  slide 
but,  if  the  stress  is  not  constant,  the  pencil  will  rise  and  fall  a< 
the  stress  is  greater  or  less.  The  line  drawn  when  the  core 
has  been  detached  from  the  indicator  (Fig.  254)  is  the  line  of  nc 
stress.  In  the  diagram,  horizontal  distance  represents  the 
position  of  the  drum,  and  vertical  distance  represents  strair 
on  the  cord.  The  perfect  diagram  would  be  two  lines  neai 
together  and  parallel  to  the  line  of  no  stress,  and  would  repre- 
sent a  constant  stress,  and  consequently  a  constant  stretch  o 
the  cord,  from  which  no  error  would  result. 

When  the  length  of  the  cord  and  the  amount  it  will  stretcr 
under  varying  stresses  is  known,  the  errors  in  the  diagram  due 
to  stretch  of  cord  caused  by  irregular  stresses  applied  by  the 
drum-spring  can  be  calculated. 


Indicator.     250  revolutions  .     Indicator.     250  revolutions 

A  B 


Indicator.     400  revolutions  Indicator.    400  revolutions 

c 

FIG.  254.— DIAGRAMS  SHOWING  VARIATION  IN  DRUM-SPRING  STRESS. 

396.  To  Adjust  and  Calibrate  a  Drum-spring. 

1.  Find  the  weight  of  the  moving  parts,  and  compute  the 
theoretic  stress  on  the  indicator-cord.     (See  Article  395.) 

2.  Attach  to  the  face-plate  of  a  lathe  in  such  a  manner 
that  the  speed  can  be  varied  within  wide  limits. 

3.  Draw  diagrams  at  various  rates  of  speed,  various  lengths 
of  stroke,  and  various  tensions  on  the  drum-spring. 

4.  Find  the  error  in  the  diagram  for  each  condition.     Plot 
the  results,  and  deduce  from  the  curve  shown  the  best  length 
of  diagram  and  best  tension  for  each  speed. 


§  397-] 


THE   STEAM-ENGINE   INDICATOR. 


543 


5.  Repeat  the  same  operations  with  the  Brown  spring  test- 
ing-device, and  compare  the  results. 

397.  Method  of  Attaching  the  Indicator  to  the  Cylinder. 
— Holes  for  the  indicator  are  drilled  in  the  clearance-spaces  at 
the  ends  of  the  cylinders,  in  such  a  position  that  they  are  not 
even  partially  choked  by  any  motion  of  the  piston.  These 
holes  are  fitted  for  connection  to  half-inch  pipe:  they  are 
located  preferably  in  horizontal  cylinders  at  the  top  of  the 
cylinder ;  but  if  the  clearance-spaces  are  not  sufficiently  great 
they  may  be  drilled  in  the  heads  of  the  cylinder,  and  connec- 
tions to  the  indicators  made  by  elbows.  The  holes  for  the  in- 


x\\\-\\\\\\\\\\\\\\\\\\\\\\\^^ 

FIG.  255.— SECTION  OF  CROSBY  THREE-WAY  COCK. 


FIG.  256. — ELEVATION  OF  CROSBY 
THREE-WAY  COCK. 


dicator-cocks  are  usually  put  in  the  cylinders  by  the  makers  of 
the  engine,  but  in  case  they  have  to  be  drilled  great  care  must 
be  exercised  that  no  drill-chips  get  into  the  cylinder.  This  may 
be  entirely  prevented  by  blocking  the  piston  and  admitting 
twenty  or  thirty  pounds  of  steam-pressure  to  the  cylinder. 

The  connections  for  the  indicator  are  to  be  made  as  short  and 
direct  as  possible.  Usually  the  indicator-cock  can  be  screwed 
directly  into  the  holes  in  the  cylinder,  and  an  indicator  attached 
at  each  end.  In  case  a  single  indicator  is  used  to  take  dia- 
grams from  both  ends  of  the  cylinder,  half-inch  piping  with  as 
easy  bends  as  possible  is  carried  to  a  three-way  cock,  as  in  Fig. 


544  EXPERIMENTAL  ENGINEERING.  [§  39$- 

194,  to  which  the  indicator  is  attached.  The  cock  is  located 
as  nearly  as  possible  equidistant  from  the  two  ends  of  the 
cylinder. 

The  form  of  the  three-way  cock  is  shown  in  Figs.  199  and 
200.  and  the  method  of  connecting  in  Fig.  194. 

In  connecting  an  indicator-cock,  use  a  wrench  very  care- 
fully;  but  on  no  account  use  lead  in  the  connections,  as  it  is 
likely  to  get  in  the  indicator  and  prevent  the  free  motion  of 
the  piston. 

398.  Directions  for  Taking  Indicator-diagrams. 

Firstly,  provide  a  perfect  reducing-motion,  and  make  ar- 
rangements so  that  the  indicator-drum  can  be  stopped  .or 
started  at  full  speed  of  the  engine.  (See  Article  391.) 

Secondly,  clean  and  oil  the  indicator,  and  attach  it  to 
the  engine  as  previously  explained.  Insert  proper  spring  ;  oil 
piston  with  cylinder-oil. 

Thirdly,  put  proper  tension  on  the  drum-spring  (see  Article 
395) ;  see  that  the  pencil-point  is  sharp  and  will  draw  a  fine 
line. 

Fourthly,  connect  the  indicator-cord  to  the  reducing-motion; 
turn  the  engine  over  and  adjust  the  cord  so  that  the  indicator- 
drum  has  the  proper  movement  and  does  not  hit  the  stops. 

Fifthly,  put  the  paper  on  the  drum  ;  turn  on  steam,  allow  it 
to  blow  through  the  relief-hole  in  the  side  of  the  cock ;  then 
admit  steam  to  the  indicator-cylinder,  close  the  indicator-cock, 
start  the  drum  in  motion,  and  draw  the  atmospheric  line  with 
engine  and  drum  in  motion ;  open  the  cock,  press  the  pencil 
lightly  and  take  the  diagram ;  close  the  cock  and  draw  a  second 
atmospheric  line.  Do  not  try  to  obtain  a  heavy  diagram,  as  all 
pressure  on  the  card  increases  the  indicator  friction  and  causes 
more  or  less  error.  Take  as  light  a  card  as  can  be  seen  ;  brass 
point  and  metallic  paper  are  to  be  used  when  especially  fine 
diagrams  are  required. 

When  the  load  is  varying,  and  the  average  horse-power  is 
required,  it  is  better  to  allow  the  pencil  to  remain  during  a 
number  of  revolutions,  and  to  take  the  mean  effective  pressure 
from  the  several  diagrams  drawn. 


§  399-]  THE   STEAM-ENGINE  INDICA  TOR.  545 

Remove  card  after  diagram  has  been  taken,  and  on  the 
back  of  card  make  note  of  the  following  particulars,  as  far  as 
conveniently  obtainable : 


No  Time.  . 

Built  by  

Length  of  stroke      .  .  <  • 

Pressure 

Barometer  reads    

Throttle 

Position  of  throttle-valve.   ..    .>...... 

Regulator 

Remarks  

*•              "         "exhaust-pipe  

..Valves.. 

Sixthly,  after  a  sufficient  number  of  diagrams  has  been  taken,, 
remove  the  piston,  spring,  etc.,  from  the  indicator  while  it  is. 
still  upon  the  cylinder ;  allow  the  steam  to  blow  for  a  moment 
through  the  indicator-cylinder,  and  then  turn  attention  to  the 
piston,  spring,  and  all  movable  parts,  which  must  be  thoroughly 
wiped,  oiled,  and  cleaned.  Particular  attention  should  be  paid 
to  the  springs,  as  their  accuracy  will  be  impaired  if  they  are  al- 
lowed to  rust ;  and  great  care  should  be  exercised  that  no  gritty 
substance  be  introduced  to  cut  the  cylinder  or  scratch  the 
piston.  Be  careful  never  to  bend  the  steel  bars  or  rods. 

399.  Care  of  the  Indicator. — The  steam-engine  indicator 
is  a  delicate  instrument,  and  its  accuracy  is  liable  to  be  im- 
paired by  rough  usage.  It  must  be  handled  with  care,  kept 
clean  and  bright ;  its  journals  must  be  kept  oiled  with  suitable 
oil.  It  must  be  kept  in  adjustment.  In  general,  all  screws  can 
be  turned  by  hand  sufficiently  tight,  and  no  wrench  should  be 
used  to  connect  or  disconnect  it.  Never  use  lead  on  the  con- 
nections. Before  using  it,  take  it  apart,  clean  and  oil  it.  Try 
each  part  separately.  See  if  it  works  smoothly ;  if  so,  put  it 
together  without  the  spring.  Lift  the  pencil-lever,  and  let  it 


546  EXPERIMENTAL   ENGINEERING.  [§  399- 

fall ;  if  perfectly  free,  insert  the  spring  as  explained,  and  see  that 
there  is  no  lost  motion  ;  oil  the  piston  with  cylinder-oil,  and  all 
the  bearings  with  nut-  or  best  sperm-oil.  Give  it  steam,  but  do 
not  attempt  to  take  a  card  until  it  blows  dry  steam  through  the 
relief.  If  the  oil  from  the  engine  gums  the  indicator,  always 
take  it  off  and  clean  it.  After  using  it  remove  the  spring,  dry 
it  and  all  parts  of  the  indicator,  then  wipe  off  with  oily  waste. 
Fasten  the  indicator  in  its  box,  in  which  .it  will  go,  as  a  rule, 
only  one  way,  but  it  requires  no  pounding  to  get  it  properly  in 
place ;  carefully  close  the  box  to  protect  it  from  dust. 


CHAPTER   XVII. 


THE   INDICATOR-DIAGRAM. 


400.  Definitions. — The  indicator-diagram  is  the  diagram 
taken  by  the  indicator,  as  explained  in  Article  378,  page  515. 

In  the  diagram  the  ordinates  correspond  to  the  pressures 
per  square  inch  acting  on  the  piston,  the  abscissae  to  the  travel 


.  257.— DIAGRAM  FROM  AN  IMPROVED  GREENE  ENGINE.     CYLINDER,  16  INCHES  IN  DIAMETER, 
36  INCHES  STROKE.    BOILER-PRESSURE,  100  LBS.    80  REVOLUTIONS  PER  MINUTE.    SCALE,  50. 

of  the  piston.  During  a  complete  revolution  of  an  engine 
occur  four  phases  of  valve-motion  which  are  shown  on  the  indi- 
cator-diagram, viz. :  admission,  CDE,  when  the  valve  is  open 
and  the  steam  is  passing  into  the  cylinder;  expansion,  EF, 
when  steam  is  neither  admitted  nor  released  and  acts  by  its 

547 


548  EXPERIMENTAL   ENGINEERING.  [§ 

expansive  force  to  move  the  piston ;  exhaust,  FGH,  when 
the  admission-port  is  closed  and  »the  exhaust  opened  so  that 
steam  is  escaping  from  the  cylinder;  and  compression,  HC> 
when  all  the  ports  are  closed  and  the  steam  remaining  in  the 
cylinder  acts  to  bring  the  piston  to  rest. 

The  Atmospheric  Line,  AB,  is  a  line  drawn  by  the  pencil  of 
the  indicator  when  the  connections  with  the  engine  are  closed 
and  both  sides  of  the  piston. are  open  to  the  atmosphere.  This 
line  represents  on  the  diagram  the  pressure  of  the  atmosphere, 
or  zero  gauge-pressure. 

The  Vacuum  Line,  OK,  is  a  reference-line  drawn  a  distance 
corresponding  to  the  barometer-pressure  (usually  about  14.7 
pounds)  by  scale  below  the  atmospheric  line.  It  represents  a 
perfect  vacuum,  or  absence  of  all  pressure. 

The  Clearance  Line,  OY,  is  a  reference-line  drawn  at  a  dis- 
tance from  the  end  of  the  diagram  equal  to  the  same  per  cent 
of  its  length  as  the  clearance  or  volume  not  swept  through  by 
the  piston  is  of  the  piston-displacement.  The  distance  between 
the  clearance  line  and  the  end  of  the  diagram  represents  the 
volume  of  the  clearance  of  the  ports  and  passages  at  the  end  of 
the  cylinder. 

The  Line  of  Boiler-pressure,  JK,  is  drawn  parallel  to  the 
atmospheric  line,  and  at  a  distance  from  it  by  scale  equal  to 
the  boiler-pressure  shown  by  the  gauge.  The  difference  in 
pounds  between  it  and  DE  shows  the  loss  of  pressure  due  to 
the  steam-pipe  and  the  ports  and  passages  in  the  engine. 

The  Admission  Line,  CD,  shows  the  rise  of  pressure  due  to 
the  admission  of  steam  to  the  cylinder  by  opening  the  steam- 
valve.  If  the  steam  is  admitted  quickly  when  the  engine  is 
about  on  the  dead-centre,  this  line  will  be  nearly  vertical. 

The  Point  of  Admission,  C,  indicates  the  pressure  when  the 
admission  of  steam  begins  at  the  opening  of  the  valve. 

The  Steam  Line,  DE,  is  drawn  when  the  steam- valve  is  open 
and  steam  is  being  admitted  to  the  cylinder. 

The  Point  of  Cut-off,  E,  is  the  point  where  the  admission 
of  steam  is  stopped  by  the  closing  of  the  valve.  It  is  difficult 
to  determine  the  exact  point  at  which  the  cut-off  takes  place. 


§400.J  THE   INDICATOR   DIAGRAM.  549 

It  is  usually  located  where  the  outline  of  the  diagram  changes 
its  curvature  from  convex  to  concave.  It  is  most  accurately 
determined  by  extending  the  expansion  line  and  steam  line  so 
that  they  meet  at  a  point. 

The  Expansion  Curve,  EF,  shows  the  fall  in  pressure  as  the 
steam  in  the  cylinder  expands  doing  work. 

The  Point  of  Release,  F,  shows  when  the  exhaust-valve 
opens. 

The  Exhaust  Line,  FG,  represents  the  change  in  pressure 
that  takes  place  when  the  exhaust-valve  opens. 

The  Backpressure  Line,  GH,  .shows  the  pressure  against 
which  the  piston  acts  during  its  return  stroke.  On  diagrams 
taken  from  non-condensing  engines  it  is  either  coincident  with 
or  above  the  atmospheric  line,  as  in  Fig.  201.  On  cards  taken 
from  condensing  engines  it  is  found  below  the  atmospheric 
line,  and  at  a  distance  greater  or  less  according  to  the  vacuum 
obtained  in  the  cylinder. 

The  Point  of  Exhaust  Closure,  H,  is  the  point  where  the 
exhaust-valve  closes.  It  canno^  be  located  very  definitely,  as 
the  first  slight  change  in  pressure  is  due  to  the  gradual  closing 
of  the  valve. 

The  Point  of  Compression,  H,  is  where  the  exhaust-valve 
closes  and  the  compression  begins. 

The  Compression  Curve,  HC,  shows  the  rise  in  pressure  due 
to  the  compression  of  the  steam  remaining  in  the  cylinder 
after  the  exhaust-valve  has  closed. 

The  Initial  Pressure  is  the  pressure  acting  on  the  piston 
at  the  beginning  of  the  stroke. 

The  Terminal  Pressure  is  the  pressure  above  the  line  of 
perfect  vacuum  that  would  exist  at  the  end  of  the  stroke  if 
the  steam  had  not  been  already  released.  It  is  found  by  con- 
tinuing  the  expansion  curve  to  the  end  of  the  diagram,  as  in 
Fig.  20 1.  This  pressure  is  always  measured  from  the  line  of 
perfect  vacuum,  hence  it  is  the  absolute  terminal  pressure. 

Admission  Pressure  is  the  pressure  acting  on  the  piston  at 
•end  of  compression,  and  is  usually  less  than  initial  pressure. 


550  EXPERIMENTAL   ENGINEERING.  [§  4OO- 

Compression  Pressure  is  the  pressure  acting  on  the  piston  at 
beginning  of  compression  ;  this  is  also  the  least  back  pressure. 

Cut-off  Pressure  is  the  pressure  acting  on  the  piston  at 
beginning  of  expansion. 

Release  Pressure  is  the  pressure  acting  on  the  piston  at  end 
of  expansion. 

Mean  Forward  Pressure  is  the  average  height  of  that  part 
of  the  diagram  traced  on  the  forward  stroke. 

Mean  Back  Pressure  is  the  average  height  of  that  part 
traced  on  the  return  stroke. 

Mean  Effective  Pressure  (M.  E.  P.)  is  the  difference  between 
mean  forward  and  mean  back  pressure  during  a  forward  and 
return  stroke,,  It  is  the  length  of  the  mean  ordinate  inter- 
cepted between  the  top  and  bottom  lines  of  the  diagram  mul- 
tiplied by  the  scale  of  the  diagram.  It  is  obtained  without 
regard  to  atmospheric  or  vacuum  lines. 

Ratio  of  Expansion  is  the  ratio  of  the  volume  of  steam  in 
tlie  cylinder  at  end  of  the  stroke,  compared  with  that  at  cut- 
off. In  computations  for  this  quantity  the  volume  of  clear- 
ance must  be  taken  into  account.  Ratio  of  expansion  is 
denoted  by  r.  For  hyperbolic  expansion,/  being  pressure  in 
pounds  per  square  foot  at  cut-off,  and  v  the  corresponding 
total  volume,  the  work  done  per  stroke  and  per  square  foot  of 
area  =  pv(\  +  Hy  log  r). 

The  volume  may  be  expressed  as  proportional  to  linear 
feet,  with  an  additional  length  equal  to  the  per  cent  of  clear- 
ance, since  the  area  of  the  cylinder  is  constant.  The  product 
of  pressure  per  square  foot  into  total  volume  is  a  constant 
quantity  for  hyperbolic  expansion.  The  ratio  of  expansion  is 
the  reciprocal  of  the  cut-off  measured  from  the  clearance  line. 
This  cut-off  is  distinguished  from  that  shown  directly  on  the 
card  by  designating  it  as  the  absolute  cut-off. 

Initial  Expansion  is  the  fall  of  pressure  during  admission, 
due  to  an  imperfect  supply  of  steam. 

Wire-drawing  is  the  fall  of  pressure  between  the  boiler 
and  cylinder ;  it  is  usually  indicated  by  initial  expansion. 


§401.] 


THE   INDICATOR-DIAGRAM. 


551 


401.  Measurement  of  Diagrams.— The  diagrams  taken 
are  on  a  small  scale,  they  are  often  irregular,  and  the  boundary 
lines  are  frequently  obscure,  so  that  the  measurement  must  be 
made  with  great  care. 

The  diagrams  may  be  taken  from  each  end  of  the  cylinder 
on  a  separate  card,  as  shown  in  Fig.  257;  or  by  the  use  of  the 
three-way  cock  (see  Article  398),  in  which  case  the  two  dia- 
grams will  be  drawn  on  the  same  card  as  shown  in  Fig.  258.  In 
the  latter  case  each  diagram  is  to  be  considered  separately;  that 
is,  the  area  of  each  diagram,  as  CDEBFC  and  GHIJKG,  is  to 


FIG.    258. 

be  determined  as  though  on  a  separate  card.  The  object  of 
diagram-measurements  is  principally  to  obtain  the  mean  effect- 
ive pressure  (M.  E.  P.). 

Two  methods  are  practised. 

First,  the  method  of  ordinates.  In  this  case  the  atmos- 
pheric line  AB  is  divided  into  ten  equal  spaces,  and  ordinates 
are  erected  from  the  centre  of  each  space.  The  sum  of  the 
length  of  these  various  ordinates  divided  by  the  number  gives 
the  mean  ordinate.  This  multiplied  by  the  scale  of  the  dia- 
gram gives  the  mean  effective  pressure.  The  sum  of  the 
ordinates  is  expeditiously  obtained  by  successively  transferring 
the  length  of  each  ordinate  to  a  strip  of  paper  and  measuring 
its  length. 

Secondly,  with  the  planimeter.  The  planimeter  gives  the 
mean  ordinate  much  more  accurately  and  quickly  than  the 


552 


EXPERIMEN  TA  L   ENGINEERING. 


[§  402. 


method  of  ordinates.  The  various  planimeters  are  fully 
'described,  pages  32  to  55. 

With  any  planimeter  the  area  of  the  diagram  can  be  ob- 
tained, in  which  case  the  mean  ordinate  is  to  be  found  by 
dividing  by  the  length  of  the  diagram.  Several  of  the  pla- 
nimeters give  the  value  of  the  mean  ordinate,  or  M.  E.  P., 
directly. 

In  some  instances  the  indicator-diagram  has  a  loop,  as  in 
Fig. 2 59, caused  by  expanding  below  the  back-pressure  line;  in 
this  case  the  ordinates  to  the  loop  are  negative  and  should  be 


FIG.  259. 

subtracted  from  the  lengths  of  the  ordinates  above.  In  case 
of  measurement  by  the  planimeter,  if  the  tracing-point  be 
made  to  follow  the  expansion-line  in  the  order  it  was  drawn  by 
the  indicator-pencil,  the  part  within  the  loop  will  be  circum- 
scribed by  a  reverse  motion,  and  will  be  deducted  automatically 
by  the  instrument,  so  that  the  reading  of  the  planimeter  will 
be  the  result  sought. 

402.  Indicated  Horse-power. — Indicated  horse-power  is 
the  horse-power  computed  from  the  indicator-diagram,  being 
obtained  by  the  product  of  M.  E.  P.  (/),  length  of  stroke  in 
feet  (/),  area  of  piston  in  square  inches  (a),  and  number  of  revolu- 
tions («),  as  represented  in  the  formula. plan  -j-  33,000.  In  this 
computation  the  area  on  the  crank  side  of  the  piston  is  to  be 
corrected  for  area  of  piston-rod,  and  the  two  ends  of  the  cylin- 
ders computed  as  separate  engines.  Further,  in  this  computa- 
tion, it  will  not  in  general  Answer  to  multiply  the  average 
M.E.P.  of  a  number  of  cards  by  the  length  of  stroke  and  by  the 


§403.]  THE   INDICATOR-DIAGRAM.  553 

average  of  the  number  of  revolutions,  but  each  card  must  be 
subjected  to  a  separate  computation  and  the  results  averaged. 
This  can  be  readily  done  for  each  engine  by  computing  a  table 
made  up  of  the  products  of  the  average  value  of  n  by  length 
of  stroke  and  area  of  piston,  and  for  different  values  of  M.  E.  P. 
from  I  to  10.  Take  from  this  table  the  values  corresponding  to 
the  given  M.  E.  P.,  increase  or  diminish  this  as  required  by 
the  per  cent  of  change  of  speed  from  the  average.  A  very 
convenient  table  for  this  purpose,  entitled  "  Horse-power  per 
Pound,  Mean  Pressure,"  is  given  in  the  Appendix  to  this  work, 
arranged  with  reference  to  diameter  of  cylinder  in  inches  and 
piston-speed  in  feet  per  minute. 

403.  Form  of  the  Indicator-diagram. — The  form  of  the 
indicator-diagram  has  been  carefully  worked  out  for  the  ideal 
case  by  Rankine  and  CotterelL*  In  the  ideal  case  the  steam 
works,  in  a  non-conducting  cylinder,  and  all  loss  of  heat  is  due 
to  transformation  into  work,  the  expansion  in  such  a  case  being 
adiabatic.  In  the  actual  case  the  problem  is  much  more  com- 
plicated, since  a  large  portion  of  the  heat  is  utilized  in  heating 
the  cylinder,  and  is  returned  to  the  steam  at  or  near  the  time 
of  exhaust,  doing  little  work.  It  is  found,  however,  in  the  best 
engines  working  with  quick-acting  valve-gear,  that  the  steam 
and  back-pressure  lines  are  straight  and  parallel  to  the  atmos- 
pheric line,  and  that  the  expansion  and  compression  lines  are 
very  nearly  hyperbolae,  asymptotic  to  the  clearance  line  and 
to  the  vacuum  line. 

If  we  denote  by/  the  pressure  measured  from  the  vacuum 
line,  and  by  v  the  volume  corresponding  to  a  distance  meas- 
ured from  the  clearance  line,  so  that/7/  shall  be  the  co-ordinates 
of  any  point,  we  shall  have  as  characteristic  of  the  hyperbola 

pv  =  constant. 

This  is  the  same  as  Mariotte's  law  for  the  expansion  of  non- 
condensible  gases,  since,  according  to  that  law,  the  pressure 
varies  inversely  as  the  volume. 

*  Steam-engine,  by  James  H.  Cotterell. 


554 


EXPERIMENTAL   ENGINEERING. 


[§404. 


Rankine  found  by  examination  of  a  great  many  actual  cases 
that  the  expression  pv§  =  constant  agrees  very  nearly  with  the 
ideal  case  of  adiabatic' expansion.  The  variation  from  the  ideal 
expansion  line  in  any  given  case  may  be  considerable,  and  the 
hyperbola  drawn  from  the  same  origin  is  considered  as  good  a 
reference-line  as  any  that  can  be  used,  and  the  student  should 
become  familiar  with  the  best  methods  of  constructing  it. 

404.  Methods  of  Drawing  an  Hyperbola. — The  methods 
of  drawing  an  hyperbola,  the  clearance  and  vacuum  lines  being 
given,  are  as  follows : 

First  Method.  (See  Fig.  260.) — CB,  the  clearance  line,  and 
CD,  the  vacuum  line,  being  given,  draw  a  line  parallel  to  the 


FIG.  260.— METHOD  OF  DRAWING  AN  HYPERBOLA. 

atmospheric  line  through  B ;  find  by  producing  the  steam  and 
expansion  lines  the  point  of  cut-off,  c.  Draw  a  series  of 
radiating  lines  from  the  point  C  to  the  points  E,  F,  G,  H,  and 
A,  taken  at  random,  and  a  line  cb  intersecting  these  lines, 
drawn  from  c  parallel  to  BC.  From  the  points  of  the  inter- 
section of  cb  with  these  radiating  lines  draw  horizontal  lines  to 
meet  vertical  lines  drawn  from  the  points  E,  F,  G,  H,  and 


§  405-] 


THE   INDICATOR-DIAGRAM. 


555 


A  ;  the  intersections  of  these  lines  at  e,  f,  gy  /?,  and  a  are  points 
in  the  hyperbola  passing  through  the  point  c.  If  it  is  desired 
to  produce  the  hyperbola  from  a  upward,  the  same  method  is 
used,  but  the  line  AB  is  drawn  through  the  point  a,  and  the 
vertical  lines  are  extended  above  AB  instead  of  below. 

Second  Method.  (See  Fig.  261.) — The  hyperbola  may  be 
drawn  by  a  method  founded  on  the  principle  that  the  inter- 
cepts made  by  a  straight  line  intersecting  an  hyperbola  and  its 
asymptotes  are  equal.  Thus  if  abed  represent  an  hyperbola, 
BC  and  CD  its  asymptotes,  then  the  intercepts  aa'  and  bb' 
made  by  the  straight  line  a'b'  are  equal. 

To  draw  the  hyperbola :  Beginning  at  any  point,  as  a,  draw 


FIG.  261.— METHOD  OF  DRAWING  AN  HYPERBOLA. 

the  straight  line  a'b1 ,  and  lay  off  from  the  line  CD  b'b,  equal  to 
a' a ;  then  will  b  be  one  point  in  the  hyperbola.  Draw  a  similar 
line  c'd'  through  b,  making  d'c  equal  c'b  ;  then  will  c  be  another 
point  in  the  hyperbola.  This  process  can  be  repeated  until  a 
suitable  number  of  points  is  found  ;  the  hyperbola  is  to  be 
drawn  through  these  points.  A  similar  method  can  be  used 
to  draw  the  hyperbola  EF. 

405.  Construction  of  Saturation  and  Adiabatic  Curves. 

—The  saturation  curve  of  steam  is  represented  almost  exactly 

by  the  equation  pv&  —  a  constant.     This  is  the  curve  whose 


556  EXPERIMEN  TA  L   ENGINEERING.  [§  4-O  5  • 

volumes  and  pressures  correspond  to  those  given  in  the  steam- 
tables  ;  no  doubt  the  easiest  way  to  construct  such  a  curve  is 
to  take  the  volumes  from  the  steam-tables  corresponding  to 
given  pressures  and  set  them  off  along  the  volume  axis  ;  lay 
off  the  corresponding  pressures  as  ordinates  ;  then  a  curve 
drawn  through  the  extremities  of  the  ordinates  will  be  the  ex- 
pansion curve,  which,  as  the  form  of  the  equation  shows,  does 
not  differ  greatly  from  an  hyperbola. 

The  adiabatic  curve,  or  that  corresponding  to  neither  gain 
nor  loss  of  heat,  is  expressed  approximately  by  pv*$  =  constant,* 
and  differs  somewhat  more  from  the  hyperbola  than  the  satu- 
ration curve. 

Any  of  the  exponential  curves  which  are  represented  by 
the  equation  pvn-  =  pjj?  =  p^v"  can  be  drawn  as  follows  : 

From  the  above  expression 


n  log  v  +  log/  =  n  log  v, 
from  which 

log/  =  n  log  vl  +  log/,  —  n  log  v  ; 

from  which,  if  n,  v^  ,  and  v  are  known,/  may  be  determined. 
The  values  of  n  are  as  follows  : 

Equilateral  hyperbola,        n  =  i  ; 
Saturation  curve  —  steam,  n  =  -J-J  =  1.0646; 
Adiabatic  curve  —  steam,    n  =  1.0^5  +0.14; 

gas,        n  =  1.408; 
Isothermal     "  "          n  —  i.o. 

These  three  expansion  curvesf  are  represented  in  Fig.  262  ; 
the  pressures  from  o  to  90  pounds  per  square  inch  are  repre- 
sented by  the  ordinates,  and  the  volumes  in  cubic  feet  corre- 
sponding to  one  pound  in  weight  are  represented  by  abscissae. 

*  Rankine's  Steam-epgine,  page  385. 

fSee  Thurston's  Engine  and  Boiler  Trials,  page  251. 


THE   INDICATOR-DIAGRAM. 


557 


In  the  figure  the  curve  A  to  G  is  the  hyperbola,  A  to  /  the 
saturation  curve,  and  A  to  L  the  adiabatic  curve.  ON  is  the 
axis  of  the  hyperbola,  of  which  OB  and  OH  are  asymptotes. 
It  is  to  be  noticed  that  the  saturation  curve  corresponds  to  a 
uniform  quality  of  steam,  the  adiabatic  curve  to  a  condition 
in  which  the  moisture  is  increasing,  and  the  hyperbolic  curve 


1800  1700 


1500    1400    1300    1200    1100    1000     900      800      700     600      500     400      300     300      100 
FIG.  262. — THE  THREE  EXPANSION  CURVES. 


to  a  condition  in  which  the  moisture  is  decreasing,  the  latter 
agreeing  more  closely  with  the  actual  condition. 

406.  Weight  of  Steam  from  the  Indicator-diagram.— 
The  diagram  shows  by  direct  measurement  the  pressure  and 
volume  at  any  point  in  the  stroke  of  the  piston ;  the  weight 
per  cubic  foot  for  any  given  pressure  may  be  taken  directly 
from  a  steam-table.  The  method,  then,  of  finding  the  weight 
of  steam  for  any  point  in  the  stroke  is  to  find  the  volume  in 
cubic  feet,  including  the  clearance  and  piston  displacement  to 
the  given  point,  which  must  be  taken  at  cut-off  or  later,  and 
multiply  this  by  the  weight  per  cubic  foot  corresponding  to 
the  pressure  at  the  given  point  as  measured  on  the  diagram. 
This  will  give  the  weight  of  steam  in  the  cylinder  accounted 
for  by  the  indicator-diagram,  per  stroke.  In  an  engine  work- 
ing with  compression,  the  weight  of  steam  at  terminal  pressure 


558'  EXPERIMENTAL   ENGINEERING.  [ 

filling  the  clearance-space  is  not  exhausted  ;  this  weight,  com- 
puted for  a  volume  equal  to  clearance  and  with  weight  per 
cubic  foot  corresponding  to  compression  pressure,  should  be 
subtracted  from  the  above.  This  may  be  reduced  to  pounds 
of  steam  per  I.  H.  P.  per  hour,  by  multiplying  by  the  number 
of  strokes  required  to  develop  one  horse-power  per  hour  of 
time. 

The  method  of  computing  would  then  be  :  Find  the  weight 
per  cubic  foot,  from  a  steam-table  corresponding  to  the  abso- 
lute pressure,  at  the  given  point,  multiply  this  by  the  corre- 
sponding volume  in  cubic  feet,  including  clearance,  and  this  by 
the  number  of  strokes  per  hour.  Correct  this  for  the  steam 
imprisoned  in  the  clearance-space.  Divide  this  by  the  horse- 
power developed,  and  we  shall  have  the  consumption  in  pounds 
of  dry  steam  per  I.  H.  P.  as  shown  by  the  diagram.  Thus  let 

A  —  area  of  piston  in  square  feet  ; 
a—     "     "        "       "        "       inches; 
N  —-  number  of  strokes  per  hour; 
n=        "        "         "         "    minute; 
w  =  weight  of  cubic  foot  of  steam  at  the  given  pressure  ; 

/  =  total  length  of  stroke  in  feet  ; 
4  =  length  of  stroke  in  feet  to  point  under  consideration  ; 

c  =  per  cent  of  clearance  ;  /'  =  la  +  cl\  b  =  corresponding 

per  cent  ; 
w'  =  weight  of  cubic  foot  of  steam  at  compression  pressure. 

Then  the  consumption  of  dry  steam  in  pounds  per  hour  per 
horse-power  (indicated). 


=  _          =  6oina(bw  -  cw')      i 

H.P/  '       144       plan  p 

33,000 

The  above  equation  corrects  for  the  steam  caught  in  the 
clearance  spaces  during  compression. 

As  an  example:  Commute  the  steam  consumption  as  shown 
in  Fig.  257  at  point  of  cut-off  E  and  at  terminal  pressure. 


§406.]  THE   INDICATOR-DIAGRAM.  559 

The  absolute  pressure  shown  by  the  diagram  is  97  pounds 
at  cut-off  and  37  at  end  of  the  stroke.  Neglect  steam  in  clear- 
ance. 

The  length  of  stroke  total  is  3  feet,  at  cut-off  is  £  foot. 

Clearance  is  3.2  per  cent.     M.  E.  P.  (/)  is  50  pounds. 

Steam-consumption  at  Cut-off.  —  From  steam-table  ze/—  0.2208. 


6.I7  Ib,  per  I.H.P.  per  hour. 


Steam-  consumption   at  End  of  Stroke.  —  From   steam-table 
w  =  0.0896. 


This,  it  should  be  noticed,  is  not  the  actual  weight  of  steam 
used  per  horse-power  by  the  engine,  but  is  that  part  which  cor- 
responds to  the  amount  of  dry  steam  remaining  in  the  cylinder 
at  the  points  under  consideration.  The  amount  is  usually  less 
when  computed  at  cut-off  than  at  the  end  of  the  stroke,  since 
some  of  the  steam  which  was  condensed  when  the  steam  first 
entered  the  cylinder  is  restored  by  evaporation  during  the  latter 
portion  of  the  period  of  expansion. 

The  equations  and  examples  as  given  above  apply  only  to 
a  simple  engine.  They  may  be  applied  to  a  compound  or  triple- 
expansion  engine  by  considering  that  all  the  work  is  done  in  the 
low-pressure  cylinder  as  represented  on  a  combined  diagram. 
In  such  a  case,  p  of  the  formula  would  equal  the  equivalent 
M.  E.  P.  for  the  combined  diagram.  .  That  is,  pf/r  +  p^/=pt 
in  which  r  is  the  ratio  of  the  areas  of  the  cylinders,  p'  the  M.  E.  P. 
of  the  high-,  and  p"  that  of  the  low-pressure  cylinder. 

If  we  consider  the  steam- consumption  only  for  the  end  of 
the  stroke,  la  of  equation  (i)  becomes  equal  to  I,  and  the  equation 
reduces  to  the  following  form : 

(2) 


560  EXPERIMENTAL   ENGINEERING. 

Neglecting  the  clearance, 

;    -    .  '.'    .....    (3) 


in  which  /  =  the  M.  E.  P.  of  the  diagram,  and  w  the  weight 
per  cubic  foot  corresponding  to  the  terminal  pressure.  For- 
mula (3)  has  been  tabulated  as  follows  : 

Thompson's  tables,  given  in  the  Appendix,  give  values  of 
I3,75ow,  and  the  tabular  values  must  be  divided  by  the  M.  E.  P, 
to  give  the  steam-consumption  per  I.  H.  P.  per  hour. 

Tabor's  tables  give  values  of  ,  and  the  tabular  values 

must  be  multiplied  by  the  weight  of  a  pound  of  steam  corre- 
sponding to  the  terminal  pressure,  to  give  the  steam-consump- 
tion. 

Williams's  tables,  published   in  the  Crosby  catalogue,  give 

values  of  —  —  —  ,  and  the  results  in  each  case  have  to  be  multi- 

42543 
plied  by  32.  32^  to  give  the  steam-consumption. 

A  graphical  correction  is  made  in  all  cases  for  compression 
by  drawing  a  horizontal  line  through  the  terminal  pressure  to 
compression  line  of  diagram,  and  multiplying  the  result  given 
in  the  table  by  the  ratio  of  the  portion  of  this  line  intercepted 
between  terminal  point  and  compression,  to  the  whole  stroke. 

407.  Clearance  Determined  by  the  Diagram.  —  The 
clearance  is  usually  to  be  determined  by  actual  measurement 
of  the  volume  of  the  spaces  not  swept  through  by  the  piston, 
and  comparing  this  result  with  the  volume  of  piston-displace- 
ment, the  ratio  being  the  clearance.  Since  the  expansion  and 
compression  lines  of  the  diagram  are  nearly  hyperbolae,  the 
clearance  line  can  be  drawn  by  a  method  nearly  the  reverse  of 
that  used  in  constructing  an  hyperbola  (Article  404). 

In  this  case  proceed  as  follows  :  Lay  off  the  vacuum  line 
CD  (Fig.  207)  parallel  to  the  atmospheric  line  FT,  and  at 
a  distance  corresponding  to  the  atmospheric  pressure.  The 
position  of  the  clearance  line  can  be  determined  by  two  methods, 
corresponding  to  those  used  in  drawing  the  hyperbola.  First 


§  408.] 


THE  INDl  CA  TOR-DIA  GRA  M. 


561 


method ':  Take  two  points,  a  and  b  in  the  expansion  curve  and 
c  and  d  in  the  compression  line,  and  draw  horizontal  and 
vertical  lines  through  these  points,  forming  rectangles  aa'bb' 
and  cc'dd '.  Draw  the  diagonal  of  either  rectangle,  as  a'b' ,  to 
meet  the  vacuum  line  CD :  the  point  of  intersection  C  will  be. 


FIG   263.— METHODS  OF  FINDING  THE  CLEARANCE. 

a  point  in  the  clearance  line  CB,  and  the  clearance  will  equal 
CN  ~-  FT.  Second  method:  Draw  a  straight  line  through 
either  curve,  as  mn  through  the  compression  curve  or  ef 
through  the  expansion  curve,  and  extend  it  in  both  direc- 
tions. On  the  line  m '  n'  lay  off  nri  equal  to  mm' ,  or  on  the 
line  e'f  lay  off  ee'  equal  to  ff ;  then  will  either  of  the  points 
e'  or  n'  be  in  the  clearance  line  and  the  line  drawn  perpendicular 
to  the  vacuum  line  through  either  of  these  points  is  the^ clear- 
ance line.  In  an  engine  working  with  much  compression  the 
clearance  will  be  given  more  accurately  from  the  compression 
curve  than  from  the  expansion  curve,  since  it  is  more  nearly 
an  hyperbola. 

408.  Re-evaporation  and  Cylinder  Condensation. — By 
considering  the  hyperbolic  curve  as  a  standard,  an  idea  can  be 
obtained  of  the  restoration  by  re-evaporation  and  the  loss  by 


562 


EXPERIMENTAL   ENGINEERING. 


is  409- 


cylinder  condensation.  Thus  in  Fig.  264,  suppose  that  a  is 
the  point  of  cut-off  at  boiler-pressure,  construct  an  hyperbola 
as  explained  ;  in  the  example  considered  it  is  seen  to  lie  above 
the  expansion  line  for  a  short  distance  after  cut-off,  then  to  cross 
the  line  at  b,  and  remain  below  it  nearly  to  the  end  of  the 
stroke.  The  amount  by  which  the  expansion  line  rises  above 
the  hyperbola  may  be  considered  as  due  to  re-evaporation. 
The  area  of  the  diagram  lying  above  would  represent  the  work 
added  by  heat  returned  to  the  steam  from  the  cylinder. 

The  methods  for  determining  the  cylinder  condensation  are 


C  b'  d' 

FIG.  264.— WORK  RESTORED  BY  RE-EVAPORATION. 

similar  to  this  process,  except  that  the  hyperbola  is  usually 
drawn  upward  from  the  point  corresponding  to  the  terminal 
pressure,  to  meet  a  horizontal  line  drawn  to  represent  the  boiler- 
pressure,  as  follows  : 

Thfs  construction  is  shown  by  the  dotted  lines  in  the 
diagrams  in  Fig.  265.  The  area  of  the  figure  enclosed  by  the 
dotted  lines,  compared  with  that  of  the  diagram,  is  the  ratio 
that  the  ideal  diagram  bears  to  the  real ;  the  difference  is  the 
loss  by  cylinder  condensation. 

The  student  should  understand  that  both  these  methods 
are  approximations  which  may  vary  much  from  the  truth. 

409.  Discussion  of  Diagrams.— Diagrams  are  often  taken 


§409-] 


THE  INDICATOR-DIAGRAM. 


563 


where  some  portion  of  the  engine  is  out  of  adjustment,  or  the 
indicator  or  reducing  motion  is  not  in  perfect  order.    It  is  often 


91  per  cent  of  ideal. 
40.0  Horse  Power 


90  per  cent  of  ideal. 
62.4  Horse  Power 


85  lba.Boiler  Press. 


Fio   265.— Loss  BY  CYLINDER-CONDENSATION. 

possible  in  such  cases  to  determine  the  defect  from  the  dia- 
gram, and  to  suggest  the  proper  remedy.  A  few  examples  are 
submitted.  Such  examples  could  be  multiplied  indefinitely, 
and  skill  and  experience  will,  in  general,  be  required  to  prop- 
Top  of  cylinder 


Vacuum  side. 
FIG.   266.— UNSYMMETRICAL  VALVE-SETTING. 


eriy  interpret  them.  Thus  Fig.  266  is  an  illustration  of  a  dia- 
gram taken  when  the  valves  were  set  unsymmetrically.  Curves 
or  waves  in  the  expansion  or  compression  lines  indicate  inertia- 


564 


EXPERIMEN  TA  L   ENGINEERING. 


[§409. 


effects  in  the  drum-motion,  which  is  sometimes  sufficient  to 
make  the  compression  line  concave  when  it  should  be  convex, 
as  shown  in  the  lower  diagram  of  Fig.  267.  Vertical  curves 
are  due  in  large  measure  to  vibrations  in  the  pencil-lever  and 
indicator-spring  ;  they  are  usually  excessive  with  a  light  spring 
and  high  speed.  In  the  case  of  an  automatic  engine  running 
under  variable  loads,  each  revolution  will  show  a  different  dia- 
gram, as  shown  in  Fig.  267. 


FIG.   267.— VARIATION'  t.F  LOAD. 

Different  Forms  of  Admission-lines. — The  form  of  the  ad- 
mission-line is  changed  *  according  to  the  relative  time  of  valve- 
opening  and  position  of  piston  in  its  stroke. 

The  normal  form  is  shown  at  A.  In  B  CD  and  E  the  valve 
opens  late,  and  after  the  piston  has  started  on  its  return  stroket 
In  F  and  G  the  exhaust-valve  closes  late,  so  that  live  steam 
escapes.  H  and  /  are  familiar  examples  of  extreme  compres- 
sion, produced  on  high-speed  automatic  engines  working  with 
a  light  load.  J  shows  a  sharp  corner  above  the  compression 

*  Power,  September  1891. 


§  4io.] 


THE   IND1 CA  TOR-DIA  GRA  M. 


565 


line,  and  in  general  indicates  too  much  lead.     In  case  the  valve 
opens  too  early,  the  admission-line  leans  as  at  K. 

410.  Diagrams  from  Compound  and  Triple-expansion 
Engines. — The  diagram  from  any  cylinder  of  a  compound  or 
triple-expansion  engine  is  not  likely  to  differ  in  any  noticeable 


K 


FIG.  268.— TYPICAL  ADMISSION-LINKS. 

particular  from  those  taken  from  a  simple  engine  as  already 
described.  They  are  usually  taken  with  different  springs  for 
the  different  cylinders,  but  may  have  very  nearly  or  exactly 
the  same  lengths. 

The  diagrams  from  a  compound  engine  may  be  reduced  to 
an  equivalent  diagram,  taken  from  a  single  cylinder  by  the  fol- 
lowing method :  Lay  off  a  vertical  line  OB,  and  a  horizontal 
line  PQ.  Let  PQ  be  the*  vacuum  line,  and  BC  the  line  of 


566  EXPERIMENTAL  ENGINEERING.  [ 

highest  steam-pressure  acting  in  the  small  cylinder.  Lay  off 
ON  proportional  to  the  volume  of  the  small  cylinder,  and  OP 
proportional  to  the  volume  of  the  large  cylinder.  Let  FA  be 
the  line  of  back  pressure  of  the  large  cylinder,  AD  that  of 
the  small  cylinder :  then  BCD  A  is  the  diagram  from  the  small 
cylinder,  EKFA  that  from  the  large  cylinder. 

To  combine  them  into  one  diagram,  draw  a  line  KGH  par- 
allel to  POQ,  intersecting  both  diagrams,  and  lay  off  upon  it 

=  KG\  and  GL  =  GH+  KG  represents  the  total  volume 


B     C 


in  both  cylinders  when  the  pressure  is  OG,  and  L  is  a  point  in 
the  expansion  line  the  same  as  though  the  action  took  place 
in  the  large  cylinder  only.  In  the  same  way  other  points  may 
be  found,  and  the  line  CDLM  drawn.  This  diagram  may  be 
discussed  as  if  it  represented  the  steam  acting  in  the  large 
cylinder  only. 

Fig.  270  is  a  combined  diagram  from  a  triple-expansion 
engine,*  in  which  the  cylinders  have  the  ratio  of  I  :  2.25  :  2.42, 
and  the  total  ratio  of  expansion  is  8.  The  length  of  each  dia- 
gram is  made  proportional  to  the  total  volume  of  the  cylinder 
from  which  it  was  taken ;  the  diagrams  are  all  drawn  to  the 
same  scale  of  pressures,  and  each  is  located  at  a  distance  from 
a  vertical  line  proportional  to  the  volume  of  its  clearance. 
From  the  point  of  cut-off  corresponding  to  boiler-pressure  an 
hyperbola  is  drawn  as  has  been  explained,  and  the  area  sur- 
rounding the  diagrams  is  shaded.  The  work  done  in  the  three 
cylinders  can  be  computed  from  the  diagram  as  though  done 
in  one  only. 

*  See  Thurston's  Engine  and  Boilef  Trials,  page  202. 


84"-] 


THE  INDICATOR-DIAGRAM. 


567 


411.  Crank-shaft  and  Steam-chest  Diagrams.— Dia- 
grams may  be  taken  with  the  motion  of  the  indicator-drum 
proportional  to  any  moving  part  of  the  engine,  as  for  instance 
the  crank-shaft 


FIG.  270. — COMBINED  DIAGRAM  FROM  TRIPLE-EXPANSION  ENGINE. 

In  such  a  case,  shown  by  Fig.  271  the  ordinates  will  be  as 
before  proportional  to  the  pressures  per  square  inch  acting  on 
the  piston,  but  the  abscissae  will  correspond  to  distances  moved 


FIG/  271,— SHAFT-DIAGRAM. 

through  by  the  crank-pin.  In  Fig.  271,  A  to  B  is  the  exhaust, 
from  B  to  C  compression,  D  to  E  steam  line,  E  to  A  expan- 
sion. Diagrams  may  also  be  taken  with  the  indicator  mounted 
on  the  valve-chest ;  in  this  case  the  indicator  would  show  vari- 
ation in  pressure  in  the  steam-chest. 


568 


EXPERIMENTAL   ENGINEERING. 


[§4I  I 


CHAPTER  XVIII. 
METHODS   OF   TESTING  THE   STEAM-ENGINE. 

412.  Standards     Employed    in     Engine-testing.  —  The 

unit  of  work  ordinarily  used  in  engine-testing  is  the  horse-power 
(H.P.),  which  may  be  either  that  shown  by  the  indicator  and 
known  as  the  indicated  horse-power  (I.H.P.),  or  that  delivered 
from  the  engine,  which  is  known  as  delivered  or  brake  horse- 
power (D.H.P.).  The  horse-power  is  equivalent  to  33,000 
foot-pounds  or  42.413  B.T.U.  per  minute,  or  to  1,980,000  foot- 
pounds or  2545  B.T.U.  per  hour. 

Fuel,  Steam,  and  Heat  Consumption. — The  ordinary  standard 
of  comparison  of  the  economy  of  the  work  done  by  different 
engines  is  the  weight  of  fuel  or  steam,  or  the  number  of  B.T.U. 
required  by  the  engine  for  each  horse-power  of  work  indicated 
or  delivered  per  hour.  The  heat  consumption,  B.T.U.  per 
H.P.  hour,  presents  the  advantages  over  the  others  of  being 
more  concise  and  definite. 

Duty. — This  term  is  applied  to  the  work  performed  by  pump- 
ing-engines,  expressed  in  foot-pounds,  for  the  consumption  of 
100  pounds  of  coal,  1000  pounds  of  steam,  or  1,000,000  B.T.U. 
See  Art.  254. 

Perfect  Engine. — The  performance  of  a  perfect  engine  is 
frequently  employed  as  a  standard  of  comparison.  The  per- 
fect engine  is  one  which  transforms  all  the  available  heat  received 
and  not  rejected  into  mechanical  work.  Such  an  engine  operates 
in  a  reversible  or  Carnot  cycle  and  has  a  thermodynamic  efficiency 
of  (Ti  —  T2)/Ti,  in  which  T\  is  the  absolute  temperature  of  the 
entering  steam  and  T2  that  of  the  exhaust. 

The  heat  (B.T.U.)  consumed  per  H.P.  hour  for  an  engine 
of  this  kind  is  evidently 

A  =  2545  T1/(T1~T2). 

The  least  possible  weight  of  steam  will  be  used  in  the  per- 

569 


57°  EXPERIMENTAL   ENGINEERING.  [§  413, 

feet  engine  when  the  difference  between  the  heat  entering,  A, 
and  that  discharged,  q,  has  all  been  converted  into  work.  Hence 
the  least  possible  steam  consumption  per  H.P.  hour  of  the  per- 
fect reversible  engine  is 

2545  /     Fi 


Rankine  Cycle.  —  The  maximum  amount  of  heat  which  can 
be  transformed  into  work  in  the  perfect  non-reversible  engine 
is  given  by  Professor  Rankine  per  pound  of  steam  as  follows: 


This  expression  is  frequently  used  as  a  standard  of  com- 
parison by  British  engineers,  and  the  cycle  on  which  such  an 
engine  works  is  termed  the  Rankine  cycle. 

The  efficiency  of  the  steam-engine  is  expressed  in  various 
ways  as  follows: 

1.  Thermal  Efficiency.  —  This  is  the  ratio  of  the  work  actu- 
ally done  (A.W.),  expressed  in  heat  units,  to  the  total  heat  sup- 
plied  (Q)  in  the  steam.     It  is  equal  to  AW/Q. 

2.  Thermodynamic  Efficiency.  —  This  is  the  greatest  possible 
ratio  of  work  done  by  the  working  substance  to  the  mechanical 
equivalent  of  the  heat  expanded  on  it  to  do  that  work.     In  the 
Carnot  reversible  cycle  this  efficiency  equals  (T1  —  T2)/Ti. 

3.  Mechanical   Efficiency.  —  This    is    the    ratio    of    the    work 
actually  delivered  (D.H.P.)  to  that  done  on  the  piston  and  shown 
by  the  indicator  (I.H.P.). 

4.  Plant  Efficiency.  —  This   is  equal   to   the  product   of   the 
several  efficiencies  of  the  various  parts  or  machines  which  com- 
pose the  plant. 

413.  Objects  of  the  Engine-test.  —The  test  may  be 
made  :  i  .  To  adjust  the  valves  or  working  parts  of  the  engine. 

2.  To   determine   the   indicated   or   dynamometric  horse-power. 

3.  To  ascertain  the  friction  for  different  speeds  or  conditions. 

4.  To  determine  the  consumption  of  fuel  or  steam  per  horse- 
power   per   hour.     5.  To    investigate    the   heat-changes    which 


§  4J4-]    METHODS  OF    TESTING    THE   STEAM-ENGINE.         $/  t 

characterize  the  passage  of  the  steam  through  the  engine. 
The  general  method  of  the  test  will  depend  largely  on  the  ot> 
ject  for  which  the  test  is  made ;  in  any  event  the  apparatus  to 
be  used  should  be  carefully  calibrated,  the  dimensions  of  the 
engine  obtained,  and  the  test  conducted  with  care. 

414.  Measurements  of  Speed. — The  various  instruments 
employed  for  measurement  of  speed  are  speed-indicators,  ta~ 
chometers,  continuous  counters,  and  chronographs. 

Where  the  number  of  revolutions  only  is  required,  it  is 
usually  obtained  either  by  counting  or  by  the  hand  speed- 
indicator.  Counting  can  be  done  quite  accurately  without  an 


FIG.  273. — DOUBLE-ENDED  SPEED-INDICATOR. 

instrument,  by  holding  a  stick  in  the  hand  in  such  a  position 
that  it  is  struck  by  some  moving  part,  as  the  cross-head  of  an 
engine,  once  in  each  revolution.  The  hand  speed-indicator,  of 
which  one  form  is  shown  in  Fig.  273*  consists  of  a  counter 
operated  by  holding  the  pointed  end  of  the  instrument  in  the 
end  of  the  rotating  shaft.  In  using  the  instrument,  the  time 
is  noted  by  a  watch  at  the  instant  the  counting  gears  are  put 
in  operation  or  are  stopped.  A  stop-watch  is  very  convenient 
for  obtaining  the  time.  The  errors  to  be  corrected  are  princi- 
pally those  due  to  slipping  of  the  point  on  the  shaft,  and  to  the 
slip  of  the  gears  in  the  counting  device  in  putting  in  and  out 
of  operation.  The  best  counters  have  a  stop  device  to  prevent 
this  latter  error,  and  the  gears  are  engaged  or  disengaged  with 


5/2 


EXPERIMENTAL   ENGINEERING. 


[§  4H. 


the  point  in  contact  with  the  shaft.  To  prevent  slipping  of 
the  point,  the  end  of  the  instrument  is  sometimes  threaded 
and  screwed  into  a  hole  in  the  end  of  the  shaft. 

The  continuous  counter  consists  of  a  series  of  gears  arranged 
to  work  a  set  of  dials  which  show  the  number  of  revolutions. 
The  arrangement  of  gearing  in  such  an  instrument  is  shown  in 
Fig.  274.  The  instrument  can  usually  be  made  to  register  by 
either  rotary  or  reciprocating  motion,  and  can  be  had  in  a 


FIG.  274. 

square  or  round  case.     The  reading  of  the  counter  is  taken  at 
stated  intervals  and  the  rate  of  rotation  calculated. 

Tachometers  (see  Fig.  275)  are  instruments  which  utilize  the 
centrifugal  force  in  throwing  outward  either  heavy  balls  or  a 
liquid.  The  motion  so  caused  moves  a  needle  a  distance  pro- 
portional to  the  speed,  so  that  the  number  of  revolutions  is 
read  directly  from  the  position  of  the  needle  on  the  graduated 
dial.  The  tachometer  is  arranged  with  a  pointed  end  to  hold 
against  the  shaft  whose^  speed  is  to  be  determined,  or  with  a 
pulley  so  that  it  may  be  driven  by  a  belt. 


§415-]    METHODS  OF    TESTING    THE   STEAM-ENGINE. 


573 


Browns  Speed-indicator  consists  of  a  U-shaped  tube  joined 
to  a  straight  tube  in  the  centre.  The  revolution  of  the  U-tube 
around  the  centre  tube  induces  a  centrifugal  force  which  ele- 


FlG.    275. —  >CHAEFFER   AND   BUDENBERG    HAND   TACHOMETER. 

vatts  mercury  in  the  revolving  arms  and  depresses  it  in  the 
centre  tube.  A  calibrated  scale  gives  the  number  .of  revolu- 
tions corresponding  to  a  given  depression. 

415.  The  Chronograph.— The  chronograph,*  Fig.  276,  con- 
sists of  a    drum    revolved    by   clock-work   so    as   to   make   a 


FIG.  276. 


definite  number  of  revolutions  per  minute.     A  carriage  hav- 
ing one  or  two  pens,  h,  g,  as  may  be  required  is  moved  parallel 
*  See  Thurston's  Engine  and  Boiler  Trials,  page  226. 


574  EXPERIMENTAL   ENGINEERING.  [§ 

to  the  axis  of  the  cylinder  by  a  screw  which  is  connected  with 
the  chronograph-drum  A  by  gearing. 

The  pen  in  its  normal  condition  is  in  contact  with  the  paper, 
and  it  is  so  connected  to  an  electro-magnet  that  it  is  moved 
axially  on  the  paper  whenever  the  circuit  is  broken.  The  cir- 
cuit may  be  broken  automatically  by  the  motion  of  a  clock,  or 
by  hand  with  a  special  key,  or  by  any  moving  mechanism. 
1  wo  pens  are  usually  employed,  one  of  which  registers  auto- 
matically the  beats  of  a  standard  clock ;  the  other  may  be  ar- 
ranged to  note  each  revolution  or  fraction  of  a  revolution  of  a 
revolving  shaft.  The  distance  between  the  marks  made  by 
the  clock  gives  the  distance  corresponding  to  one  second  of 
time ;  the  distance  between  the  marks  made  by  breaking  the 
-circuit  at  other  intervals  represents  the  required  time  which  is 
to  be  measured  on  the  same  scale. 

This  instrument  has  been  in  use  by  astronomers  for  a  long 
time  for  minute  measurements  of  time,  and  by  its  use  intervals 
-as  short  as  one  one-hundredth  (.01)  part  of  a  second  can  be 
.measured  accurately. 

Tuning-fork  Chronograph. — A  tuning-fork  emitting  a  musi- 
cal note  makes  a  constant  and  known  number  of  vibrations. 
The  number  of  vibrations  of  the  fork  corresponding  to  the 
musical  tones  are  as  follows : 

Note   C        D        E          F          G         A        B        C2 

Vibrations    )       0 

per  second.  \  I28      J44      160      i/of      192      213^     240     256 

If  now  a  small  point  or  stylus  be  attached  to  one  of  the 
;arms  of  a  tuning-fork,  as  shown  in  Fig  276,* — in  which  Fis  one 
-of  the  arms  of  the  tuning-fork,  and  CAED  a  piece  of  elastic 
metal  to  which  the  stylus,  AP,  is  .attached, — and  if  the  fork 
be  put  in  vibration  and  the  stylus  permitted  to  come  in  contact 
with  any  surface  that  can  be  marked,  as  a  smoked  and  var- 
nished cylinder  moved  at  a  uniform  rate,  the  vibrations  of  the 
tuning-fork  will  be  recorded  on  the  cylinder  by  a  series  of 
wavy  lines,  as  shown  in  Fig.  279 ;  the  distance  between  the 

*  See  Thurston's  Engine  and  Boiler  Trials,  page  233. 


§415-]    METHODS  OF    TESTING    THE   STEAM-ENGINE.         575 


waves  corresponding  to  known  increments  of  time.     If  each 
revolution  or  portion  of  a  revolution  of  the  shaft  whose  speed 
is  required  be  marked   on  the  cylin- 
der, the  distance  between  such  marks, 
measured   to   the    same    scale  as   the 
wavy   lines  made  by  the  tuning-fork, 
would   represent   the  time  of  revolu- 
tion. 

Fig.  278  (from  Thurston's  Engine 
and  Boiler  Trials)  represents  the  Ran- 
son  chronograph  ;  in  this  case  the  tun- 
ing-fork is  moved  axially  by  a  carriage 
operated  by  gears,  and  is  kept  in 
vibration  by  an  electro-magnet.  The  operation  of  the  instru- 
ment is  the  same  as  already  described.  The  form  of  the 
record  being  shown  in  Fig.  279;  the  wavy  marks  being  those 


FIG.  277.— STYLUS  FOR  TUNING- 
FORK. 


FIG.  278. — TUNING-FORK  CHRONOGRAPH. 

made  by  the  tuning-forks,  those  at  right  angles  being  made  at 
the  end  of  a  revolution  of  the  shaft  whose  speed  is  required. 

The  tuning-fork  with  stylus  attached,*  as  in  Fig.  277,  can 
be  made  to  draw  a  diagram  on  a  revolving  cylinder  connected 


*  See  Engine  and  Boiler  Trials,  page  234. 


5;6  EXPERIMENTAL   ENGINEERING.  [§  4*  7- 

directly  to  the  main  shaft  of  the  engine,  or  the  shaft  itself 
may  be  smoked  and  afterward  varnished.  If  the  fork  be 
moved  axially  at  a  perfectly  uniform  rate,  the  development  of 
the  lines  drawn  will  be  for  uniform  motion,  straight  and  o{ 
uniform  pitch  ;  but  for  variations  in  speed  these  lines  will  be 


FIG.  279. — SPEED-RECORD  FROM  CHRONOGRAPH. 

curved  and  at  a  varying  distance  apart.  From  such  a  diagram 
the  variation  in  speed  during  a  single  revolution  can  be  deter- 
mined. 

4160  Autographic  Speed-recorder. — Variations  in  speed 
are  shown  autographically  in  several  instruments  by  recording 
on  a  strip  of  paper  moved  by  clock-work  the  variation  in  cen- 
trifugal force  of  revolving  weights.  In  the  Moscrop  speed- 
recorder,  shown  in  Fig.  280,  the  shaft  B  is  connected  with  the 
shaft  whose  speed  is  to  be  measured.  The  variation  in  the 
height  of  the  balls  near  B,  caused  by  variation  in  speed,  gives 
the  arm  C  a  reciprocating  motion,  so  that  an  attached  pencil 
makes  a  diagram,  FED,  on  the  strip  of  paper  moved  by  clock- 
work. The  ordinates  of  this  diagram  are  proportional  to  the 
speed. 

417.  The  Surface  Condenser. — In  the  measurement  of 
the  steam  used  by  the  engine  the  surface  condenser  is  fre- 
quently employed.  The  surface  condenser  usually  consists  of 
a  vessel  in  which  are  a  great  many  brass  tubes.  It  is  usually 
arranged  so  that  the  exhaust  steam  comes  in  contact  with  the 
outer  surface  of  these  tubes,  and  the  condensing  water  flows 
through  the  tubes.  The  condensed  steam  falls  to  the  bottom 
ot  the  condenser  and  is  removed  by  an  air-pump ;  the  heat  of 
the  steam  being  taken  up  by  the  condensing  water.  If  the 
condenser  is  free  from  leaks,  the  air-pump  of  ample  size  and 
with  little  clearance,  and  i£  the  proper  temperatures  are  main- 


§417-]    METHODS   OF    TESTING    THE   STEAM-ENGINE.         577 

tained,  nearly  all  the  atmospheric  pressure  can  be  removed 
from  the  condenser  and  the  back-pressure  on  the  engine  cor- 
respondingly  reduced. 

The   surface   condenser   affords   more   accurate  means  of 


FIG.  280  — THE  MOSCROP  SPEED-RECORDER. 


obtaining  the  water-consumption  of  a  steam-engine  than  the 
measurement  of  feed-water  during  a  boiler-test,  since  the 
effect  of  steam-leaks  are  to  a  great  extent  eliminated. 

The  condenser  should  be  tested   for  leaks  by  noting  how 


5/8  EXPERIMENTAL  ENGINEERING.  |_§  41**. 

long  a  given  reading  of  the  vacuum-gauge  can  be  maintained 
when  all  the  connecting  valves  are 'closed,  or  by  turning  on 
steam  when  the  water-pipes  are  empty,  or  vice  versa,  and  noting 
whether  there  is  any  leakage. 


FORM    FOR   TEST  ON   CONDENSER. 
Date 

Duration  of  test mjn 

Barometer inches Ibs.  per  sq.  in. 

Temperature,  entering  steam C.         p 

Temperature,  condensed  steam C.         p 

Temperature,  cold  condensing  water C.          p 

Temperature,  hot  condensing  water C.         p 

Hook-gauge  reading  (corrected) inches 

(Hook-gauge  reading)  $ 

Temperature  at  weir C p 

Weight  of  condensed  steam ,, 

Breadth  of  weir inches 

End  area  of tubes , . . .  , 

'•r  •   •• sq.  tt. 

Area  steam  surface , 

Area  water  surface 

Sq.  ft. 

Weight  steam  condensed  per  hour ,, 

Weight  condensing  water  used  per  hour tm 

Weight  steam  condensed  per  pound  of  water 

•  •••••»,..»,  ,  •  • •  •••«*, 1 DS . 

Weight  steam  condensed  per  sq.  ft.  steam  surface  per  hour lbs 

Weight  steam  condensed  per  sq.  ft.  water  surface  per  hour |  lbs 

Velocity  of  water  through  tubes. . 

ft.  per  sec. 

Heat  acquired  by  condensing  water  used  per  hour B   T    U 

Heat  given  up  by  steam  condensed  per  hour. B   T    U 

Signed 

418.  Calibration  of  Apparatus   for   Engine-testing  - 

ore  commencing  any  important  test,  all  instruments  and 
apparatus  to  be  used  should  be  adjusted  and  carefully  com- 
pared wrth  standards,  under  the  same  conditions  as  in  actual 
pract.ce.  The  errors  or  constants  of  all  instruments  .nouJd  be 


§41 8.]    METHODS   OF    TESTING    THE    STEAM-ENGINE.         579 

noted  in  the  report  of  the  test,  and  corresponding  corrections 
made  to  the  data  obtained. 

The  instruments  to  be  calibrated  are : 

1.  Steam-gauge. — Compare  with   mercury  column,  or  with 
standard   square-inch  gauge,  for  each  five  pounds  of  pressure, 
reading  both  up  and  down  throughout  the  range  of  pressures 
likely  to  be  used  in  the  test.     (See  Article  282,  page  366.) 

2.  Steam-engine  Indicator-springs. — Put  the  indicator  under 
actual  steam-pressure  (see  Art.  393,  p.  535)  and  compare  the 
length  of  ordinate  of  the  card  with  the  reading  of  the  mercury 
column  or  a  standard  gauge  for  the  same  pressure.     Take  ten 
readings,  both  up  and  down,  through  an  extreme  range  equal 
to  two  and  one-half  times  the  number  on  the  spring.     The 
steam-pressure  may  be  varied   by  throttling  the  supply  and 
exhaust.     The   ordinate  may  also  be   compared  by  a  special 
method  with  readings  of  a  standard  scale ;  the  indicator  being 
heated  by  the  flow  of  steam   through  a  rubber  tube  wound 
around  it. 

3.  Speed-indicators. — The  accuracy  can  be  checked  by  hand 
counting.     For  the  best  work  chronographs  should  be  used. 
Continuous  counters  are  necessary  for  accuracy  in  a  long  run. 
(See  Articles  414  and  415.) 

4.  Indicator  Reducing-motion. — This  may  be  tested  by  divid- 
ing the  stroke  of  the  engine  on  the  guides  into  twelve  equal 
parts  and  noting  whether  the  card   is  similarly  divided.     It 
should  be  tested  for  both  return  and  forward  stroke.     When 
the  form  of  the  card  is  considered,  this  is  an  imports*  matter, 
as  many  reducing-motions  distort  its  shape.     (See  Article  390, 
page  528.) 

5.  Indicator-cords  and  Connections. — See  that  the  connecting 
cords  do  not  stretch  at  high  speeds,  and  that  the  drum-spring 
of  the  indicator  has  a  proper  tension  and  gives  a  correct  motion 
of  the  drum.     This  is  important.     (See  Article  395.) 

6.  Weighing-scales. — Compare  the  readings  with  standard 
weights. 

7.  Water-meters. — Calibrate  by  actually  weighing  the  dis- 
charge under  conditions  of  use  as  regards  pressure  and  flow. 


$8o 


EXPERIMENTAL   ENGINEERING. 


[§418 


In  case  meters  are  used,  temperatures  of  the  water  must  be 
taken  in  order  to  obtain  the  weight.  (See  Article  213,  page 
283.) 

8.  Thermometers. — Test  the  thermometer  for  freezing-point 
by  comparison  with  water  containing  ice  or  snow  ;  test  for  boil- 
ing-point by  comparison  with  steam  at  atmospheric  pressure  in 
the  special  apparatus  described  on  page  381,  the  correct  boiling- 
point  being  determined  by  readings  of  the  standard  barometer. 
The  other  tests  of  the  thermometer  can  in  general  be  left  to 
the  makers  of  the  instrument.     In  cases  where  great  accuracy 
is  required  the  readings  should  be  compared  throughout  the 
whole  scale  with  a  standard  air-thermometer,  as  described  on 
page  350.   • 

9.  Pyrometer. — Compare    with    a    standard    thermometer 
while  immersed  in  steam  for  the  lower  ranges  of  temperature, 
and  with   known  melting-points  of   metals   for  higher.     The 
correction  may  also  be  determined  by  cooling  heated  masses 
of  metals  in  large  bodies  of  water  and  calculating  the  temper- 
ature from  the  known  relations  of  specific  heats.     (See  Articles 
298  to  304). 

10.  The  Planimeter,  which  is  used  for  measuring  the  indi- 
cator-diagram, should  be  calibrated  by  making  a  comparison 
with  a  standard  area,  as  explained  in  Article  38,  page  52.     The 
following  form  is  useful  to  record  the  results  of  calibrations : 


BLANK   FORM   FOR   CALIBRATION   OF    INSTRUMENTS. 

STEAM-ENGINE  INDICATOR-SPRINGS. 


Used  on 

Head. 

Crank. 

Maker's  name  

Maker's  number  

Scale  of  spring  

Number  of  spring.  .  . 

\\hen  tested  

How  tested  

Per  cent  error  

4 1 9-]    METHODS   OF   TESTING    THE   STEAM-ENGINE.         58  I 

STEAM-GAUGES. 


Maker. 

Position. 

Number. 

Error,  Ibs. 

When  Tested. 

How  Tested. 

THERMOMETERS. 


Position. 

Registered 
Number. 

Boiling-point. 

Freezing-point. 

Barometer. 

Read- 
ing. 

Per  Ba- 
rometer. 

Error. 

Read- 
ing. 

Error. 

419.  Preparations  for  Testing.— The  preparations  re- 
quired will  depend  largely  on  the  object  of  the  test.  They 
should  always  be  carefully  made,  and  in  general  are  to  include 
"ihe  following  operations : 

1.  Weighing  of  Steam. — Prepare   to  weigh  all  the   steam 
supplied  the  engine.     This  may  be  done  by  weighing  or  meas- 
uring all  the  feed-water  supplied  the  boiler  (see  Article  375), 
provided  there  is  no  waste  nor  other  use  of  steam  ;  or  it  may 
be  done  by  condensing  (see  Article  417)  and  weighing  all  the 
exhaust  from  the  engine.     In  the  first  case  especial  precaution 
must  be  taken  to  prevent  leaks,  and  in  the  latter  to  reduce  the 
iemperature  of  the  condensed  steam  to  1 10°  F.  before  weigh- 
ing.    The  weights  may  in  some  cases  be  determined  from  a 
meter-reading  (see  Article  214). 

2.  Quality  of  Steam. — Attach  a  calorimeter  (see  Articles  330 
•o  336),  which  may  be  of  the  throttling  or  separator  kind,  to  the 

.main  steam-pipe,  near  the  engine.  This  attachment  may  be 
made  by  a  half-inch  pipe,  cut  with  a  long  thread  and  ex- 
tending  three  fourths  across  the  main  steam-pipe.  This  pipe 


582 


EXPERIMENTAL   ENGINEERING.  [§  4IC> 


should   be   provided  with    large  holes  so  that  steam  will   be 
drawn  from  all  parts  of  the  main  steam-pipe  (see  page  370). 

3.  Leaks.— The  engine  should  be  tested  for' piston-leaks  by 
turning  on  steam  with  the  piston  blocked  and  cylinder-cocks 
opened  on  the  end  opposite  that  at  which  steam  is  supplied. 
If  leaks  are  found,  they  should  be  stopped  before  beginning: 
the  test. 

4.  Indicator  A ttachments.— Arrange  a  perfect  reducing-mo- 
tion.     The  kind  to  be  used  will  depend  entirely  upon  circum- 
stances.    The  lazy-tongs  or  pantograph  is  reliable  for  speeds 
less  than  125,  and  can  be  easily  applied.     The  pendulum  piv, 
oted  above  and  furnished  with  an  arc,  although  not  perfectly 
accurate,  is  much  used.     Make  yourself  familiar  with  the  vari* 
ous  devices  in  use.     (See  Article  390). 

5.  An  Absorption  Dynamometer  may  be  required  ;  if  so,  ar- 
range a  Prony  brake  to  absorb  the  power  of  the  engine,  and 
make  provision  for  lubricating  it  and  removing  the  heat  gen- 
erated (see  Article  178,  page  528).     In  many  commercial  tests 
the  power  is  absorbed  by  machinery  or  in  useful  work,  and  the 
efficiency  is  wholly  determined  by  measurements  of  the  amount 
and  quality  of  steam  and  from  the  indicator-diagram. 

6.  Weight  of  Coal. — This  is  generally  taken  during  an  engine- 
test,  but  will  be  treated  here  as  pertaining  to  boiler-testing  ;, 
the  methods  of  weighing  are  fully  described  under  that  head 
(see  Article  375). 

An  engine  fitted  completely  for  a  test  is  shown  in  Fig.  272, 
from  Thurston's  Engine  and  Boiler  Trials.  In  this  case  two 
indicators  are  employed,  the  drum-motion  being  derived  from  a 
pendulum  reducing-motion;  a  Prony  brake  is  attached  to  absorb 
and  measure  the  power  delivered,  water  for  keeping  the  brake 
cool  being  delivered  near  the  bottom  and  on  the  inside  of  the 
flanged  brake-wheel  by  a  curved  pipe,  and  drawn  out  by  an- 
other pipe  the  end  of  which  is  funnel-shaped  and  bent  so  as  to 
meet  the  current  of  water  in  the  wheel.  The  speed  is  taken  by 
a  Brown  speed-indicator  mounted  on  top  of  the  brake,  and  also 
by  a  hand  speed-indicator.  The  steam-pressure  is  measured 


§421-]    METHODS   OF   TESTING    THE   STEAM-ENGINE. 

near  the  engine  ;  the  quality  of  steam  is  determined  by  a  sam- 
ple drawn  from  the  vertical  pipe  near  the  engine. 

420.  Measurement  of   Dimensions  of    Engine.— Make 
careful  measurements  of  the  dimensions  of  engine  ;  the  diam- 
eter of  piston,  length  of  stroke,  and  diameter  of  piston-rod, 
as  may  be  required. 

Piston-displacement. — This  is  the  space  swept   through  by- 
the  piston  ;  it  is  obtained  by  multiplying  the  area  of  the  piston 
by  the  length  of  stroke.     For  the  crank  end  of  the  cylinder 
the  area  of  the  piston-rod  is  to  be  deducted  from  the  area  of 
the  piston. 

Clearance  is  the  space  at  the  end  of  cylinder  and  between 
valve  and  piston,  filled  with  steam,  but  not  swept  through  by 
the  piston.  To  measure  the  clearance,  put  the  piston  at  end- 
of  its  stroke  and  fill  the  space  with  a  known  weight  of  water, 
ascertaining  that  no  leaks  occur  by  watching  with  valve-chest 
cover  and  cylinder-head  removed.  Make  this  determination 
for  both  ends  of  the  cylinder,  and  from  the  known  weight  of 
water  compute  the  volume  required. 

This  is  usually  reduced  to  percentage,  by  dividing  by  the 
volume  of  piston-displacement. 

This  last  reduction  may  be  obviated,  as  suggested  by  Prof. 
Sweet,  by  finding,  after  the  clearance-spaces  are  full  of  water, 
how  far  the  piston  will  have  to  move  in  order  to  make  room 
for  an  equal  amount  of  water  ;  this  distance  divided  by  the  full, 
stroke  is  the  percentage  required.  Another  approximate  way 
sometimes  necessary  is  to  fill  the  whole  cylinder  and  clearance- 
spaces  with  water ;  from  this  volume  deduct  the  piston-dis« 
placement  and  divide  by  2. 

Preliminary  Run. — It  will  be  found  advisable -to  make  a  pre- 
liminary run  of  several  hours  before  beginning  the  regular 
test,  to  ascertain  if  all  the  arrangements  are  perfect. 

421.  Quantities  to  be  observed. — The  observations  to  be 
taken  on   a   complete  engine-test  are  given  in  the  following, 
list. 

Fill  out  the  following  blank  spaces. 


584 


EXPERIMENTAL   ENGINEERING. 


422. 


Kind  of  engine 

Maker's  name 

Brake-arm *eet> 

Diameter  cylinder inches. 

Length  stroke feet 

Diameter  piston-rod inches. 

Diameter  crank-pin 

Length  crank-pin 

Diameter  wrist-pin 

Travel  valve 


DESCRIPTION   OF    ENGINE. 

Lap  of  valve inches. 

Scale  indicator-spring 

Piston  area sq.  in. 

Steam-port  area 

Exhaust-port  area 

Diameter  fly-wheel  inches. 

Clearance,  head Ibs.  water. 

"          crank "        " 

"          per  cent  P.  D.  head 

"    "      "      crank... 


LOG  Of 


Number 

Time - 

Revolutions : 

Continuous  counter 

Speed-indicator 

Gauge-readings : 

Boiler Ibs. 

Steam-pipe " 

Steam-chest *' 

Exhaust inches  hg. 

Condenser "       " 

Barometer "      " 

Temperatures  : 

External  air 


TEST. 
Temperatures  : 

Engine-room 

Condensed  steam. 

Feed-water 

Injection-water.. . 

Discharge-water. . 
Calorimeter : 

Steam-pipe 

Steam-chest 

Weights: 

Condensed  steam. 

Feed-water 

Injection-water. . . 

Calorimeter 


422.  Special  Engine-tests. — Preliminary  Indicator  Prac- 
tice.— A  simple  test  with  the  indicator  will  be  found  a 
useful  exercise  in  rendering  the  student  familiar  with  the 
methods  of  handling  the  indicator  and  of  reducing  and  conv 
puting  the  data  to  be  obtained  from  the  indicator-diagrams^ 
The  directions  are  as  follows: 

Apparatus. — Throttling  calorimeter  ;  steam-gauge  ;  two  indi' 
cators;  reducing-motion,  and  indicator-cord. 

I.  Obtain  dimensions  of  engines.  Measure  the  clearance  ; 
see  that  indicators  are  oile^i  and  in  good  condition,  and  that 


§422.]    METHODS   OF    TESTING    THE   STEAM-ENGINE.         585 

the  reducing-motion  gives  a  perfect  diagram.  Adjust  the 
length  of  cord  so  that  the  indicator  will  not  hit  the  stops.  Pre- 
pare to  take  cards  as  explained  in  Article  398,  page  545. 

2.  Take  diagrams  once  in  each  five  minutes,  simultaneously 
from  head  and  crank  end  of  cylinder  ;  take  reading  of  boiler- 
gauge,  barometer,  gauge   on   steam-pipe    or  on    steam-chest, 
vacuum-gauge  if  condenser  is  used,  temperature  or  pressure  of 
entering  steam,  temperature  of  room,  and  number  of  revolu- 
tions. 

3.  Measure  or  weigh  the  condensed  steam  during  run. 

4.  From  the  cards  taken  compute  the  M.  E.  P.  and  I.  H.  P. 
for  each  card  as  required  by  the  log. 

5.  Take  a  sample  pair  of  diagrams,  one  from  head  and  one 
from  crank  end.    (a)  Find  clearance  from  diagrams  (see  Article 
407,  page  561) ;  (b)  draw  hyperbolae  respectively  from  cut-off  and 
release  and  find  re-evaporation  and  cylinder  condensation  (see 
Article  408) ;  (c)  produce  hyperbola  from  release  to  meet  hori- 
zontal line  representing  boiler-pressure  ;  complete  the  diagram 
with  hyperbola  from  point  of  admission.     Compute  the  work 
(I.  H.  P.)  from  this  new  diagram,     Draw  conclusions  from  the 
form  of  card  (see  Article  409). 

6.  Compute    the   steam-consumption  per   stroke    and   per 
I.  H.  P.  at  cut-off  and  at   end  of  stroke  from  the  diagram  (see 
Article  406).     Compare  this  with  the  actual  amount  as  deter- 
mined by  the  test. 

7.  From  the  weight  of  dry  steam  as  shown  by  the  indicator- 
diagram,  and  the  actual  weight  as  determined  by  the  amount 
of  condensed  steam,  determine  the  quality  at  cut-off  and  re- 
lease. 

8.  Make  report  of  test  on  the  following  form : 

REPORT   OF   TEST   ON ENGINE. 

Date 

Duration  of  test .........  min. 

Revolutions  per  min 

Steam  used  per  min. Ibs 

Barometer in.         


586 


EXPERIMENTAL  ENGINEERING. 


[§  423* 


Crank  End. 

cu.  ft. 

Head  F.nd. 
cu.  f  t, 

" 

Ibs. 

Ibs, 

« 

t« 

M 

M 

« 

M 

Piston-displacement 
Clearance  (per  ce 
Engine  constant. 
Cut-off  (per  cent 
Release  (per  cent 
Compression  (pe 
Pressure  at  cut-off 
Pressure  at  release 
Pressure  ac  compre 
Mean  effective  pressure 

Revolutions  per  minute 

Horse-power * C.  E.; 


....H.  E Total 


PerS 
C.E. 

.roke. 
H.  E. 

Per  Revo- 
lution. 

Per 
I.H.P. 

Weight  of  steam  at  cut-off. 
Weight  of  steam  at  release. 
Weight  of  steam  during  compression. 

Re-evaporation  per  H.  P.  per  hour Ibs. 

Weight  of  water  per  revolution,  actual " 

Weight  of  mixture  in  cylinder  per  revolution " 

Per  cent  of  mixture  accounted  for  as  steam  at  cut-off 

Per  cent  of  mixture  accounted  for  as  steam  at  release 

Weight  of  water  per  H.  P.  per  hour,  actual Ibs. 

Weight  of  water  per  H.  P.  per  hour,  by  indicator " 

Signed. 

423.  Valve-setting. — This  exercise  will  consist,  first,  in 
obtaining  dimensions  of  ports  and  valves,  and  in  drawing  the 
valve-diagram  corresponding  to  a  given  lead  and  angular  ad- 
vance, and  setting  the  valve  by  measurement  with  a  lead  cor- 
responding to  that  shown  on  the  diagram.  The  valve-diagram 
may  be  drawn  by  Zeuner's  *  or  Bilgram's  method,  as  may  be 
convenient  ;f  from  the  valve-diagram  draw  the  probable  in- 
dicator-diagram and  compute  its  area,  and  from  that  figure 
the  indicated  horse-power.J 

*  See  Valve-gears,  by  Halsey.     D.  Van  Nostrand  Co.,  N.  Y. 
f  Valve-gears,  by  Peabody.     J.  Wiley  &  Sons,  N.  Y. 
\  Valve-gears,  by  Spangle*.     J.  Wiley  &  Sons.  N.  Y. 


§423.]    METHODS  OF   TESTING    THE   STEAM-ENGINE.         587 

The  method  of  drawing  the  indicator-diagram  by  projection 
from  the  valve-diagram  is  well  shown  in  Fig.  281,  from  Thurs- 
ton's  Manual  of  the  Steam-engine.  The  steam-pressure  and 
back-pressure  lines  being  assumed,  the  various  events  as  shown 
on  the  valve-diagram  are  projected  upon  these  lines,  and  the 
indicator-diagram  completed  as  shown. 

Secondly,  in  attaching  the  indicators  and  taking  diagrams 


U\S'  Steam  Line 

5>tut-off 

2>^ 

Release.     Indicator  Diagram 


II. 


FIG.  281. — INDICATOR-DIAGRAM  CONSTRUCTED  FROM  VALVE-DIAGRAM. 

from  which  the  error  in  the  position  of  the  valve  is  determined. 
Its  position  is  corrected  as  required,  to  equalize  the  indicator- 
diagrams  taken  from  each  end  of  the  cylinder. 

The  special  directions  are  as  follows: 

Apparatus. — Scale,  dividers,  and  trammel-point,  the  latter 
:onsisting  of  a  rod  the  pointed  end  of  which  can  be  set  on  a 
mark  on  the  floor  and  which  carries  a  marking  point  at  the 
Dther  end. 

I.  Measure  dimensions  of  valves  and  ports,  throw  of  ec- 
:entric,  and  other  dimensions  called  for  by  engine-log. 


588  EXPERIMENTAL   ENGINEERING.  [§  423 

2.  From    these  data,  with  a  definite   lead   assumed,  drau 
valve-diagram,  and  note  position  of  piston  for  cut-off,  release 
compression,  and  admission. 

3.  Set  the  valve  to  the  assumed  lead,  and  with  angular  ad 
vance   as   indicated  by  the  valve-diagram.     Turn  the  engine 
over  and  see  that  the  lead  is  the  same  at  both  ends  of  th< 
cylinder. 

This  requires  the  engine  to  be  set  on  its  centre;  this  i: 
done  by  bringing  the  piston  to  the  extreme  end  of  the  strok< 
at  either  cylinder-end,  so  that  the  piston-  and  connecting-rod: 
form  one  straight  line.  As  the  motion  of  the  piston  is  ver) 
slow  near  the  end  of  the  stroke,  this  position  is  determinec 
most  accurately  as  follows  :  Mark  a  coincident  line  on  cross 
head  and  guides  corresponding  to  the  position  of  the  cranl 
when  at  an  angle  of  about  20°  measured  from  its'  horizonta 
position  ;  then,  from  a  fixed  point  on  the  floor,  swing  th< 
trammel-point  as  a  radius,  and  mark  a  line  on  the  circumference 
of  the  fly-wheel  ;  turn  the  engine  over  until  the  marks  agair 
coincide  with  the  crank  on  the  other  side  of  the  centre  anc 
make  a  second  mark  on  the  fly-wheel  with  the  trammel-point 
bisect  the  distance  on  the  wheel  between  these  marks  and  ob 
tain  a  third  line  ;  turn  the  wheel  until  this  line  is  shown  by  the 
trammel  to  be  at  the  same  distance  from  the  reference-point 
on  the  floor,  as  the  other  marks :  the  engine  will  then  be  or 
its  centre.  Move  the  valve  the  proper  amount  to  make  iti 
position  correspond  with  that  shown  on  the  diagram.  In  set- 
ting the  valve  remember  that  to  change  angular  advance,  the 
eccentric  must  be  rotated  on  the  shaft  ;  and  to  equalize  event. 
for  both  ends  of  cylinder,  the  valve  must  be  moved  on  the 
stem.  These  adjustments  must  be  made  together,  as  they  are 
to  some  extent  mutually  dependent. 

4.  From  the  valve-diagram  draw  an  ideal  indicator-diagrarr 
as  explained,  assuming  initial  steam-pressure  to  be   (a)  pounds 
:per  square  inch,  absolute  back  pressure  5  pounds  absolute,  anc. 
that  expansion  and  compression  curves  are  true  hyperbolae. 

Calculate  its  area  by  formula. 

Area  =  PV(v  +  loger)  -  P0J7(i  + 


§  425-]    METHODS   OF   TESTING    THE   STEAM-ENGINE.         589 

in  which  V  =  volume  at  cut-off,  and  P  —  corresponding  pres- 
sure ;  F0  =  clearance  volume,  and  P9  =  clearance  pressure ; 
r  =  number  of  expansions,  and  r'  =  number  of  compressions. 
5.  Compute  the  horse-power  of  the  diagram  so  drawn,  and 
compare  with  that  shown  by  the  diagram  taken. 

424.  Friction-test. — For  this  test  the   engine   should  be 
fitted  with  a  Prony  brake  (see  Article  169,  page  239,  to  absorb 
and   measure    the  power   developed.     Indicator-diagrams  are 
to    be   taken    and    the    indicated  horse-power  computed  (see 
Article  402,  page  552).    The  indicated  horse-power  being  the 
work  done  by  the  steam  on  the  piston  of  the  engine,  the  dyna- 
mometer horse-power,  that  delivered  by  the  engine,  the  dif- 
ference will  be  the  power  absorbed  by  the  engine  in  friction, 
or  the  friction  horse-power.     It  is  customary  to  reduce  this 
amount  to  equivalent   mean  pressure  acting  on  the  piston  by 
dividing  by  product  of  area  of  piston   in   square   inches  and 
speed  in  feet  per  minute.     In  making  the  test  for  friction  of 
the  engine  the  loads  on  the  brake-arm  should  be  varied,  with 
the  speed  uniform,  or  the  load  on  the   brake-arm  should  be 
constant  with  varied  speed,  noting   in   each   case   the   effect 
on  the  frictional  work.     It  has  been  shown  by  an  extended 
series  of  experiments  *  that  the  friction  of  engines  is  practically 
constant  regardless  of  the  work  performed,  and  that  the  work 
shown  by  the  indicator-diagram,  when  the  engine  is  running 
light  or  not  attached  to  machinery,  is  practically  equal  to  the 
engine-friction  in  case  the  speed  is   maintained   uniform.     In 
the  case  of  variation  in  speed  the  friction  work  increases  nearly 
in  proportion  to  increase  of  speed. 

Detailed  directions  for  this  test  are  not  considered  neces- 
sary. 

425.  Simple   Efficiency-test— Engines     are     frequently 
sold  on  a  guarantee  as  to  coal  or  water  consumption  per  in- 
dicated  horse-power  (I.  H.  P.),  or  in  some  instances  per  dyna- 
mometer horse-power  (D.  H.  P.);   in  such  a  case  a  test  is  to  be 
made  showing  the  I.  H.  P.  or  the  D.  H.  P.  as  may  be  required, 
and  the  water  and  coal  consumed. 

*  See  Transactions  Am.  Soc.  Mech.  Engineers,  Vol.  VIII.,  page  86. 


590 


EXPERIMENTAL   ENGINEERING.  [§  426. 


The  I.  H.  P.  is  to  be  obtained  as  already  explained  in 
Article  402;  the  D.  H.  P.  by  readings  from  a  Prony  brake, 
Article  178.  The  coal-consumption  is  to  be  obtained  by  a 
boiler-test,  Article  375  ;  the  total  water  consumed,  by  the  feed 
water  used  in  the  boiler-test,  corrected  for  leaks  and  quality; 
or  by  condensing  the  steam  in  a  surface  condenser,  Article  417. 
The  quality  of  the  steam  should  be  taken  near  the  engine,  as 
explained  h\  Article  336,  page  433.  The  principal  quantities 
to  be  observed  are  quantities  required  for  a  boiler-test,  quality  of 
steam  near  engine,  number  of  revolutions  of  engine  per  minute, 
and  weight  of  feed-water  or  weight  of  condensed  steam.  These 
observations  should  be  taken  regularly  and  simultaneously 
once  in  ten  or  fifteen  minutes,  and  at  the  same  instant  an  in- 
dicator-diagram should  be  taken.  From  these  data  are  com- 
puted the  quantities  required. 

426.  The  Calorimetric  Method  of  Engine-testing.— 
Hirris  Analysis. — The  calorimetric  method  of  testing  engines 
as  developed  from  Hirn's  theory  by  Professor  V..Dwelshauvers- 
Dery  of  Liege  enables  the  experimenter  to  determine  the 
amount  of  heat  lost  and  restored  and  that  transformed  into 
work  in  the  passage  of  the  steam  through  the  cylinder.* 

The  principle  on  which  the  method  is  founded  is  as  follows: 
The  amount  of  heat  supplied  the  engine  is  determined  by 
measuring  the  pressure,  quality,  and  weight  of  the  steam  ;  that 
removed  from  the  engine  is  obtained  by  measuring  the  heat  in 
the  condensed  steam  and  that  given  to  the  condensing  water. 
The  amount  of  heat  remaining  in  the  cylinder  per  pound  of 
steam  at  any  point  after  cut-off  can  be  calculated  from  the  data 
obtained  from  the  indicator-diagram ;  this  multiplied  by  the 
known  weight  gives  the  total  heat. 

The  heat  supplied  to  the  engine  added  to  that  already 
existing  in  the  clearance-spaces  gives  the  total  amount  of  heat 
available ;  if  from  this  sum  there  be  taken  the  heat  existing  at 
cut-off  and  the  heat  equivalent  of  the  work  done  during 
admission,  the  difference  will  be  the  loss  during  admission,  due 

*  See  Table  Properties  of   Steam,  V.  Dwelshauvers-Dery,  Trans.  Am.  Soc. 
M.  E.,  Vol.  XI. 


§426-]    METHODS   OF   TESTING    THE    STEAM-ENGINE.         591 

principally  to  cylinder-condensation.  The  difference  between 
the  heat  in  the  cylinder  at  cut-off  and  that  at  release  after  de- 
ducting the  work  equivalent  is  that  lost  or  restored  during 
expansion.  This  method  applied  to  all  the  events  of  the 
stroke,  and  at  as  many  places  as  required,  gives  full  informa- 
tion of  the  transfer  of  heat  to  and  from  the  metal. 

In  the  fundamental  equations  of  this  analysis  which  follow, 
the  following  symbols  are  used  : 


Quantity. 


Symbol. 


Quantity. 


Symbol. 


Heat  admitted  per  stroke 

Weight  of  steam  per  stroke. . . 

Absolute  pressure  of  entering 
steam,  per  sq.  inch 

Temperature,  degrees    Fahr. 

Heat  of  the  liquid 

Internal  latent  heat 

Total  latent  heat 

Quality  of  the  steam 

Degree  of  superheat 

Per  cent  of  moisture 

Specific  heat  of  steam  of  con- 
stant pressure 


Q 

M 

P 
t 

q 
p 

r 

x 

D 

I  —  x 


Heat  equivalent  of  energy  of 
steam  in  the  cylinder  at  any 
instant  

Joule's  equivalent 

Reciprocal  of  Joule's  equiva- 
lent   

Weight  of  i  cu.  foot  of  steam. 

Vol.  of  r  Ib.  of  steam,  cu.  ft. . 

Volume  of  cylinder  to  any 
point  under  consideration 
moved  through  by  the  piston, 
cu.  ft 

Volume  of  clearance,  cu.  ft. . . 

External  work  in  foot-pounds. 

Vol.  of  i  Ib.  of  water  in  cu.  ft . 


V 

Vc 

w 

(7 


The  value  of  the  quantity  at  any  point  under  discussion  if 
denoted  by  the  following  subscripts  :  clearance,  c ;  beginning  of 
admission,  o;  cut-off,  i;  release,  2 ;  beginning  of  compression. 

3- 

The  equations  are  as  follows  for  wet  or  saturated  steam : 

Heat  in  the  Entering  Steam. — 


(I) 


if  the  steam  is  superheated  D  degrees, 


592  EXPERIMENTAL   ENGINEERING.  [§  426. 

Heat  in  the  Cylinder.  —  Since  the  steam  in  this  case  is  in- 
variably moist,  we  have  the  following  equations  : 

In  the  clearance  spaces,     hc  =  M0(qc  +  xcpc)  ;      .     .     .     '3) 
At  admission,  k.  =  M0(g0  +  *0p0)  ;  .     .         .     (4) 

At  cut-off,  *,=(^+^.X?,  +  *,/>,);    •     (5) 

Al  release,  h,  =  (M  +  J/0)fe  +  *3pa)  ;  .     (6) 

At  compression,  ^,  =  M0(qt  -\-  xtp9).  ...      (7) 

The  external  work  is  to  be  determined  from  the  indicator- 
diagram.  Let  the  heat  equivalent  of  this  work  be  represented 
as  follows: 

During  admission,  AWa\      .......  (8) 

During  expansion,  AWb;       .....     .     .  (9) 

During  exhaust,  AWC\  ........  (10) 

During  compression,  AWd.  .     ......     .  (li) 

The  volume  in  cubic  feet,  F,  of  a  given  weight  of  steam, 
My  can  always  be  expressed  by  the  formula 


(12) 


in  which  u  equal  the  excess  of  volume  of  one  pound  of  steam 
over  that  of  one  pound  of  water  ;  u  =  v  —  a. 

Substituting  the  value  of  u  in  the  above  equation, 


As  o-  is  a  very  small  quantity,  (i  —  x)v  can  be  safely 
dropped  as  less  than  the  errors  of  observation,  and  in  all  prac- 
tical applications  the  formula  used  is 


F=  Mxv. 


§426.]    METHODS  OF   TESTING    THE   STEAM-ENGINE.        593 

In  the  exact  equation  (13)  or  the  approximate  equation 
(14),  if  the  pressure,  weight,  and  volume  of  steam  are  known, 
its  specific  volume,  v,  can  be  found,  and  x  may  be  computed. 

At  any  point*  in  the  stroke  after  the  steam-valve  is  closed. 
the  volume  and  pressure  of  steam  in  the  cylinder  can  be 
determined  from  the  indicator-diagram  if  the  dimensions  of 
the  engine  and  its  clearance  are  known.  If  the  weight  of  steam 
used  is  known  from  an  engine-test,  there  can  be  determined 
from  the  indicator-diagram  both  the  quality  and  amount  of 
heat  in  the  cylinder  at  any  point,  with  the  single  exception  of 
the  steam  remaining  in  the  clearance  spaces.  Thus  let  Ve 
equal  volume  of  clearance;  F0  -f-  Vc,  volume  at  admission, 
usually  equal  to  Vc  ;  Vl  -f-  Vc  ,  volume  at  cut-off  ;  F,  +  Vc  ,  at 
release;  F9  +  Vc  ,  at  compression;  M,  the  weight  of  steam 
used  ;  J/Q  ,  the  weight  of  steam  caught  and  retained  in  the 
clearance  spaces.  Then,  by  method  used  in  equation  (12), 

.     .-:.  V   .     .     (15) 
i       .....     (16) 

1+<r1);  ...    (17) 

+<r,);    .     .:    .     (18) 
l  ......     (19) 


In  the  above  equations  we  know  the  volumes  and  pressures 
for  each  point,  and  the  weight  of  steam,  M,  passing  through 
the  engine.  So  that  in  the  five  equations  there  are  six  un- 
known quantities  :  M0  ,  xc  ,  X0  ,  xl  ,  x^  ,  and  x^  ,  of  which  x^  may 
be  assumed  as  i.oo  without  sensible  error.  In  the  above  equa- 
tions, (15)  and  (16)  are  usually  identical  ;  they  differ  from  each 
other  only  when  there  is  a  sensible  lead  which  shows  on  the 
diagram. 

The  weight  of  steam  in  the  clearance  space  is  computed 
from  equation  (15): 

M0  =  (  Ve)  -r-  (xcuc  +  O  =  Vc  -f-  xcvc  ,  nearly. 


594  EXPERIMENTAL   ENGINEERING.  [§  426. 

Assume  x  =  i.oo: 

M.=  Ve  +  ve..     ...........     (20) 

» 

In  computing  the  heat  at  any  point,  it  is  customary  to  com- 
pute  the  sensible  and  internal  heat  in  two  operations.  Thus 
in  equation  (4)  make  /z,  the  total  heat,  equal  to  H,  the  sensible 
heat,  plus  Hr,  the  internal  heat  ;  then 


or                         9=9g99  ...........  (21) 

H0'=x0p0M0;    ..........  (22) 

and  in  equation  (5), 

H^q,(M.-\-M\     .......  (23) 

H;  =  (X^(M,  +  M\  .    .    .....  (24) 

From  equation  (17), 

M.+  M=  v>  +  v<  =-J^±^_    .rt+v. 

xlu,  +  <rl       *u  +  o(i-x)-  ~'" 

By  substituting  in  (24), 


which  form  is  used  in  the  computations  that  follow. 

The  analysis  determines  the  loss  of  heat  during  a  given 
period,  by  finding  the  difference  between  the  heat  in  the  cylin- 
der at  the  beginning  of  the  period  and  the  sum  of  that  utilized 
in  work  during  the  period  and  that  remaining  at  the  end  of 
the  period. 

The  following  directions  and  example  should  make  the 
method  clearly  understood. 


§  42/.]     METHODS   OF   TESTING    THE  STEAM-ENGINE.     595 

The  total  heat  received  and  discharged  per  stroke  is  obtained 
by  testing.  The  distribution  of  the  heat  and  its  relations  to  the 
work  performed  is  obtained  by  measurements  from  the  indicator 
diagram.  For  this  purpose  the  diagram  is  divided  as  indicated 
in  Fig.  282,  so  that  the  mechanical  work  for  the  respective  periods 
of  admission,  expansion,  release,  and  compression  can  be  com- 
puted. The  heat  received  at  the  beginning  and  discharged  al 
the  end  of  each  of  these  periods  is  compared  with  the  mechanical 


b  a 

FIG.  282. — DIAGRAM  FROM  A  GREENE  ENGINE.       CYLINDER,  26  INCHES  IN  DIAMETER  BY 
36  INCHES  STROKE.     BOILER-PRESSURE,  80  REVOLUTIONS  PER  MINUTE.    SCALE,  50. 

work  expressed  in  heat-units  done  during  that  period.  From 
this  comparison  the  amount  of  heat  interchanged,  plus  or  minus, 
is  computed  for  each  period.  It  is  to  be  noted  that  work  done  on 
the  forward  stroke  is  positive  and  that  on  the  back  stroke  negative. 

427.  Directions  for  Engine-testing  by  Hirn's  Analysis. 

Directions. — i.  Make  a  complete  engine- test  with  a  constant 
load,  weigh  the  condensing  water,  and  measure  its  temperature 
before  and  after  condensing  the  steam.  Obtain  the  quality  of 
the  entering  steam  either  in  the  steam-pipe  or  steam-chest;  if 
convenient,  make  calorimetric  determinations  of  the  quality  of 


596  EXPERIMENTAL  ENGINEERING.  [ 

the  steam  in  the  exhaust,  which  may  be  used  as  a  check  on  the 
results,  but  which  is  necessary  in  case  the  exhaust  steam  is 
not  condensed. 

2.  Calibrate  all  the  instruments  used,  and  correct  all  obser- 
vations where  required. 

3.  From  the   average  quantities   on  the   log,  corrected  as 
shown  by  the  calibration,  fill  out  form   I,  of  data  and  results. 
The  steam  and  condensing  water  used  per  revolution  to  be  di- 
vided between  the  forward  and  backward  strokes  of  the  piston 
in  proportion  to  the  M.  E.  P.  of  these  respective  strokes,  as 
shown  on  the  log. 

4.  Draw  on  each  diagram  as  explained  lines  corresponding  to 
zero  volume  and  to  zero  pressure,  and  divide  the  diagrams  as 
shown  in  Fig.  226  into  sections,  by  drawing  lines  to  points  of 
admission  IV,  cut-off  en,  release  Oe,  and  compression  od. 

Measure  for  each  diagram  the  percentages  of  cut-off,  release, 
and  compression,  calling  the  original  length  of  the  diagram 
without  clearance  100  per  cent. 

5.  Measure  the  absolute  pressure  from  each  card  and  enter 
the  averages  in  blank  form  No  II,  using  subscripts  as  follows:  o, 
admission  ;  i,  cut-off;  2,  release ;  3,  compression  ;  c,  clearance. 

Take  from  a  steam-table  the  heat  of  liquid,  internal  latent 
heat,  total  latent  heat,  total  heat,  and  specific  volume,  corre- 
sponding to  each  of  the  above  pressures. 

6.  Compute  the  volumes  in  cubic  feet  for  clearance,  total 
volumes,  including  clearance,  at  admission,  cut-off,  release,  and 
compression,   and   place    the   average    results   in    the   proper 
columns. 

7.  Compute  the.  area  corresponding  to  each  period  into 
which  the  diagram  is  divided  and  find  the  mean  pressure  for 
that  period.   Also  find  the  work  done  in  each  period,  expressed 
in  foot-pounds  and  also  in  B.  T.  U.   (It  is  to  be  noted  that  the 
work  done  during  the  return  stroke  is  negative.)     Enter  the 
average  of  these  results  in  the  proper  place,  noting  the  use  of 
the  subscripts  a,  b,  c,  and  d. 

8.  Calculate  the  heat-losses  as  indicated  on  Form  III,  which 
is  an  account  of  the  heat  useoV during  100  strokes  of  the  engine. 


§42/«]    METHODS  OF    TESTING    THE   STEAM-ENGINE.        597 

The  weight  of  steam,  M,  in  pounds  is  100  times  the  amount  used 
for  one  stroke  as  given  on  Form  I.  The  weight  of  steam  in 
clearance  is  to  be  calculated  for  admission,  pressure,  and  volume, 
and  with  x  equal  i.oo.  M0,  to  be  calculated  in  the  same  manner. 
Calculate  from  known  weights  and  temperatures  the  heat  ex- 
hausted from  the  engine  in  the  condensed  steam  Kr  and  in  the 
condensing  water  K. 

Calculate  by  the  formulae,  as  explained,  the  heat  supplied 
the  engine,  and  the  sensible  and  internal  heat,  at  each  event  in 
the  stroke  of  the  engine. 

9.  Calculate  the  cylinder-loss  at  admission  as  the  difference 
between  that  supplied  added  to  that  already  in  the  clearance, 
and  that  remaining  at  cut-off  added  to  that  used  in  work.     If 
the  heat  is  flowing  from  the  metal,  the  sign  will  be  negative, 
otherwise  positive. 

10.  Perform  the  same  operation  for  each   period  of   the 
engine ;  the  difference  between  the  heat  at  the  beginning  of 
each  period  and  that  at  the  end,  taking  into  account  the  work 
done,  is  the  loss. 

11.  Take  the  algebraic  sum  of  these  losses  and  of  the  heat 
equivalent  of  the  external  work,  and  if  no  error  has  been  made 
in  the  calculations,  this  sum,  which  is  the  total  transformation, 
will  equal  the  difference  between  the  heat  supplied   and  that 
-exhausted.    That  is,  using  the  symbols  of  the  analysis,  D  =  D.' 
It  is  also  evident  that  this  quantity  is  the  loss  by  radiation. 

The  importance  of  this  check  on  the  accuracy  of  the  com- 
putations should  not  be  overlooked.  If  no  errors  of  computa- 
tion are  made,  in  each  case  the  value  of  D  will  equal  that  of  D'. 

12.  Make  the  remaining  calculations  as  on  Form  IV  ;  these 
give  the  quality  which  the  steam  must  have  at  various  portions 
of  the  stroke  to   correspond  with  the  foregoing  calculations. 
The  quality  is  calculated  from  the  volume  remaining  in  the 
cylinder.     Compute  the  various  efficiencies. 

Note  that  the  heat  lost  during  admission  is  in  some  respects 
a  measure  of  the  initial  cylinder-condensation. 

The  following  forms  are  given  partially  filled  out  with  the 
results  of  a  test  made  by  application  of  Hirn's  analysis. 


598 


EXPERIMENTAL   ENGINEERING. 


[§  428. 


428.  Forms  for  Hirn's  Analysis. 


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§  428.]    METHODS  OF   TESTING    THE  STEAM-ENGINE.         S99 

FORM  No.  I. 

APPLICATION    OF    HIRN'S    ANALYSIS   TO   SIMPLE   CONDENSING 

ENGINE. 
DATA  AND  RESULTS. 

Test  of  steam-engine  made  by at  Cornell  University. 

Kind  of  engine,  slide-valve  throttling.      Diameter  cylinder 6.06  inches. 

Length  stroke 8  inches.  Diameter  piston-rod. .  \\\      " 

Volume  cylinder crank  end,  0.12921  cu.  ft.;  headend,     o.  13354  cu.  ft. 

Volume  clearance,  cubic  foot,  head 0.01744 

Clearance  in  per  cent  of  stroke 13.06 

Volume  clearance,  cubic  foot,  crank 0.01616 

Clearance  in  per  cent  of  stroke 12.51 

Boiler-pressure  by  gauge 69.4.        Barometer 29.276 

Boiler  pressure  absolute,  pounds. . . .-. 83.7 

Boiling  temperature,  atmospheric  pressure,  deg.  F 210.7 

Revolutions  per  hour 11898 

Steam  used  during  run,  pounds 716.424 

Quality  of  steam  in  steam-pipe 0.99 

Quality  of  steam  in  steam-chest 0.9941 

Quality  of  steam  in  compression i.ooi 

Quality  of  steam  in  exhaust 0.9021 

Weight  of  condensed  steam  per  hour 259.92 

Pounds  of  wet  steam*  per  stroke head,  0.0109707;  crank,     0.0109383 

Temperatures  condensed  steam 103.47    deg.  F. 

Temperatures  condensing  water cold,  42.758  deg.  F.;  hot,  92.219  " 

Pounds  of  condensing  water,  per  hour 5044.878 

"   revolution 0.42429 

"        "  "    stroke-head 0.212016 

"       "  "  "          "   crank  0.212274 

SYMBOLS. 

To  denote  different  portions  of  the  stroke,  the  following  subscripts  are  used: 
Admission,  a;  expansion,  b\  exhaust,  c\  compression,  d. 

To  denote  different  events  of  the  stroke,  the  following  sub-numbers  are  used; 
Cut-off,  i;  release,  2;  compression,  beginning  of,  3;  admission,, beginning  of, 
o;  in  exhaust,  5.  Quality  of  steam  denoted  by  X. 

Cut-off,  crank  end,  per  cent  of  stroke. . .  20.544.    Release,  crank  end. .    93.958 
Cut-off,  head  end,  per  cent  of  stroke... .    18.963.    Release,  head  end. . .    94.971 

Compression,  crank  end,  per  cent  of  stroke 52.341 

Compression,  head  end,  per  cent  of  stroke 39-77° 

Pounds  of  steam  per  I.  H.  P. ..    / 39-351 

Pounds  of  steam  per  brake  H.  P 55-314 

I.  H.  P.-  Head 3-3152.     Crank 3-3Q54-     Total 6.6206 

Brake  horse-power 4- 71 

*  Wet  steam  is  the  steam  uncorrected  for  calorimetric  determinations. 


6oo 


EXPERIMENTAL  ENGINEERING. 

FORM  No.  II. 


[§  428, 


ABSOLUTE   PRESSURES   FROM    INDICATOR-DIAGRAMS   AND 
CORRESPONDING   PROPERTIES   OF   SATURATED   STEAM. 


Cut-off. 

Release. 
t 

Beginning 

Symbols. 

Com- 
pression. 

Of  Ad- 
mission. 

Ran- 
kine. 

Clau- 
sius. 

I 

2 

3 

0 

P 

s 
I 

L 
H 
C 

P 
I 

P 
r 
A 

V 

Absolute  pressure.  . 
Heat  of  liquid  

Internal  latent  heat. 
Latent-heat   evapo- 

Head 
Crank 
Head 
Crank 
Head 
Ciank 
Head 
Crank 
Head 
Crank 
(  Head 
\  Crank 

Vol.  lib.  cu.  ft.... 

V  4-  V 

V  4-  V 

V     -1-     V* 

V     \     V 

Volumes  head,  cu.  f 
Volumes  crank,  cu.  1 

0     1 

c    1 

C      1 

\        c 

0 

[t  .    . 

MEAN    PRESSURES    AND    HEAT    EQUIVALENTS    OF    EXTERNAL 

WORK. 


Subscripts. 

Head  End. 

Crank  End. 

Mean 
Pressures. 

External  Work. 

Mean 
Pressures. 

External  Work. 

Foot-lbs. 

B.  T.  U. 

Foot-lbs. 

B.  T.  U. 

Symbols     

MP 

w 

AW* 

MP 

W 

AW* 

Expansion   ...... 

b 
c 
d 

Compression.  .  .  . 
Total  

n  =  volume  in  clearance-spaces. 


§  428.]     METHODS  OF   TESTING    THE  STEAM-ENGINE.        6oi 


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§  430.]    METHODS  OF   TESTING    THE   STEAM-ENGINE.         603 

429.  Hirn's  Analysis  applied  to  Non-condensing  En- 
gines.—In  this  case:   I.  Determine  the  weight  of  water  used, 
by  weighing  that   supplied   the  boiler,  taking  precautions  to- 
prevent   loss  of  steam  between  the  engine  and  the  boiler  by 
leaks.     Apply  the  calorimeter  and  ascertain  the  quality  near 
the  engine.     The  heat  in  one  pound  of  steam  above  32°  Fahr. 
will    be    represented    by   the    formula   xr  +  q,    as   previously 
explained.     This  quantity  multiplied  by  the  weight,  M,  is  the 
heat  supplied.     M  may  be  taken   for  i  or  for  100  strokes,  as 
convenient. 

2.  Determine  the  quality  of  the  exhaust-steam  by  attaching 
a  calorimeter  in  the  exhaust-pipe,  close  to  the  engine.     The 
heat  discharged  by  one  pound  will  be,  as  explained  in  Article 
$11,  xer,  +  ge;  in  which  the  symbols  denote  quantities  taken 
at  exhaust-steam  pressure.     This  quantity  multiplied  by  the 
weight,  M,  is  the  heat  discharged,  and  is  equal  to  K -\-  K'  in 
the  Form  III,  page  543. 

3.  With  these  exceptions,  the  method  is  exactly  as  explained 
for  the  condensing  engine,  and  the  same  forms  are  to  be  used. 

In  obtaining  the  quality  of  the  exhaust-steam,  a  separating 
calorimeter  (see  Art.  337)  through  which  the  steam  is  drawn 
by  suction,  can  be  used  with  success. 

430.  Application    of    Hirn's    Analysis    to    Compound 
Engines. — Compound  engines  are  usually  run  condensing,  and 
the  special  directions  are  for  that  case  ;  but  in  case  the  engine 
is  run  non-condensing  the  method  of  Article  429  can  be  applied. 

Directions.  —  With  calorimeter  between  the  cylinders : 

1.  Attach  a  calorimeter  in  the  exhaust  of  the  high-pressure 
cylinder,  and  determine   the  heat  exhausted   from   the  high- 
pressure  cylinder  as  explained  for  non-condensing  engines. 

Treat  the  high  pressure  cylinder  as  a  simple  non-condensing 
engine,  as  explained  in  Article  429. 

2.  Determine  by  the  calorimeter  between  the  cylinders  the 
heat  supplied  to  the  low-pressure  engine.     This  quantity  will 
be  the  same  as  that  exhausted  from  the  high-pressure,  corrected 
for  steam  used  by  the  calorimeter  and  for  radiation  from  the 
connecting  pipes. 


604  EXPERIMENTAL   ENGINEERING.  [§  43! 

3.  Fill  out  the  forms  for  each  cylinder  as  a  separate  engine. 

By  using  two  calorimeters  between  cylinders  the  same 
method  can  be  applied  to  a  triple-expansion  engine. 

In  case  the  pressure  of  the  steam  between  the  cylinders  is 
less  than  atmospheric  a  calorimeter  can  be  used  by  attaching  a 
special  air-pump  and  condenser,  so  as  to  secure  a  flow  of  steam 
through  the  calorimeter. 

Without  calorimeter  between  the  cylinders  : 

1.  Determine  the  weight  of  steam,  M,  for  both  cylinders 
from  the  condensed  steam  of  the  low-pressure  cylinder.     This 
will  give  the  quantity  M. 

2.  For  the  high-pressure  cylinder  compute  the  quantities 
as  in  Form  III,  omitting  those  terms  containing  K  and  AT7,,  the 
heat  exhausted. 

3.  Determine  K  and  K'  as   follows:  K -|-  K'  is  evidently 
equal  to  the  heat  supplied  the  high-pressure  engine,  less  the 
heat  transformed  into  work,  expressed  in  B.  T.  U.,less  the  loss 
by  radiation.     The  total  loss  by  radiation  in  the  whole  engine 
is  equal  to  the  heat  supplied  the  first  cylinder,  less  the  work 
done  by  all  the  cylinders,  less  the  heat  discharged  from  the  last 
one.      As  an  approximation,   divide  this   total  radiation-loss 
equally  between  the  cylinders,  assuming  that  the  lower  tem- 
perature of  the  low-pressure  cylinder  will  offset  its  increased 
size.     This  will  give  us  in  Form  III  the  value  of  D  —  Q  —  B. 
Compute  B,  substitute  this  value  in  the  equation  B  —  K  -\~ 
K'  -\-  A  W.     Compute  K  +  K'  and  complete  the  analysis  for 
the  high-pressure  cylinder. 

4.  For   the   low-pressure   cylinder,  determine   the    entering 
heat  as  that  discharged  from  the  high-pressure  cylinder,  K-\-K ', 
plus  the  assumed  radiation  as  given  above. 

Make  a  complete  analysis  for  each  cylinder  as  explained  for 
a  simple  engine. 

431.  Hirn's  Analysis  applied  to  a  Triple-expansion  En- 
gine.— When  the  quality  of  the  steam  between  the  cylinders 
can  be  determined,  treat  the  engine  as  three  separate  engines 
as  explained. 


§431-]    METHODS  OF   TESTING    THE   STEAM-ENGINE.        605 

When  the  quality  cannot  be  determined,  treat  the  case  as 
explained  for  a  compound  engine,  as  follows : 

1.  Find  the  entire  loss  as  equal  to  the  difference  between 
that  supplied  to  the  first  cylinder  and  that  discharged  from  the 
last,  increased  by  the  work  done  in  the  whole  system  reduced 
to  thermal  units.     Divide  this  by  the  number  of  cylinders  to 
find  the  assumed  radiation-loss  from  each. 

2.  Take  the  cylinders  in  series,  and  assume  the  discharged 
heat  to  equal  the  heat  supplied,  diminished  by  that  transformed 
into   external   work,   and   make   a  separate  analysis   for  each 
cylinder  as  explained  for  a  simple  engine. 

The  following  is  an  application  of  Hirn's  analysis  to  a 
triple-expansion  engine  by  Prof.  C.  H.  Peabody  at  the  Massa- 
chusetts Institute  of  Technology. 

The  main  dimensions  of  the  engine  are  as  follows: 

Diametei  of  the  high-pressure  cylinder 9    inches. 

Diameter  of  the  intermediate  cylinder 16         " 

Diameter  of  the  low-pressure  cylinder 24         " 

Diameter  of  the  piston-rods 2r\    " 

Stroke 30         " 

Clearance  in  per  cent  of  the  piston  displacements  : 

High-pressure  cylinder,     head  end,     8.83;     crank  end,  9.76 

Intermediate  10.4  "  10.9 

Low-pressure  11.25  "  8.84 

The  following  table  gives  the  data  and  results  of  a  test 
with  Hirn's  analysis,  made  by  the  graduating  class: 

Duration  of  test,  minutes 60 

Total  number  of  revolutions 5299 

Revolutions  per  minute 88.3 

Steam-consumption  during  test,  pounds: 

Passing  through  cylinders 1193 

Condensation  in  high-pressure  jacket 57 

"  in  first  receiver  jacket .   61 

in  intermediate  jacket 85 

in  second  receiver  jacket 53 

in  low-pressure  jacket 89 

Total   .  1538 


606                          EXPERIMENTAL   ENGINEERS^.  [§43*- 

Condensing  water  for  test,  pounds 22847 

Priming,  by  calorimeter 0,013 

Temperatures,  Fahrenheit: 

Condensed  steam 95.4 

Condensing  water,  cold 41.9 

Condensing  water,  hot 96. 1 

Pressure  of  the  atmosphere,  by  the  barometer,  Ibs.  per  sq.  in 14.8 

Boiler-pressure,  Ibs.  per  sq.  inch,  absolute ~. 155-3 

Vacuum  in  condenser,  inches  of  mercury 25.0 

Events  of  the  stroke: 

High-pressure  cylinder — 

Cut-off,  crank  end '. .  o.  192 

"        headend 0.215 

Release,  both  ends j .00 

Compression,  crank  end 0.05 

"              headend.... 0.05 

Intermediate  cylinder — 

Cut-off,  both  ends o.  29 

Release,  both  ends i.oo 

Compression,  crank  end 0.03 

"            headend 0.04 

"Low-pressure  cylinder — 

Cut-off,  crank  end 0. 38 

"       headend 0.39 

Release,  both  ends I.oo 

Quality  of  the  steam  in  the  cylinder — (at  admission  and  at  compression 

the  steam  was  assumed  to  be  dry  and  saturated:) 
High-pressure  cylinder — 

At  cut-off x\  0.785 

At  release x*  0.899 

Intermediate  cylinder — 

At  cut-off x*  o.  899 

At  release x*  0.994 

Low-pressure  cylinder — 

At  cut-off , jci  0.978 


Interchanges  of  heat  between  the  steam  and  the  walls  of  the  cylinders, 
in  B.  T.  U.     Quantities  affected  by  the  positive  sign  are 
absorbed  by  the  cylinder- walls;  quantities  affected  by  the 
negative  sign  are  yielded  by  the  walls. 
High-pressure  cylinder — 

Brought  in  by  steam Q          132.92 

During  admission Qa  23.54 

During  expansion Qt      —18.69 

During  exhaust Qe      —    8.36 


METHODS   OF   TESTING    THE   STEAM-ENGINE.         607 


During  compression  ..................................  Qd  0.45 

Supplied  by  jacket  ...................................  Oj  4.56 

Lost  by  radiation  ....................................  Qe  i  .  50 

First  intermediate  receiver  — 

Supplied  by  jacket  ...................................  QJR  4.92 

Lost  by  radiation  ...........   ........................  QeR  o.  58 

Intermediate  cylinder  — 

Brought  in  by  steam  ................................  .  (X  131.89 

During  admission  ..................................  Qa'  13.62 

During  expansion  .  .  .................  ,  ...............  Qb  —  18.65 

During  exhaust  ......................................  Qc'  0.22 

During  compression  .................................  Qd  0.44 

Supplied  by  jacket  ..............................  .  ----  Q/  6.82 

Lost  by  radiation   ...................................  Qe  2.45 

Second  intermediate  receiver  — 

Supplied  by  jacket  .....................  «  .............  QJR  4.20 

Lost  by  radiation  ....................................  QtR  1.20 

Low-pressure  cylinder  — 

Brought  in  by  steam  ...........................  .  .....  Q'  132.  14 

During  admission  ...................................  Qa'  5-85 

During  expansion  ............  .......................  Qb"  —9.51 

During  exhaust  ............  .........................  Qc'  2.  53 

During  compression  .................................  Qd"  o.oo 

Supplied  by  jacket  ...................................  <X'  7«o8 

Lost  by  radiation  .............................  r  ......  Q"  4.34 

Total  loss  by  radiation  : 

By  preliminary  test  .................................  ^Q«  10.07 

By  equation  (49)  .......................................  n.68 

Absolute  pressures  in  the  cylinder,  Ibs.  per  sq.  inch  : 

High-pressure  cylinder  — 

Cut-off,  crank  end  ......................................  I45«9 

headend  .......................................  *43-2 

Release,  crank  end  ..............................  ........  4J'3 

headend  ......................................  4^5 

Compression,  crank  end  ................................  43-7 

headend  .................................  48.7 

Admission,  crank  end  ...................................  64.5 

"             headend  ....................................  75-3 

Intermediate  cylinder  — 

Cut-off,  crank  end  .....................................  -  3'/-2 

headend  .......................................  35-<> 

Release,  crank  end  ......................................  J3-6 

"         headend  .....................................  "3-4 

Compression,  crank  end  .....  .  ...........................  *°'3 

"              headend  .................................  17-9 


608                          EXPERIMENTAL   ENGINEERING.  [§  431- 

Admission,  crank  end 20.4 

"           headend 21.1 

Low-pressure  cylinder — 

Cut-off,  crank  end 12. 1 

"        head  end 12.0 

Release,  crank  end 5.6 

"         headend (   5.4 

Compression  and  admission,  crank  end 3.7 

"               "             "           headend 4.3 

Heat  equivalents  of  external  work,  B.  T.  U.,  from  areas  on  indicator- 
diagram  to  line  of  absolute  vacuum  : 
High-pressure  cylinder — 

During  admission,  A  Wa  ,  crank  end 5.71 

"               "                        headend 6.61 

During  expansion,  A  Wb ,  crank  end 10.65 

"               "                        headend 10.81 

During  exhaust,  A  Wc ,  crank  end 7. 75 

"             "                      headend 8.08 

During  compression,  A  Wd ,  crank  end 0.48 

"                 "                           headend 0.62 

Intermediate  cylinder — 

During  admission,  A  Wa ,  crank  end 7. 58 

"                "                       headend 7.43 

During  expansion,  A  Wb ,  crank  end 9. 54 

"                                        headend 9.22 

During  exhaust,  A  Wc  ,  crank  end 9.27 

"                                    headend 9.27 

During  compression,  A  Wd ,  crank  end 0.39 

"                                             headend 0.60 

Low-pressure  cylinder — 

During  admission,  A  Wa,  crank  end 7.75 

head  end 7.99 

During  expansion,  A  Wb ,  crank  end 6.83 

"                                        headend 6.87 

During  exhaust,  A  Wc,  crank  end 5.08 

head  end 5.08 

During  compression,  A  Wd ,  crank  end o.oo 

"                 "                            headend o.oo 

Power  and  economy  : 

Heat  equivalents  of  work  per  stroke — 

High-pressure  cylinder A  W  8.44 

Intermediate  cylinder A  W'  7. 12 

Low-pressure  cylinder AW"  9.64 

Total 25.20 

Total  heat  furnished  by  jackets 27.58 


§43r-]    METHODS  OF   TESTING    THE   STEAM-ENGINE.         609 

Distribution  of  work  : 

High-pressure  cylinder i.oo 

Intermediate  cylinder 0.84 

Low-pressure  cylinder i  r^ 

Horse-power 104.9 

Steam  per  horse-power  per  hour 14.65 

B.  T.  U.  per  horse-power  per  minute 258.3 

THE  SATURATION-CURVE. — By  drawing  on  the  indicator- 
diagram  a  curve  corresponding  to  the  volume  of  an  equal 
weight  of  dry  and  saturated  steam,  the  quality  may  be 
determined  at  any  point  during  the  expansion,  and  by  calcula- 
tions similar  to  those  used  in  Hirn's  analysis  the  heat  exist- 
ing in  the  cylinder  may  be  computed.  The  method  of 
drawing  the  saturation-curve  may  be  explained  as  follows: 
first,  determine  the  weight  of  steam  per  stroke  by  the  usual 
methods  of  engine-testing.  Second,  find  the  corresponding 
volume  for  dry  and  saturated  steam  by  multiplying  the  weight 
of  steam  per  stroke  by  the  volume  corresponding  to  one 
pound  as  obtained  from  the  steam  tables,  for  several  points  in 
the  expansion-curve.  Third,  draw  in  connection  with  the 
indicator-diagram  a  clearance-line  and  a  vacuum-line  in 
accordance  with  the  scale  of  volume  and  pressure,  from  which 
initial  measurements  can  be  taken. 

Fourth,  determine  the  volume  occupied  by  the  steam 
caught  in  the  clearance-space  when  compressed  to  the  steam- 
line;  for  this  operation  we  can  assume  with  little  error  that 
the  steam  is  dry  and  saturated  at  the  end  of  compression,  and 
that  it  remains  in  this  condition  during  compression.  Thus 
in  Fig.  283  the  compression-line  is  produced  from  ab  to  a 
by  drawing  a  saturation-curve,  which  is  drawn  by  taking 
ordinates  proportional  to  pressures  and  abscissa  proportional 
to  volumes  as  given  in  the  steam  table,  those  for  at  being 
known.  This  curve  may  be  considered  the  curve  of  volume 
for  dry  and  saturated  compression.  Very  little  error  would 
be  made  by  assuming  the  compression-curve  hyperbolic.  By 
producing  the  saturation-curve  aab  downward  the  quality 
during  compression  could  be  determined. 


6io 


EXPERIMEN  TA  L   ENGINEERING. 


Fifth,  lay  off  from  the  compression-curve  for  saturated 
steam  horizontal  distance  corresponding  to  the  volume  of  dry 
and  saturated  steam  at  different  pressures,  obtained  as  ex- 
plained above.  Through  the  various  points  so  determined 
draw  a  curve;  such  a  curve  will  be  the  saturation-curve. 

To  obtain  the  quality  of  the  steam  at  any  point  en  the 
expansion-lines  divide  the  horizontal  distance  measured  from 
the  clearance-line  to  the  expansion-line  by  the  corresponding 
distance  to  the  saturation-curve.  Thus  in  Fig.  283  the 


<  OF  STROKE 


FIG.  283. 


quality  at  d^  is  equal  to  b^djb^c^  —  that  is,  the  quality  is  the 
ratio  of  the  actual  volume  of  the  steam  to  that  of  dry  and 
saturated  steam,  and  this  is  true  provided  the  volume  occupied 
by  the  condensed  steam,  which  is  exceedingly  small  in  every 
case,  is  neglected.  The  quality  at  different  points  during 
expansion  can  be  determined  in  a  similar  manner,  and  a  curve 
showing  the  variation  of  quality  may  be  laid  off  as  shown  in 
the  lower  portion  of  Fig.  283. 

The  comparative  quality  during  compression  can  be 
obtained  in  a  similar  manner  by  comparing  the  volume  during 
compression  with  that  of  an  equal  volume  of  d;y  and  saturated 
steam. 


§43!-]  METHODS   OF   TESTING    THE   STEAM-ENGINE.       6ll 

The  en  or  involved  in  the  above  construction  is  the  same 
as  that  made  in  Hirn's  analysis,  since  in  both  cases  the 
quality  of  the  steam  at  end  of  compression  is  assumed  and  the 


FIG.  284. 


volume  of  water  entrained  is  neglected  ;  such  errors  are,  how- 
ever, exceedingly  small.  Fig.  284  shows  the  saturation- 
curves  of  a  combined  diagram  reduced  from  cards  taken  on 
the  Sibley  College  experimental  engine.  It  will  be  noticed 
that  the  saturation-curve  is  not  continuous  for  the  three 


612 


EXPERIMENTAL   ENGINEERING. 


cylinders,  which  is  due  to  the  fact  that  clearance  and  com- 
pression of  the  different  cylinders  is  not  uniform. 

To  calculate  the  interchanges  of  heat  in  an  engine  during 
expansion  and  compression,  first  determine  the  quality  as 
explained.  Also  determine  the  weight  of  steam  used  per 
stroke,  the  weight  of  and  the  rise  in  temperature  of  the  con- 
densing water.  Using  the  same  symbols  as  for  Hirn's 
analysis,  the  heat  supplied  to  the  engine  will  be 


that  discharged  from  the  engine  is  equal  to  the  heat  of  the 
condensed  steam  above  32°  F.,  Mqs  plus  that  absorbed  by  the 
inject  ion-  water  G(qk  —  q)  that  utilized  in  work  A  W.  The 


HEAT-INTERCHANGES   CALCULATED    BY  SATURATION-CURVE. 

QUANTITY    PER    IOO   STROKES. 


Obtain  by  measurement: 

Weight  of  steam,  in  pounds 
Weight  of  injection  water, 

M 

G 

Heat  transformed  into  work  : 
Admission  (a)  A  Wa  =  a 

Expansion  (b)  A  Wb  =  b 

Temperature   of   condensed 
steam  above  32°  F       .... 

Qp 

Exhaust  (c  )  A  IV  c  ~~  c 

Rise    in  temperature   injec- 

<Jk  —  Qi 

Compression  (d\  A  }Vd  ~"  tf 

Wt.  of  steam  in  clearance  .  . 

Quality  steam  entering  
Quality  cut-off,  release,  and 

Mo 

X 

Heat-interchanges  .* 
Admission  H  —  (Hi  -f-  a) 

Expansion  H±  —  (H*  +  ^) 

Quality  end  of  compres'n,  % 
Obtain  by  computation  : 

IOO 

H 

Exhaust  H*  —  (K+  Ki  -f-  c  +  H^ 
Compression  HI  —  (</-{-  H±) 

Heat  at  cut-off, 
Heat  at  release, 
Heat  at  compression, 
Heat  discharged,  condensed 

H, 
H* 

Total   loss  equals  algebraic  sum 
of  heat-interchanges,  and   this 
affords  a  check  on  the  numer- 
ical work. 

Heat  discharged,    injection 

M(gk  —  Qi)  —  J^\ 

H  -  (K  +  KJ) 

§431-]   METHODS   OF  TESTING    THE  STEAM-ENGINE.        613 

difference  between  that  received  and  that  discharged  is  the 
total  loss  due  to  radiation. 

The  heat  remaining  in  the  steam  at  any  point  can  be 
obtained  by  multiplying  the  weight  of  steam  used  per  stroke, 
increased  by  that  caught  in  the  clearance,  by  the  sum  of 
sensible  heat  and  product  of  internal  latent  heat  and  quality. 
Thus 


The  work  done  while  the  piston  is  passing  from  point  to  point 
under  consideration  may  be  obtained  by  integrating  the 
diagram  and  reducing  to  heat-units  by  dividing  by  778.  The 
table  on  the  foregoing  page  indicates  the  operations  to  be 
performed  in  calculating  the  heat-interchanges  by  the  satura- 
tion-curve. 

NOTE.  —  The  method  of  determining  the  heat  interchanges  in  a  steam 
engine  which  have  been  given  apply  directly  to  the  use  of  saturated  or 
wet  steam  only.  The  same  general  method  is  applicable  when  super- 
heated steam  is  used,  but  for  that  case  the  relation  of  volume  and  weights 
to  heat  values  will  be  essentially  different. 


CHAPTER   XIX. 

METHODS   OF    TESTING   PUMPING   ENGINES   AND 
STEAM    LOCOMOTIVES. 

432.  Special  Methods  of  Engine-testing.— Engines  em- 
ployed for  certain  specific  purposes,  as  for  pumping  water  or 
for  locomotive  service,  are  constructed  with  peculiar  features 
rendered  necessary  by  the  work  to  be  accomplished.     In  suck 
cases   it   is    frequently  difficult   to  arrange   to  make   all   the 
measurements  in  the  manner  prescribed  for  the  tests  of  the 
general  type  of  the  steam-engine ;  further,  it  is  often  of  impor- 
tance that  the  amount  and  character  of  the  work  accomplished 
be  taken  into  consideration.     To  secure  results  that  can  safely 
be  compared,  it  is  essential  that  certain  methods  of  testing  be 
adopted  and  that  the  results  be  expressed  in  the  same  form 
and  referred  to  the  same  standards. 

433.  Method  of  Testing   Steam  Pumping-engines. — A 
standard  method  of  testing  steam  pumping-engines  has  been 
adopted  by  the  American  Society  of    Mechanical  Engineers 
(see  Vol.  XL  of  the  Transactions).     The  method  is  as  follows : 

(l)  TEST  OF  FEED-WATER  TEMPERATURES. 

The  plant  is  subjected  to  a  preliminary  run,  under  the  con- 
ditions determined  upon  for  the  test,  for  a  period  of  three 
hours,  or  such  a  time  as  is  necessary  to  find  the  temperature 
of  the  feed-water  (or  the  several  temperatures,  if  there  is  more 
than  one  supply)  for  use  in  the  calculation  of  the  duty.  During 
this  test  observations  of  the  temperature  are  made  every  fifteen 
minutes.  Frequent  observations  are  also  made  of  the  speed, 
length  of  stroke,  indication  of  water-pressure  gauges,  and  other 

614 


§  432-]  TESTING  PUMPING-ENGINES.  615. 

instruments,  so  as  to  have  a  record  of  the  general  conditions 
under  which  this  test  is  made. 

Directions  for  obtaining  Feed-water  Temperatures. — When 
the  feed-water  is  all  supplied  by  one  feeding  instrument,  the 
temperature  to  be  found  is  that  of  the  water  in  the  feed-pipe 
near  the  point  where  it  enters  the  boiler.  If  the  water  is  fed 
by  an  injector  this  temperature  is  to  be  corrected  for  the  heat 
added  to  the  water  by  the  steam,  and  for  this  purpose  the 
temperature  of  the  water  entering  and  of  that  leaving  the 
injector  are  both  observed.  If  the  water  does  not  pass  through 
a  heater  on  its  way  to  the  boiler  (that  is,  that  form  of  heater 
which  depends  upon  the  rejected  heat  of  the  engine,  such  as. 
that  contained  in  the  exhaust-steam  either  of  the  main  cylin- 
ders or  of  the  auxiliary  pumps),  it  is  sufficient,  for  practical 
purposes,  to  take  the  temperature  of  the  water  at  the  source 
of  supply,  whether  the  feeding  instrument  is  a  pump  or  an 
injector. 

When  there  are  two  independent  sources  of  feed-water 
supply,  one  the  main  supply  from  the  hot-well,  or  from  some 
other  source,  and  the  other  an  auxiliary  supply  derived  from 
the  water  condensed  in  the  jackets  of  the  main  engine  and  in 
the  live-steam  reheater,  if  one  be  used,  they  are  to  be  treated 
independently.  The  remarks  already  made  apply  to  the  first, 
or  main,  supply.  The  temperature  of  the  auxiliary  supply,  if 
carried  by  an  independent  pipe  either  direct  to  the  boiler  or  to 
the  main  feed-pipe  near  the  boiler,  is  to  be  taken  at  convenient 
points  in  the  independent  pipe. 

When  a  separator  is  used  in  the  main  steam-pipe,  arranged 
so  as  to  discharge  the  entrained  water  back  into  the  boiler  by 
gravity,  no  account  need  be  made  of  the  temperature  of  the 
water  thus  returned.  Should  it  discharge  either  into  the 
atmosphere  to  waste,  to  the  hot-well,  or  to  the  jacket-tank,  its 
temperature  is  to  be  determined  at  the  point  where  the  water 
leaves  the  separator  before  its  pressure  is  reduced. 

When  a  separator  is  used,  and  it  drains  by  gravity  into  the 
jacket-tank,  this  tank  being  subjected  to  boiler-pressure,  the 


6l6  EXPERIMENTAL  ENGINEERING.  [§  432- 

temperature  of  the  separator-water  and  jacket-water  are  each 
to  be  taken  before  their  entrance  to  the  tank. 

Should  there  be  any  other  independent  supply  of  water,  the 
temperature  of  that  is  also  to  be  taken  on  this  preliminary  test. 

Directions  for  Measurement  of  Feed-water. — As  soon  as  the 
feed-water  temperatures  have  been  obtained  the  engine  is 
stopped,  and  the  necessary  apparatus  arranged  for  determin- 
ing the  weight  of  the  feed-water  consumed,  or  of  the  various 
supplies  of  feed-water  if  there  is  more  than  one. 

In  order  that  the  main  supply  of  feed-water  may  be  meas- 
ured, it  will  generally  be  found  desirable  to  draw  it  from  the 
cold-water  service-main.  The  best  form  of  apparatus  for 
weighing  the  water  consists  of  two  tanks,  one  of  which  rests 
upon  a  platform-scale  supported  by  staging,  while  the  other  is 
placed  underneath.  The  water  is  drawn  from  the  service-main 
into  the  upper  tank,  where  it  is  weighed,  and  it  is  then  emptied 
into  the  lower  tank.  The  lower  tank  serves  as  a  reservoir,  and 
to  this  the  suction-pipe  of  the  feeding  apparatus  is  connected. 

The  jacket-water  may  be  measured  by  using  a  pair  of  small 
barrels,  one  being  filled  while  the  other  is  being  weighed  and 
emptied.  This  water,  after  being  measured,  may  be  thrown 
away,  the  loss  being  made  up  by  the  main  feed-pump.  To 
prevent  evaporation  from  the  water,  and  consequent  loss  on 
account  of  its  highly  heated  condition,  each  barrel  should  be 
partially  filled  with  cold  water  previous  to  using  it  for  collect- 
ing the  jacket-water,  and  the  weight  of  this  water  treated  as 
tare. 

When  the  jacket-water  drains  back  by  gravity  to  the  boiler, 
waste  of  live  steam  during  the  weighing  should  be  prevented 
by  providing  a  small  vertical  chamber,  and  conducting  the 
water  into  this  receptacle  before  its  escape.  A  glass  water- 
gauge  is  attached,  so  as  to  show  the  height  of  water  inside  the 
chamber,  and  this  serves  as  a  guide  in  regulating  the  discharge- 
valve. 

When  the  jacket-water  is  returned  to  the  boiler  by  means 
of  a  pump,  the  discharge-valve  should  be  throttled  during  the 
test,  so  that  the  pump  may  work  against  its  usual  pressure, 


§  432-]  TESTING  PUMPING-ENGINES.  6l/ 

that  is,  the  boiler-pressure  as  nearly  as  may  be,  a  gauge  being 
attached  to  the  discharge-pipe  for  this  purpose. 

When  a  separator  is  used  and  the  entrained  water  dis- 
charges either  to  waste,  to  the  hot-well,  or  to  the  jacket-tank, 
the  weight  of  this  water  is  to  be  determined,  the  water  being 
drawn  into  barrels  in  the  manner  pointed  out  for  measuring 
the  jacket-water.  Except  in  the  case  where  the  separator  dis- 
charges into  the  jacket-tank,  the  entrained  water  thus  found  is 
treated,  in  the  calculations,  in  the  same  manner  as  moisture 
shown  by  the  calorimeter-test.  When  it  discharges  into  the 
jacket-tank,  its,  weight  is  simply  subtracted  from  the  total 
weight  of  water  fed,  and  allowance  made  for  heat  of  this  water 
lost  by  radiation  between  separator  and  tank. 

When  the  jackets  are  drained  by  a  trap,  and  the  condensed 
water  goes  either  to  waste  or  to  the  hot-well,  the  determination 
of  the  quantity  used  is  not  necessary  to  the  main  object  of  the 
duty  trial,  because  the  main  feed-pump  in  such  cases  supplies 
all  the  feed-water.  For  the  sake  of  having  complete  data,  how- 
ever, it  is  desirable  that  this  water  be  measured,  whatever  the 
use  to  which  it  is  applied. 

Should  live  steam  be  used  for  reheating  the  steam  in  the 
intermediate  receiver,  it  is  desirable  to  separate  this  from  the 
jacket-steam,  if  it  drain  into  the  same  tank,  and  measure  it 
independently.  This,  likewise,  is  not  essential  to  the  main 
object  of  the  duty  trial,  though  useful  for  purposes  of  in- 
formation. 

The  remarks  as  to  the  manner  of  preventing  losses  of  live 
steam  and  of  evaporation,  in  the  measurement  of  jacket-water, 
apply  to  the  measurement  of  any  other  hot  water  under  press- 
ure, which  may  be  used  for  feed-water. 

Should  there  be  any  other  independent  supply  of  water  to 
the  boiler,  besides  those  named,  its  quantity  is  to  be  deter- 
mined independently,  apparatus  for  all  these  measurements 
being  set  up  during  the  interval  between  the  preliminary  ru» 
and  the  main  trial,  when  the  plant  is  idle. 


6l8  EXPERIMENTAL   ENGINEERING.  [§  432- 

(2)   THE   MAIN   DUTY-TRIAL. 

The  duty-trial  is  here  assumed  to  apply  to  a  complete 
plant,  embracing  a  test  of  the  performance  of  the  boiler  as 
well  as  that  of  the  engine.  The  test  of  the  two  will  go  on 
simultaneously  after  both  are  started,  but  the  boiler-test  will 
begin  a  short  time  in  advance  of  the  commencement  of  the 
engine-test,  and  continue  a  short  time  after  the  engine-test  is 
finished.  The  mode  of  procedure  is  as  follows : 

The  plant  having  been  worked  for  a  suitable  time  under 
normal  conditions,  the  fire  is  burned  down  to  a  low  point  and 
the  engine  brought  to  rest.  The  fire  remaining  on  the  grate  is 
then  quickly  hauled,  the  furnace  cleaned,  and  the  refuse  with- 
drawn from  the  ash-pit.  The  boiler-test  is  now  started,  and 
this  test  is  made  in  accordance  with  the  rules  for  a  standard 
method  recommended  by  the  Committee  on  Boiler  Tests  of 
the  American  Society  of  Mechanical  Engineers.  This  method, 
briefly  described,  consists  in  starting  the  test  with  a  new  fire 
lighted  with  wood,  the  boiler  having  previously  been  heated  to 
its  normal  working  degree ;  operating  the  boiler  in  accordance 
with  the  conditions  determined  upon  ;  weighing  coal,  ashes, 
and  feed-water ;  observing  the  draught,  temperatures  of  feed- 
water  and  escaping  gases,  and  such  other  data  as  may  be  inci- 
dentally desired  ;  determining  the  quantity  of-  moisture  in  the 
coal  and  in  the  steam ;  and  at  the  close  of  the  test  hauling  the 
fire,  and  deducting  from  the  weight  of  coal  fired  whatever 
unburned  coal  is  contained  in  the  refuse  withdrawn  from  the 
furnace,  the  quantity  of  water  in  the  boiler  and  the  steam-press- 
ure being  the  same  as  at  the  time  of  lighting  the  fire  at  the 
beginning  of  the  test. 

Previous  to  the  close  of  the  test  it  is  desirable  that  the  fire 
should  be  burned  down  to  a  low  point,  so  that  the  unburned 
coal  withdrawn  may  be  in  a  nearly  consumed  state.  The  tem- 
perature of  the  feed-water  is  observed  at  the  point  where  the 
water  leaves  the  engine  heater,  if  this  be  used,  or  at  the  point 
where  it  enters  the  flue-heater,  if  that  apparatus  be  employed. 
Where  an  injector  is  used  for  supplying  the  water,  a  deduction 


§432-]  TESTING  PUMP1NG-ENGINES.  619 

is  to  be  made  in  either  case  for  the  increased  temperature  of 
the  water  derived  from  the  steam  which  it  consumes. 

As  soon  after  the  beginning  of  the  boiler-test  as  practicable 
the  engine  is  started  and  preparations  are  made  for  the  begin- 
ning of  the  engine-test.  The  formal  commencement  of  this 
test  is  delayed  till  the  plant  is  again  in  normal  working  con- 
dition, which  should  not  be  over  one  hour  after  the  time  of 
lighting  the  fire.  When  the  time  for  commencement  arrives 
the  feed-water  is  momentarily  shut  off,  and  the  water  in  the 
lower  tank  is  brought  to  a  mark.  Observations  are  then  made 
of  the  number  of  tanks  of  water  thus  far  supplied,  the  height 
of  water  in  the  gauge-glass  of  the  boiler,  the  indication  of  the 
counter  on  the  engine,  and  the  time  of  day ;  after  which  the 
supply  of  feed-water  is  renewed,  and  the  regular  observations 
of  the  test,  including  the  measurement  of  the  auxiliary  supplies 
of  feed-water,  are  commenced.  The  engine-test  is  to  continue 
at  least  ten  hours.  At  its  expiration  the  feed-pump  is  again 
momentarily  stopped,  care  having  been  taken  to  have  the 
water  slightly  higher  than  at  the  start,  and  the  water  in  the 
lower  tank  is  brought  to  the  mark.  When  the  water  in  the 
gauge-glass  has  settled  to  the  point  which  it  occupied  at  the 
beginning,  the  time  of  day  and  the  indication  of  the  counter 
are  observed,  together  with  the  number  of  tanks  of  water  thus 
far  supplied,  and  the  engine-test  is  held  to  be  finished.  The 
engine  continues  to  run  after  this  time  till  the  fire  reaches  a 
condition  for  hauling,  and  completing  the  boiler-test.  It  is 
then  stopped,  and  the  final  observations  relating  to  the  boiler- 
test  are  taken. 

The  observations  to  be  made  and  data  obtained  for  the 
purposes  of  the  engine-test,  or  duty-trial  proper,  embrace  the 
weight  of  feed-water  supplied  by  the  main  feeding  apparatus, 
that  of  the  water  drained  from  the  jackets,  and  any  other  water 
which  is  ordinarily  supplied  to  the  boiler,  determined  in  the 
manner  pointed  out.  They  also  embrace  the  number  of  hours* 
duration,  and  number  of  single  strokes  of  the  pump  during  the 
test ;  and,  in  direct-acting  engines,  the  length  of  the  stroke, 
together  with  the  indications  of  the  gauges  attached  to  the 


620  EXPERIMENTAL   ENGINEERING.  [§  432. 

force  and  suction  mains,  and  indicator-diagrams  from  the  steam- 
cylinders.  It  is  desirable  that  pump-diagrams  also  be  obtained. 

Observations  of  the  length  of  stroke,  in  the  case  of  direct- 
acting  engines,  should  be  made  every  five  minutes ;  observa- 
tions of  the  water-pressure  gauges  every  fifteen  minutes; 
observations  of  the  remaining  instruments — such  as  steam- 
gauge,  vacuum-gauge,  thermometer  in  pump-well,  thermome- 
ter in  feed-pipe ;  thermometer  showing  temperature  of  engine- 
room,  boiler-room,  and  outside  air ;  thermometer  in  flue,  ther- 
mometer  in  steam-pipe,  if  the  boiler  has  steam-heating  surface, 
barometer,  and  other  instruments  which  may  be  used — every 
half-hour.  Indicator-diagrams  should  be  taken  every  half-hour. 

When  the  duty-trial  embraces  simply  a  test  of  the  engine, 
apart  from  the  boiler,  the  course  of  procedure  will  be  the  same 
as  that  described,  excepting  that  the  fires  will  not  be  hauled, 
and  the  special  observations  relating  to  the  performance  of  the 
boiler  will  not  be  taken. 

Directions  regarding  Arrangement  and  Use  of  Instrument s> 
and  other  Provisions  for  the  Test. — The  gauge  attached  to  the 
force-main  is  liable  to  a  considerable  amount  of  fluctuation 
unless  the  gauge-cock  is  nearly  closed.  The  practice  of 
choking  the  cock  is  objectionable.  The  difficulty  may  be 
satisfactorily  overcome,  and  a  nearly  steady  indication  se- 
cured, with  cock  wide  open,  if  a  small  reservoir  having  an  air- 
chamber  is  interposed  between  the  gauge  and  the  force-main. 
By  means  of  a  gauge-glass  on  the  side  of  the  chamber  and  an 
air-valve,  the  average  water-level  may  be  adjusted  to  the 
height  of  the  centre  of  the  gauge,  and  correction  for  this 
element  of  variation  is  avoided.  If  not  thus  adjusted,  the 
reading  is  to  be  referred  to  the  level  shown,  whatever  this 
may  be. 

To  determine  the  length  of  stroke  in  the  case  of  direct  act- 
ing engines,  a  scale  should  be  securely  fastened  to  the  frame 
which  connects  the  steam  and  water  cylinders,  in  a  position 
parallel  to  the  piston-rod,  and  a  pointer  attached  to  the  rod  so 
as  to  move  back  and  forth  over  the  graduations  on  the  scale. 
The  marks  on  the  scale,  which  the  pointer  reaches  at  the  two 


§  432-]  TESTING  PUM PING-ENGINES.  62  I 

ends  of  the  stroke,  are  thus  readily  observed,  and  the  distance 
moved  over  computed.  If  the  length  of  the  stroke  can  be  de- 
termined by  the  use  of  some  form  of  registering  apparatus, 
such  a  method  of  measurement  is  preferred.  The  personal 
errors  in  observing  the  exact  scale-marks,  which  are  liable  to 
creep  in,  may  thereby  be  avoided. 

The  form  of  calorimeter  to  be  used  for  testing  the -quality 
of  the  steam  is  left  to  the  decision  of  the  person  who  conducts 
the  trial.  It  is  preferred  that  some  form  of  continuous  calo- 
rimeter be  used,  which  acts  directly  on  the  moisture  tested.  If 
either  the  separating  calorimeter*  or  the  wire-drawing  f 
instrument  be  employed,  the  steam  which  it  discharges  is  to  be 
measured  either  by  numerous  short  trials,  made  by  condensing 
it  in  a  barrel  of  water  previously  weighed,  thereby  obtaining  the 
rate  by  which  it  is  discharged,  or  by  passing  it  through  a  sur- 
face-condenser of  some  simple  construction,  and  measuring  the 
whole  quantity  consumed.  When  neither  of  these  instruments 
is  at  hand,  and  dependence  must  be  placed  upon  the  barrel 
calorimeter,  scales  should  be  used  which  are  sensitive  to  a 
change  in  weight  of  a  small  fraction  of  a  pound,  and  thermom- 
eters which  may  be  read  to  tenths  of  a  degree.  The  pipe 
which  supplies  the  calorimeter  should  be  thoroughly  warmed 
and  drained  just  previous  to  each  test.  In  making  the  calcu- 
lations the  specific  heat  of  the  material  of  the  barrel  or  tank 
should  be  taken  into  account,  whether  this  be  of  metal  or  of 
wood. 

If  the  steam  is  superheated,  or  if  the  boiler  is  provided 
with  steam-heating  surface,  the  temperature  of  the  steam  is  to 
be  taken  by  means  of  a  high-grade  thermometer  resting  in  a 
cup  holding  oil  or  mercury,  which  is  screwed  into  the  steam- 
pipe  so  as  to  be  surrounded  by  the  current  of  stearn.  The 
temperature  of  the  feed-water  is  preferably  taken  by  means  of 
a  cup  screwed  into  the  feed-pipe  in  the  same  manner. 

Indicator-pipes  and  connections  used  for  the  water-cylin- 

*  Vol.   vn,   p.   178,   1886,   Transactions  A.  S.  M.  E.     See  page  430  of  this 
volume. 

fVol.  xi,  1890,  p.  193,  Transactions  A.  S.  M.  E.     See  page  419  of  this  volume 


622  EXPERIMENTAL   ENGINEERING.  [§  432- 

ders  should  be  of  ample  size,  and,  so  far  as  possible,  free  from 
bends.  Three-quarter-inch  pipes  are  preferred,  and  the  indi- 
cators should  be  attached  one  at  each  end  of  the  cylinder.  It 
should  be  remembered  that  indicator-springs  which  are  correct 
under  steam  heat  are  erroneous  when  used  for  cold  water.  When 
such  springs  are  used,  the  actual  scale  should  be  determined, 
if  calculations  are  made  of  the  indicated  work  done  in  the 
water-cylinders.  The  scale  of  steam-springs  should  be  deter- 
mined by  a  comparison,  under  steam-pressure,  with  an  accurate 
steam-gauge  at  the  time  of  the  trial,  and  that  of  water-springs 
by  cold  dead-weight  test. 

The  accuracy  of  all  the  gauges  should  be  carefully  verified 
by  comparison  with  a  reliable  mercury-column.  Similar  veri- 
fication should  be  made  of  the  thermometers,  and  if  no  stand- 
ard is  at  hand,  they  should  be  tested  in  boiling  water  and 
melting  ice. 

To  avoid  errors  in  conducting  the  test,  due  to  leakage  of 
stop-valves  either  on  the  steam-pipes,  feed-water  pipes,  or 
blow-off  pipes,  all  these  pipes  not  concerned  in  the  operation 
of  the  plant  under  test  should  be  disconnected. 

(3)   LEAKAGE-TEST  OF  PUMP. 

As  soon  as  practicable  after  the  completion  of  the  main 
trial  (or  at  some  time  immediately  preceding  the  trial)  the  en- 
gine is  brought  to  rest,  and  the  rate  determined  at  which  leak- 
age takes  place  through  the  plunger  and  valves  of  the  pump, 
when  these  are  subjected  to  the  full  pressure  of  the  force- 
main. 

The  leakage  of  the  plunger  is  most  satisfactorily  determined 
by  making  the  test  with  the  cylinder-head  removed.  A  wide 
board  or  plank  may  be  temporarily  bolted  to  the  lower  part  of 
the  end  of  the  cylinder,  so  as  to  hold  back  the  water  in  the 
manner  of  a  dam,  and  an  opening  made  in  the  temporary  head 
thus  provided  for  the  reception  of  an  overflow  pipe.  The 
plunger  is  blocked  at  some  intermediate  point  in  the  stroke  (or, 
if  this  position  is  not  practicable,  at  the  end  of  the  stroke),  and 


§4320  TESTING  PUMPING-ENGINES.  623 

the  water  from  the  force-main  is  admitted  at  full  pressure  be. 
hind  it.  The  leakage  escapes  through  the  overflow  pipe,  and 
it  is  collected  in  barrels  and  measured. 

Should  the  escape  of  the  water  into  the  engine-room  be 
objectionable,  a  spout  may  be  constructed  to  carry  it  out  of  the 
building.  Where  the  leakage  is  too  great  to  be  readily  meas- 
ured in  barrels,  or  where  other  objections  arise,  resort  may  be 
had  to  weir  or  orifice  measurement,  the  weir  or  orifice  taking 
the  place  of  the  overflow-pipe  in  the  wooden  head.  The  ap- 
paratus may  be  constructed,  if  desired,  in  a  somewhat  rude 
manner,  and  yet  be  sufficiently  accurate  for  practical  require- 
ments. The  test  should  be  made,  if  possible,  with  the  plunger 
in  various  positions. 

In  the  case  of  a  pump  so  planned  that  it  is  difficult  to  re- 
move the  cylinder-head,  it  may  be  desirable  to  take  the  leakage 
from  one  of  the  openings  which  are  provided  for  the  inspection 
of  the  suction-valves,  the  head  being  allowed  to  remain  in 
place. 

It  is  here  assumed  that  there  is  a  practical  absence  of  valve- 
leakage,  a  condition  of  things  which  ought  to  be  attained  in  all 
well-constructed  pumps.  Examination  for  such  leakage  should 
be  made  first  of  all,  and  if  it  occurs  and  it  is  found  to  be  due 
to  disordered  valves,  it  should  be  remedied  before  making  the 
plunger-test.  Leakage  of  the  discharge-valves  will  be  shown 
by  water  passing  down  into  the  empty  cylinder  at  either  end 
when  they  are  under  pressure.  Leakage  of  the  suction-valves 
will  be  shown  by  the  disappearance  of  water  which  covers 
them. 

If  valve-leakage  is  found  which  cannot  be  remedied,  the 
quantity  of  water  thus  lost  should  also  be  tested.  The  deter- 
mination of  the  quantity  which  leaks  through  the  suction-valves, 
where  there  is  no  gate  in  the  suction-pipe,  must  be  made  by 
indirect  means.  One  method  is  to  measure  the  amount  of 
water  required  to  maintain  a  certain  pressure  in  the  pump- 
cylinder  when  this  is  introduced  through  a  pipe  temporarily 
erected,  no  water  being  allowed  to  enter  through  the  discharge- 
valves  of  the  pump. 


624  EXPERIMENTAL  ENGINEERrNG.  [§  432. 

The  exact  methods  to  be  followed  in  any  particular  case,  in 
determining  leakage,  must  be  left  to  the  judgment  and  ingenu- 
ity of  the  person  conducting  the  test. 

(4)  TABLE  OF  DATA  AND  RESULTS. 

In  order  that  uniformity  may  be  secured,  it  is  suggested 
that  the  data  and  results,  worked  out  in  accordance  with  the 
standard  method,  be  tabulated  in  the  manner  indicated  in  the 
following  scheme : 

DUTY-TRIAL  OF  ENGINE. 
Dimensions. 

1.  Number  of  steam-cylinders . 

2.  Diameter  of  steam-cylinders ins. 

3.  Diameter  of  piston-rods  of  steam-cylinders ins. 

4.  Nominal  stroke  of  steam-pistons ft. 

5.  Number  of  water-plungers 

6.  Diameter  of  plungers ins. 

7.  Diameter  of  piston-rods  of  water-cylinders ins. 

8.  Nominal  stroke  of  plungers ft. 

9.  Net  area  of  plungers sq.  ins. 

10.  Net  area  of  steam-pistons sq.  ins. 

11.  Average  length  of  stroke  of  steam-pistons  during  trial ft. 

12.  Average  length  of  stroke  of  plungers  during  trial ft. 

(Give  also  complete  description  of  plant.) 

Temperatures. 

13.  Temperature  of  water  in  pump-well degs. 

14.  Temperature  of  water  supplied  to  boiler  by  main  feed-pump,  degs. 

15.  Temperature  of  water  supplied  to  boiler  from  various  other 

sources degs, 

Feed-water. 

16.  Weight  of  water  supplied  to  boiler  by  main  feed-pump Ibs. 

17.  Weight  of  water  supplied  to  boiler  from  various  other  sources.  Ibs. 

18.  Total  weight  of  feed-water  supplied  from  all  sources.  - Ibs. 

Pressures. 

ig.  Boiler-pressure  indicated  by  gauge Ibs. 

20.  Pressure  indicated  by  gauge  on  force-main Ibs. 

21.  Vacuum  indicated  by  gauge  on  suction-main ins. 

22.  Pressure  corresponding  to  vacuum  given  in  preceding  line Ibs. 

23.  Vertical  distance  between  the  centres  of  the  two  gauges ins. 

24.  Pressure  equivalent  to  distance  between  the  two  gauges Ibs. 


§  432-]  TESTING  PUMPING-ENGINES.  62$ 

Miscellaneous  Data. 

25.  Duration  of  trial hrs. 

26.  Total  number  of  single  strokes  during  trial 

27.  Percentage  of  moisture  in  steam  supplied  to  engine,  or  num- 

ber of  degrees  of  superheating %  or  deg. 

28.  Total  leakage  of  pump  during  trial,  determined  from  results  of 

leakage-test Ibs. 

29.  Mean  effective  pressure,  measured  from  diagrams  taken  from 

steam-cylinders M.E.  P. 

Principal  Results. 

30.  Duty ft. -Ibs. 

31.  Percentage  of  leakage % 

32.  Capacity gals. 

33.  Percentage  of  total  frictions % 

Additional  Results* 

34.  Number  of  double  strokes  of  steam-piston  per  minute 

35.  Indicated    horse-power    developed    by  the    various    steam- 

cylinders  I.  H.  P. 

36.  Feed-water  consumed  by  the  plant  per  hour Ibs. 

1       37.  Feed-water  consumed  by  the  plant  per  indicated  horse-power 

per  hour,  corrected  for  moisture  in  steam Ibs. 

38.  Number  of  heat-units  consumed  per  indicated  horse-power  per 

hour B.  T.U. 

39.  Number  of  heat-units  consumed  per  indicated  horse-power  per 

minute B.  T.U. 

40.  Steam  accounted  for  by  indicator  at  cut-off  and  release  in  the 

various  steam-cylinders Ibs. 

41.  Proportion  which  steam  accounted  for  by  indicator  bears  to 

the  feed-water  consumption 

Sample  Diagrams  taken  from  Steam-cylinders. 

[Also,  if  possible,  full  measurements  of  the  diagrams,  embracing  pressures 
at  the  initial  point,  cut-off,  release,  and  compression  ;  also  back-pressure,  and 
the  proportions  of  the  stroke  completed  at  the  various  points  noted.] 

42.  Number  of  double  strokes  of  pump  per  minute 

43.  Mean  effective  pressure,  measured  from  pump-diagrams M.  E.P. 

44.  Indicated  horse-power  exerted  in  pump-cylinders I.  H.  P. 

*  These'are  not  necessary  to  the  main  object,  but  it  is  desirable  to  give  them. 


626  EXPERIMENTAL   ENGINEERING.  [§432. 

Sample  Diagrams  taken  from  Pump-cylinders. 

DATA  AND   RESULTS  OF   BOILER -TEST. 

[iN    ACCORDANCE   WITH     THE   SCHEME    RECOMMENDED    BY   THE   BOILER-TEST 
COMMITTEE  OF  THE  SOCIETY.] 

1.  Date  of  trial 

2.  Duration  of  trial hrs. 

Dimensions  and  Proportions. 

3.  Grate-surface  wide  long  Area sq.  ft. 

4.  Water-heating  surface sq.  ft. 

5.  Superheating-surface sq.ft. 

6.  Ratio  of  water-heating  surface  to  grate-surface 

(Give  also  complete  description  of  boilers.) 

Average  Pressures. 

7.  Steam-pressure  in  boiler  by  gauge Ibs. 

8.  Atmospheric  pressure  by  barometer Ibs. 

9.  Force  of  draught  in  inches  of  water ins. 

Average   Temperatures. 

10.  Of  steam degs. 

11.  Of  escaping  gases degs. 

12.  Of  feed-water .... 

Fuel. 

13.  Total  amount  of  coal  consumed  * Ibs. 

14.  Moisture  in  coal   % 

15.  Dry  coal  consumed Ibs. 

16.  Total  refuse  (dry) Ibs. 

17.  Total  combustible  (dry  weight  of  coal,  item  15,  less  refuse, 

item  16) Ibs. 

18.  Dry  coal  consumed  per  hour Ibs. 

Results  of  Calorimetric   Test. 
ig.   Quality  of  steam,  dry  steam  being  taken  as  unity 

20.  Percentage  of  moisture  in  steam % 

21.  Number  of  degrees  superheated ...    degs. 

*  Including  equivalent  of  wood  used  in  lighting  fire.  One  pound  of  wood 
equals  0.4  of  a  pound  of  coal,  not  including  unburned  coal  withdrawn  from  fire 
at  end  of  test. 


§432-]  TESTING  PUMPING-ENGINES.  627 

Water. 

22.  Total    weight  of   water    pumped  into    boiler   and  apparently 

evaporated  *  Ibs. 

23.  Water  actually  evaporated  corrected  for  quality  of  steam Ibs. 

24.  Equivalent   water   evaporated   into   dry  steam   from   and   at 

212°  F.f Ibs. 

25.  Equivalent  total  heat  derived  from   fuel,  in    British  thermal 

units B.  T.U« 

26.  Equivalent   water   evaporated   into    dry   steam  from  and   at 

212°  F.  per  hour Ibs. 

Economic  Evaporation. 

27.  Water  actually  evaporated  per  pound  of  dry  coal  from  actual 

pressure  and  temperature Ibs. 

28.  Equivalent   water  evaporated   per  pound  of    dry  coal  from 

and  at  212°  F Ibs. 

29.  Equivalent  water  evaporated  per  pound  of  combustible  from 

and  at  212°  F Ibs. 

30.  Number  of  pounds   of  coal   required  to  supply  one  million 

British  thermal  units Ibs. 

Rate  of  Combustion. 

31.  Dry  coal  actually  burned  per  square  foot  of  grate-surface  per 
hour Ibs. 

Rate  of  Evaporation. 

32.  Water  evaporated  from  and  at  212*  F.  per  square  foot  of 

heating-surface  per  hour Ibs. 

To  determine  the  percentage  of  surface  moisture  in  the  coal 
a  sample  of  the  coal  should  be  dried  for  a  period  of  twenty- 
four  hours,  being  subjected  to  a  temperature  of  not  more  than 
212°.  The  quantity  of  unconsumed  coal  contained  in  the 
refuse  withdrawn  from  the  furnace  and  ash-pit  at  the  end  of  the 
test  may  be  found  by  sifting  either  the  whole  of  the  refuse,  or 

*  Corrected  for  inequality  of  water-level  and  of  steam-pressure  at  beginning 
and  end  of  test. 

f  Factor  of  evaporation  =  — ,  H  and  h  being,  respectively,  the   total 

heat-units  in  steam  of  the  average  observed  pressure  corrected  for  quality, 
and  in  water  of  the  average  observed  temperature  of  feed. 


628  EXPERIMENTAL  ENGINEERING.  [§432. 

a  sample  of  the  same,  in  a  screen  having  f-inch  meshes.  This, 
deducted  from  the  weight  of  dry  coal  fired,  gives  the  weight 
of  dry  coal  consumed,  for  line  15. 

Results   of   actual    trial,  as    illustrated  by  the  committee, 
would  be  computed  by  the  use  of  the  following  formulae  : 

Foot-pounds  of  work  done 
I.  Duty  =  Total  number  of  heat-units  consumed  X  l»coo'oao 


A(P±p  + 
=  —  -  -    '      --  X  i,  000,000  (foot-pounds). 

C  X  144 

2.  Percentage  of  leakage  =  A       L      ^  X  100  (per  cent). 

3.  Capacity  =  number  of   gallons  of  water  discharged  in  24 

hours 

_  A  x  L  X  \N  x  7.4805  X  24 
"  D  X  144 

AxLxNx  1.24675 

—  —  -  -  (gallons). 

4.  Percentage  of  total  friction 

LH.P.  - 


f         A(P±pXs)  x  L  x  N~\ 

L1  -   WfcriT-J  x  I00^er  cent);  • 


or,  in  the  usual  case,  where  the  length  of  the  stroke  and  num- 
ber of  strokes  of  the  plunger  are  the  same  as  that  of  the  steam- 
piston,  this  last  formula  becomes  — 

Percentage  of  total  frictions  =  [^i—  ^    M  ITf  \  X  IOO(P'C')' 


§  432-]  TESTING  PUMPING-ENGINES.  629 

In  these  formulae  the  letters  refer  to  the  following  quanti- 
ties : 

A  —  Area,  in  square  inches,  of  pump-plunger  or  piston, 
corrected  for  area  of  piston-rod.  (When  one  rod 
is  used  at  one  end  only,  the  correction  is  one  half 
the  area  of  the  rod.  If  there  is  more  than  one 
rod,  the  correction  is  multiplied  accordingly.) 

P=  Pressure,  in  pounds  per  square  inch,  indicated  by 
the  gauge  on  the  force-main. 

p  =  Pressure,  in  pounds  per  square  inch,  corresponding 
to  indication  of  the  vacuum-gauge  on  suction- 
main  (or  pressure-gauge,  if  the  suction-pipe  is 
under  a  head).  The  indication  of  the  vacuum- 
gauge,  in  inches  of  mercury,  may  be.  converted 
into  pounds  by  dividing  it  by  2.035. 

S  =  Pressure,  in  pounds  per  square  inch,  corresponding 
to  distance  between  the  centres  of  the  two  gauges. 
The  computation  for  this  pressure  is  made  by 
multiplying  the  distance,  expressed  in  feet,  by  the 
weight  of  one  cubic  foot  of  water  at  the  tempera- 
ture of  the  pump-well,  and  dividing  the  product 
by  144 ;  or  by  multiplying  the  distance  in  feet  by 
the  weights  of  one  cubic  foot  of  water  at  the 
various  temperatures. 

L  =  Average  length  of  stroke  of  pump-plunger,  in  feet. 

N=  Total  number  of  single  strokes  of  pump-plunger 
made  during  the  trial. 

A  =  Area  of  steam-cylinder,  in  square  inches,  corrected 
for  area  of  piston-rod.  The  quantity  As  X  M.E.P., 
in  an  engine  having  more  than  one  cylinder,  is 
the  sum  of  the  various  quantities  relating  to  the 
respective  cylinders. 

X,  =  Average  length  of  stroke  of  steam-piston,  in  feet. 

fft  =  Total   number   of   single   strokes    of   steam-piston 

during  trial. 
M.E.P.  =  Average   mean   effective   pressure,   in   pounds  per 


630  EXPERIMENTAL   ENGINEERING.  [§  432. 

square  inch,  measured  from  the  indicator-diagrams 
taken  from  the  steam  cylinder. 

LH.P.  =  Indicated    horse-power   developed    by   the   steam- 
cylinder. 

C  =  Total  number  of  cubic  feet  of  water  which  leaked 
by  the  pump-plunger  during  the  trial,  estimated 
from  the  results  of  the  leakage-test. 

D  =  Duration  of  trial,  in  hours. 

H  =  Total  number  of  heat-units  [B.  T.  U.]  consumed  by 
engine  =  weight  of  water  supplied  to  boiler  by 
main  feed-pump  X  total  heat  of  steam  of  boiler- 
pressure  reckoned  from  temperature  of  main  feed- 
water  -f-  weight  of  water  supplied  by  jacket-pump 
X  total  heat  of  steam  of  boiler-pressure  reckoned 
from  temperature  of  jacket-water  -f-  weight  of  any 
other  water  supplied  X  total  heat  of  steam  reck- 
oned from  its  temperature  of  supply.  The  total 
heat  of  the  steam  is  corrected  for  the  moisture  or 
superheat  which  the  steam  may  contain.  For 
moisture,  the  correction  is  subtracted,  and  is  found 
by  multiplying  the  latent  heat  of  the  steam  by  the 
percentage  of  moisture,  and  dividing  the  product 
by  100.  For  superheat,  the  correction  is  added, 
and  is  found  by  multiplying  the  number  of 
degrees  of  superheating  (i.e.,  the  excess  of  the 
temperature  of  the  steam  above  the  normal  tem- 
perature of  saturated  steam)  by  0.48.  No  allow- 
ance is  made  for  heat  added  to  the  feed-water, 
which  is  derived  from  any  source,  except  the 
engine  or  some  accessory  of  the  engine.  Heat 
added  to  the  water  by  the  use  of  a  flue-heater  at 
the  boiler  is  not  to  be  deducted.  Should  heat  be 
abstracted  from  the  flue  by  means  of  a  steam- 
reheater  connected  with  the  intermediate  receiver 
of  the  engine,  this  heat  must  be  included  in  tb*» 
total  quantity  supplied  by  the  boiler. 
The  following  example  is  one  of  those  given  by  the  com- 


^  43 2 •]  TES  TING  P  UMPING-ENGINES.  6  3  I 

mittee  to  illustrate  the  method  of  computation.  The  figures 
are  not  obtained  from  tests  actually  made,  but  they  correspond 
in  round  numbers  with  those  which  were  so  obtained: 

EXAMPLE. —  Compound  Fly-wheel  Engine. — High-pressure 
cylinder  jacketed  with  live  steam  from  the  boiler.  Low-press- 
ure cylinder  jacketed  with  steam  from  the  intermediate  re- 
ceiver, the  condensed  water  from  which  is  returned  to  the 
boiler  by  means  of  a  pump  operated  by  the  engine.  Main 
steam-pipe  fitted  with  a  separator.  The  intermediate  receiver 
provided  with  a  reheater  supplied  with  boiler-steam.  Water 
drained  from  high-pressure  jacket,  separator,  and  reheater  col- 
lected in  a  closed  tank  under  boiler-pressure,  and  from  this 
point  fed  to  the  boiler  direct  by  an  independent  steam-pump. 
Jet-condenser  used  operated  by  an  independent  air-pump. 
Main  supply  of  feed-water  drawn  from  hot-well  and  fed  to  the 
boiler  by  donkey  steam-pump,  which  discharges  through  a 
feed-water  heater.  All  the  steam-pumps,  together  with  the 
independent  air-pump,  exhaust  through  the  heater  to  the  at- 
mosphere. 

DIMENSIONS. 

Diameter  of  high-pressure  steam-cylinder  (one) 2O  in. 

Diameter  of  low-pressure  steam-cylinder  (one) 40   " 

Diameter  of  plunger  (one) 2O   " 

Diameter  of  each  piston-rod « 4 

Stroke  of  steam-pistons  and  pump-plunger 3  ft- 

GENERAL  DATA. 

1.  Duration  of  trial  (D) IO       hrs. 

2.  Boiler-pressure  indicated  by  gauge  (barometric  press- 

ure, 14.7  IDS.).  -. I2°       lbs- 

3.  Temperature  of  water  in  pump-well 60       degs 

4.  Temperature  of  water  supplied  to  boiler  by  main  feed- 

pump, leaving  heater 2I5 

5.  Temperature  of  water  supplied  by  low-pressure  jacket- 

22S  '* 

pump 

6.  Temperature    of    water    supplied    by    high-pressure 

jacket,  separator,  and  reheater-pump,  that  derived 
from  separator  being  340°,  and  that  from  jackets 
290° 3oo 


632  EXPERIMENTAL   ENGINEERING.  [§  432, 

7.  Weight  of  water  supplied  to  boiler  by  main  feed-pump        18,863       Ibs. 

8.  Weight  of  water  supplied  by  low-pressure  jacket-pump  615         " 

9.  Weight  of  water  supplied  by  pump  for  high-pressure 

jacket,  separator,  and  reheater-tank,  of  which  210 

Ibs.  is  derived  from  separator 1 ,025         " 

10.  Total  weight  of  feed-water  supplied  from  all  sources         20,503         " 

11.  Percentage  of  moisture  in  steam  after  leaving  sepa- 

rator   1.5$ 

DATA    RELATING   TO    WORK    OF    PUMP. 

12.  Area  of  plunger  minus  \  area  of  piston-rod  (A) 307.88  sq.  in. 

13.  Average  length  of  stroke  (L  and  Ls) 3       ft. 

14.  Total  number  of  single  strokes  during  trial  (A7" and  Ns)  24,000 

15.  Pressure  by  gauge  on  force-main  (P) 95       Ibs. 

16.  Vacuum  by  gauge  on  suction-main 7.5    in. 

17.  Pressure  corresponding  to  vacuum  given  in  preceding 

line(/) 3.6glbs. 

18.  Vertical  distance  between  centres  of  two  gauges 10       ft. 

19.  Pressure  equivalent  to  distance  between  two  gauges  (j)  4.33  lbsr 

20.  Total  leakage  of  pump  during  trial,  determined  from 

results  of  leakage-test  (C) 3,078       cu.  ft. 

21.  Number  of  double  strokes  of  pump  per  minute 20 

22.  Mean   effective   pressure   measured   from    pump-dia- 

grams   105       Ibs. 

23.  Indicated  horse-power  exerted  in  pump-cylinders....  H7'55  I.H.P. 

DATA   RELATING   TO   WORK    OF    STEAM-CYLINDERS. 

24.  Area  of  high-pressure  piston  minus  |  area  of  rod  (Asl)  307.88  sq.  in. 

25.  Area  of  low-pressure  piston  minus  \  area  of  rod  (AS2)  1,250.36  "     " 

26.  Average  length  of  stroke,  each 3       ft. 

27.  Mean  effective  pressure  measured  from  high-pressure 

diagrams  (M.E.P.i) 59-25  Ibs. 

28.  Mean  effective  pressure  measured  from  low-pressure 

diagrams  (M.E. P. 2). 13.60    " 

29.  Number  of  double  strokes  per  minute  (line  21) 20 

30.  Indicated  horse-power  developed  by  H.-P.  cylinder..  66-33  I.H.P. 

31.  Indicated  horse-power  developed  by  L.-P.  cylinder..  61.82      " 

32.  Indicated  horse-power  developed  by  both  cylinders..  128.15      " 

33.  Feed-water  consumed  by  plant  per  indicated  horse- 

power per  hour,  corrected  for  separator-water  and 

for  moisture  in  steam 15.60  Ibs. 

34.  Number  of  heat-units  consumed  per  indicated  horse- 

power per  hour 15,652.1    B.T.U. 

35.  Number  of  heat-units  consumed  per  indicated  horse- 

power per  minute \         260.9        " 


§  43  2  •]  rES  TING  P  UM  PING-EN  G  WES.  63  3 

TOTAL   HEAT   OF   STEAM    RECKONED   FROM   THE  VARIOUS  TEMPERATURES  OF 
FEED-WATER,  AND    COMPUTATIONS   BASED   THEREON. 

36.  Total  heat  of  I  Ib.  of  steam  at  120  Ibs.  gauge-pressure, 

containing  1.5$  of  moisture,  reckoned  from  o°  F.= 

1220.6  -(1.5*  of  866.7)  ..........................  1,207.6    B.T.U. 

37.  Ditto,  reckoned  from  215°  temperature  of  main  feed- 

water  =  1207.6  —  215.9  ...........................  991-7        " 

38.  Ditto,  reckoned  from  225°  temperature  of  low-pressure 

jack'et-water  =  1207.6  —  226.  1  .....................  981.5         " 

39.  Ditto,  reckoned  from  290°  temperature  of  high-pres- 

sure jacket  and  reheater  water  =  1207.6—  292.3  =  .  .  915-3        " 

40.  Heat  of  separator-water  reckoned  from  340°  =  353.9  — 

343-8  .........................  -----    .........  io.I         '• 

41.  Heat  consumed  by  engine  (//)  =  (18.863  X  991.7)-}- 

(615  X  981-5)  +  (815  X  9!5.3)  +  (210  X  10.1)  =  .....  20,058,150  " 

RESULTS. 

Substituting  these  quantities  in  the  formulae,  we  have: 


,.  Duty  = 

20,058,150 

=  113,853,044  foot-pounds. 

C 

2.  Percentage  of  leakage  =  —  ~^~       T~     ~N~  X  IOO=2. 

307.88  X  3  X  24,000 

3.  Capacity  =  30^88  X  3  X  24.£>o  X  1.24675 

10 

=  2,763,716  gallons. 

4.  Percentage  of  total  frictions 

A  P          p  t 

307.88  x  (95  +  3.69  +  4.33) 


Aa 

(307.88  x  59-25)  +  (1250.  36  x  13-6) 


634  EXPERIMENTAL  ENGINEERING.  [§434- 

In  the  use  of  a  system  like  the  preceding,  every  precaution 
should  be  observed  in  the  adoption  of  methods,  as  well  as  in 
taking  observations.  The  water  discharged  by  a  pumping, 
engine,  for  example,  should  never  be  obtained  by  computation 
from  the  measured  dimensions  of  the  pump  and  the  observed 
number  of  strokes,  but  should  be  measured  directly.  A  weir 
is  commonly  arranged  for  this  purpose.  Where  the-delivery 
of  the  pump  has  been  actually  measured,  and  the  pump  thus 
standardized,  its  use  as  a  meter  is  less  liable  to  error,  but  it  is 
best  avoided  whenever  possible. 

434.  Standard  Method  of  Testing  Locomotives. — 
The  following  is  a  reprint  of  a  report  of  a  committee  on 
standard  methods  of  testing  locomotives  appointed  by  the 
American  Society  of  Mechanical  Engineers,  and  submitted  at 
the  San  Francisco  meeting  in  1892  : 

Locomotive-testing  is  conducted  under  r.uch  unfavorable 
circumstances  and  surroundings  that  many  of  the  exact  methods 
employed  in  testing  stationary  engines  or  boilers  cannot  be 
used.  It  is  desirable,  therefore,  that  locomotive-tests  be 
always  made  with  a  special  train  when  possible,  so  that  the 
same  cars  shall  be  used  for  the  different  trips,  and  the  weight  of 
train  be  uniform.  The  speed  of  the  train  can  also  be  under 
control,  and  the  tests  not  hampered  by  the  rules  governing  a 
regularly  scheduled  train.  Special  and  peculiar  apparatus  is 
employed  by  nearly  every  different  experimenter  as  having 
some  extra  merit  of  convenience  or  accuracy,  and  we  have 
endeavored  to  ascertain  the  best  practical  instruments  and 
methods  for  the  various  measurements,  and  to  illustrate  or 
explain  them. 

When  a  dynamometer-car  is  not  used: 

As  a  final  basis  of  comparison  of  locomotives,  we  recom- 
mend as  a  unit  the  number  of  thermal  units  used  per  indicated 
horse-power  per  hour.  The  object  in  view  in  testing  a  loco- 
motive  will  determine  the  methods  employed  and  the  extent 
kind  of  data  necessary  to  obtain.  Some  tests  are  made  to 
ascertain  the  economy  of  a  particular  kind  of  boiler  or  fire 


§434-1  TESTING   LOCOMOTIVES.  635 

box;  others,  the  value  of  employing  compound  cylinders; 
others,  to  ascertain  the  relative  merits  of  certain  coals  for 
locomotive  use. 

As  a  practical  and  commercial  unit  the  amount  of  coal- 
consumed  per  ton-mile  may  be  used. 

For  a  coal-test  we  give  a  separate  method  and  test  blanksr 
Form  D,  for  tabulating  results. 

For  a  unit  of  comparison  of  boiler-test  we  recommend  the 
number  of  thermal  units  F.  taken  up  every  hour  by  the  water 
and  steam  in  the  boiler. 

For  a  measurement  of  the  resistance  overcome  in  hauling  a 
train,  a  dynamometer-car  is  essential,  and  we  give  a  method  of 
operating  a  dynamometer-car  and  of  recording  results. 

For  a  uniform  method  of  recording  results  of  indicator- 
tests,  we  recommend  the  blank  Form  A. 

For  tabulating  general  results,  Form  B  is  presented. 

The  waste  from  the  injector  should  be  ascertained  by  catch- 
ing it  in  a  vessel  conveniently  attached,  or  by  starting  the  in- 
jector several  times  in  the  engine-house  and  catching  the  over- 
flow in  a  tub. 

The  total  weight  of  the  water  caught  divided  by  the  num- 
ber of  applications  of  the  injector  gives  the  average  waste. 
The  observer  in  the  cab  should  keep  a  record  of  the  number 
of  times  the  injector  is  applied  during  the  trips,  and  thus  obtain 
data  for  estimating  the  total  waste. 

FUEL  MEASUREMENTS. 

The  measurement  of  fuel  in  locomotive-tests  is  not  difficult 
so  far  as  a  determination  of  the  total  amount  shovelled  into  the 
fire  is  concerned.  A  weighed  amount  may  be  shovelled  into* 
the  tank,  and  the  amount  remaining,  after  a  given  run,  be 
weighed  to  determine  the  amount  used,  provided  no  water  is 
used  to  wet  down  the  coal.  But  it  is  next  to  impossible  to 
determine  the  amount  of  coal  used  at  any  particular  portion 
of  a  run  when  the  coal  is  put  in  the  tender  in  bulk.  If  coal  is 
put  in  sacks  containing  125  pounds  each,  with  a  small  amount  of 
weighed  coal  on  the  foot-plate,  even  with  heavy  firing  it  is 


636  EXPERIMENTAL   ENGINEERING.  [§434- 

found  quite  possible  for  the  fireman  to  cut  open  the  bags,  and 
dump  the  coal  on  the  foot-plate  as  needed.  In  this  way  the 
rate  of  consumption  on  difficult  portions  of  the  run  could 
readily  be  estimated.  The  use  of  water-meters  and  of  coal  in 
sacks  obviates  any  need  of  weighing  the  tender,  and  thus  re- 
moves one  of  the  largest  inaccuracies  incident  to  the  ordinary 
locomotive-tests.  To  determine  the  amount  of  coal  used  dur- 
ing the  trip,  it  is  only  necessary  to  count  the  number  of  bags 
which  have  been  emptied.  However,  the  determination  of 
the  amount  of  fuel  used  during  a  run  is  not  all  that  is  neces- 
sary for  a  test.  The  measurement  of  the  fire-line  before  and 
after  a  test  is  very  essential  and  extremely  difficult.  If  the 
run  is  a  long  one,  then  the  errors  in  the  determination  of  the 
fire-line  may  not  be  great ;  but  for  short  runs  there  seems  to 
be  no  way  of  measuring  the  difference  between  the  heat-value 
of  coal  in  the  fire  before  the  test  and  after  with  sufficient 
accuracy  to  give  reliable  data.  In  tests  made  on  a  heavy 
grade,  one  trip  closely  succeeding  another,  it  is  of  course  im- 
practicable to  drop  the  fire  and  measure  the  amount  of  fuel  in 
the  ashes  remaining.  Such  measurements  are  unsatisfactory 
and  inaccurate  in  any  case,  because  it  is  not  practicable  to 
draw  the  fire  without  wetting  it,  as  the  ashes  rise  into  the 
machinery,  and  they  are  too  hot  to  handle.  When  one  run 
succeeds  another  within  a  short  space  of  time,  some  other 
method  is  necessary  for  measuring  fuel  used  than  by  dumping 
the  coal. 

The  test  is  commenced  with  a  good  fire  in  the  furnace,  and 
the  height  of  coal  estimated  by  two  or  more  assistants  engaged 
in  the  trial.  At  the  end  of  the  run  the  fire  should  be  in  the 
same  condition  as  near  as  possible.  No  raw  coal  should  be  in 
the  box  and  steam-pressure  and  pyrometer-pressure  falling. 

APPLICATION   OF  THE   INDICATOR. 

If  the  power  of  the  engine  is  to  be  determined,  the  action 
of  the  valve-gear  examined,  or  the  coal  and  water  used  per 
unit  of  power  in  a  unit  of  time,  the  indicator  must  be  used. 


§  434-] 


TESTING   LOCOMOTIVES. 


637 


This  instrument  should  be  attached  to  a  three-way  cock  just 
at  the  outer  edge  of  the  steam-chest,  in  order  that  the  con- 
necting pipes  (which  should  be  f  inch  in  diameter)  can  go 
directly  in  a  diagonal  direction  to  holes  tapped  into  the  sides 
of  the  cylinder  rather  than  into  the  heads  (Fig.  285).  By  this 
arrangement  the  pipes  are  shorter  than  when  they  pass  over 


FIG  285. — REDUCING-MOTION  FOR  LOCOMOTIVES. 

the  steam-chest  into  the  heads,  and  have  but  short  horizontal 
portions,  thus  facilitating  the  rapid  draining  of  the  pipes. 
Moreover,  if  a  cylinder-head  is  knocked  out  ths  pipes  are  not 
dragged  off,  and  the  operator  and  indicator  escape  injury. 
The  indicator  should  not  be  placed  on  horizontal  pipes  on  a 
level  with  the  axis  of  the  cylinder-heads. 

The  indicator-pipes  and  three-way  cock  should  be  covered 
with  a  non-conductor,  wrapped  with  canvas  and  painted.  The 
indicator  itself  should  be  wrapped  as  high  as  the  irent-holes 
in  its  steam-cylinder. 


638 


EXPERIMENTAL  ENGINEERING. 


[§434- 


The  indicator-gear  may  be  a  rigid,  true  pantograph  motion, 
either  fixed  or  adjustable  in  height  (Fig.  286) ;  or  it  may  be  a 
simple  pendulum  connected  by  link  to  the  cross-head  with  a 
wooden  quadrant  2  inches  thick,  and  having  a  radius  such  as 
will  make  the  indicator-card  3  inches  long. 

The  cord  of  the  indicator  should  be  8- or  10  inches  long, 
and  connected  with  a  rod  reaching  forward  from  the  panto- 
graph. 

In  order  to  determine  the  steam-chest  pressure,  the  indica- 
tor should  be  so  piped  that  a  steam-chest  diagram  can  be 


lid-position 

Rigid   Non  Adjustable 

FlG.  286.— DEDUCING-MOTION. 

drawn  by  it.  A  steam-gauge  on  the  chest  is  inaccurate  and 
difficult  to  use. 

Indicator-diagrams  should  be  taken  at  equal  distances  in- 
stead of  at  equal  time-intervals,  in  order  to  properly  average 
the  power.  They  should  therefore  be  taken  at  mile-posts. 
The  signal  for  taking  diagrams  should  be  given  by  the  observer 
in  the  cab,  who  can  pull  a  cord  and  ring  a  bell  at  the  front  of 
the  engine,  or  blow  the  whistle. 

For  the  safety  of  the  operator  at  the  indicator,  it  is  recom- 
mended that  the  seat  be  on  a  piece  of  boiler-plate  above  the 
cylinder,  and  so  arranged  that  a  piston  or  cylinder-head  can 
pass  out  without  injuring  him. 


§  434-3  TESTING   LOCOMOTIVES.  639 

The  person  who  takes  the  indicator-diagrams  should  be 
thoroughly  sheltered  by  a  temporary  box  containing  a  seat 
placed  on  the  front  end  of  the  engine.  Besides  the  usual  indi- 
cator, there  should  be  located  near  the  observer  a  revolution- 
counter,  which  should  be  so  arranged  that  after  starting  out 
the  instrument  will  continue  to  record  the  revolutions  for  a 
period  of  exactly  one  minute,  starting  every  time  from  zero, 
and  when  the  minute  has  elapsed  the  counter  will  stop.  Such 
an  instrument  is  already  in  existence  for  taking  the  continuous 
revolutions  of  dynamos  and  high-speed  engines,  and  little  or 
no  difficulty  would  be  experienced  in  obtaining  an  instrument 
capable  of  taking  the  revolutions  from  some  reciprocating 
part  of  the  machinery. 

It  is  desirable  also  to  have  an  electric  connection  between 
the  indicator  and  the  recording  apparatus  in  the  dynamometer- 
car,  so  that  at  the  instant  an  indicator-diagram  is  taken,  the 
fact  may  be  registered  on  the  dynamometer-diagram,  see 
Article  181,  page  246;  and  the  cards  should  be  numbered  con- 
secutively, and  the  record  likewise. 

Besides  the  person  taking  the  indicator-diagrams,  another 
person  should  be  located  in  the  cab  of  the  engine,  whose  duty 
it  should  be  to  observe  the  point  of  cut-off  given  by  the  posi- 
tion of  the  reverse-lever,  the  position  of  the  throttle-lever,  and 
the  boiler-pressure,  all  of  which  conditions  should  be  recorded 
in  a  log-book  for  this  purpose. 

Besides  recording  on  the  dynamometer-diagram  the  fact 
that  an  indicator-card  is  being  taken,  a  bell  should  be  rung 
at  the  same  time,  so  as  to  call  the  attention  of  the  observers  in 
the  dynamometer-car  to  this  lact. 

LOCOMOTIVE-BOILER  TESTS. — GENERAL  DIRECTIONS. 

First.  The  drawing  of  the  boiler  to  accompany  the  report  of 
tests  should  be  particular  in  specifying  the  construction  in  de- 
tail, with  reference  to  coal-burning  and  generating  steam,  such 
as  heating  surface,  grate  area  and  the  distribution  of  openings 
through  the  grate,  volume  of  fire-box,  size  and  thickness  of 


640  EXPERIMENTAL  ENGINEERING.  [§434^ 

flues  size  of  smoke-box,  and  the  arrangement  for  draught, 
together  with  the  thickness  of  walls  between  the  heated  gases 
and  the  water  in  the  boiler;  the  weight  of  the  boiler  itself 
should  be  given,  and  the  number  of  cubic  feet  of  water-space 
and  of  steam-space  in  the  boiler,  the  division  between  the  two 
to  be  taken  at  the  middle  of  the  range  of  the  gauges. 

Second.  Boilers  for  tests  should  be  thoroughly  cleaned  on 
both  sides  of  the  heating  surface,  by  a  removal  of  the  flues, 
before  any  test  is  commenced,  and  these  surfaces  should  be 
kept  clean  by  frequent  washing  during  the  test. 

Exception.— When  it  is  desired  to  make  a  comparison  of 
boilers  for  the  purpose  of  determining  a  difference  between 
them  as  to  incrustation,  they  should  first  be  tested  as  above 
when  clean,  and  then  tested  again  without  cleaning  further 
than  the  ordinary  washing  out  of  the  boilers  after  the  lapse  of 
some  months'  service.  The  results  are  to  be  reduced  to 
evaporation  per  square  foot  of  heating  surface ;  both  boilers 
using  the  same  water  during  the  period  of  testing. 

Third.  In  case  the  measure  of  the  capacity  of  the  locomo- 
tive boiler  for  generating  steam  be  desired,  without  reference 
to  the  engines  forming  the  locomotive,  this  capacity  should  be 
measured  by  the  number  of  British  thermal  units,  taken  up 
per  hour  by  the  water  and  steam  in  the  boiler,  which  may  be 
readily  determined  from  the  observed  data  of  temperature 
of  water  fed  to  the  boiler,  pounds  of  water  evaporated  per 
hour,  and  steam-pressure  under  which  this  evaporation  occurs. 
Use  any  good  set  of  steam-tables,  such  as  Peabody's  or  Por- 
ter's, found  in  Appendix,  or  in  Richard's  Steam-engine  Indica- 
tor. In  such  cases  it  will  be  necessary  to  specify  all  the  perti- 
nent conditions  under  which  such  measure  of  the  capacity  of 
the  boiler  is  made,  so  that  in  comparing  with  the  capacity  of 
another  boiler  all  such  conditions  may  be  made  as  nearly  alike 
as  possible.  It  is,  however,  believed  that  a  measure  of  the 
capacity  of  a  locomotive  boiler,  without  any  reference  to  the 
capacity  or  efficiency  and  method  of  working  of  the  engines 
on  the  locomotive  which  such  boiler  feeds,  will  not  be  of  par- 
ticular value  in  comparison  of  boilers,  unless  the  conditions 


§  434-]  TESTING   LOCOMOTIVES.  64 [ 

under  which  the  entries  are  worked  with  different  boilers  are 
identical,  or  nearly  so. 

Fourth.  On  account  of  the  important  influence  which  the 
temperature,  and  especially  the  moisture  of  the  atmosphere, 
has  upon  the  results  obtained  in  a  boiler-test,  it  is  necessary  to 
compare  two  or  more  boilers  at  the  same  place  and  at  the  same 
time,  to  get  results  which  may  be  strictly  comparable.  The 
temperature  of  the  air  should  then  be  noted  for  record. 

Fifth.  To  properly  determine  the  amount  of  water  fed  to 
a  locomotive  boiler  in  service  on  a  locomotive  during  any  test, 
it  is  necessary  to  use  a  good  water-meter,  which  should  have 
its  maximum  error  determined  by  previous  tests  and  given 
with  the  report. 

Sixth.  The  coal  used  should  be  dry  when  weighed,  and 
placed  in  sacks,  each  containing  100  or  125  Ibs.,  care  being 
taken  to  insure  that  all  scales  used  are  accurate.  When  an  un- 
usually large  amount  of  coal  is  needed,  a  weighed  quantity  of 
coal  may  be  placed  in  the  front  of  the  tender  and  used  first, 
and  the  test  finished  with  coal  from  the  sacks.  An  analysis  of 
the  coal  used  should  accompany  the  report,  which  should 
show  the  volatile  matter,  the  fixed  carbons,  etc.,  the  moisture, 
and  the  ash  contained  in  the  coal.  The  ashes  should  be  dried 
if  they  contain  any  moisture,  and  carefully  weighed  and  re- 
corded after  each  test-run. 

Seventh.  The  temperature  of  the  smoke-box  gases  should 
be  measured  by  a  good  pyrometer,  located  near  enough  to  the 
flues  in  the  smoke-box  to  get  the  average  temperature  of  the 
gases  after  they  have  passed  the  heating  surface,  and  before 
they  are  mixed  with  the  exhaust  steam.  It  is  suggested  that 
pyrometers,  such  as  that  offered  by  Schaeffer  &  Budenberg, 
or  Weiskopf,  are  suitable  for  this  purpose. 

The    location  of    pyrometers     is     shown     in     Fig.    288. 
These  instruments  cost  about  thirty-five  dollars.     They  should 
register  up  to  1000°  F.     See  Article  296. 

Eighth.  The  degree  of  exhaustion  in  the  smoke-box  should 
be  measured  and  recorded  by  means  of  a  simple  manometer 
gauge.  See  Article  27*. 


642 


EXPERIMENTAL  ENGINEERING. 


[§434- 


Ninth.  The  quality  of  the  steam  furnished  by  the  boiler 
to  the  engines  should  be  determined  by  the  most  approved 
methods:  See  Chapter  XIII. 

Tenth.  Samples  of  gases  passing  from  the  flues  to  the 
smoke-box  should  be  analyzed  and  results  reported.  The 


FIG.  a88. 


nsure 


COAL  TESTS. 


selected  should  be  in  good  condition. 


§  434-]  TESTING   LOCOMOTIVES.  643 

and  either  a  new  engine  or  one  that  has  lately  undergone 
repairs. 

The  boiler  should  be  washed  before  commencing  the  trial, 
the  steam-gauge  tested,  the  flues  cleaned,  and  the  exhaust 
nozzles  cleaned  and  measured,  which  operations  should  be  per- 
formed also  whenever  the  kind  of  coal  is  changed.  Instruc- 
tions should  be  given  to  round-house  foremen  that  no  repairs 
or  alterations  of  any  sort  be  made  to  the  engine  without  the 
approbation  of  the  conductor  of  the  trial.  The  same  engine- 
man  and  fireman  should  operate  the  engine  throughout  the 
trial,  and  the  same  methods  of  firing  and  running  should  be 
strictly  adhered  to.  The  run  selected  should  be  one  in  which 
the  same  distance  is  covered  on  each  trip.  The  trains  should 
be  through  trains  and  unbroken  from  end  to  end  of  the  run, 
and  the  same  number  of  cars  and  same  lading  should  be  pro- 
vided each  trip.  The  same  speed  should,  if  possible,  be  pre- 
served on  all  trips. 

The  conductor  of  the  trial  should  be  familiar  with  correct 
methods  of  firing  and  running  locomotives,  and  should  insist 
that  the  fireman  adhere  to  approved  methods  of  firing,  and 
that  the  same  methods  be  preserved  throughout  the  duration 
of  the  trial,  so  that  all  coals  shall  receive  the  same  treatment. 
(See  Chapter  XIV,  on  Heating  Values  of  Fuels,  and  Chapter 
XV,  on  Steam-boiler  Trials.) 

He  should  also  see  that  the  coal  supplied  at  coaling  points 
is  of  the  proper  kind,  and  should  weigh  the  coal  personally,  and 
keep  an  accurate  record  of  the  following  items : 

The  coal  consumed. 

The  amount  of  ash. 

The  amount  of  cinders  in  smoke-box. 

The  water  evaporated. 

The  number  of  cars  in  train. 

The  weight  of  cars  as  marked  thereon. 

The  weight  of  lading. 

The  state  of  the  weather. 

The  direction  and  estimated  velocity  of  wind. 

The  temperature  of  the  atmosphere. 


644  EXPERIMENTAL  ENGINEERING.  [§434- 

The  temperature  of  the  feed-water. 
The  time  on  road. 
The  steam-pressure. 
The  exhaust-nozzles. 

The  conductor  should  enter  the  above  observations  in  a 
'log-book,  together  with  notes  of  repairs  to  engine,  and  any 
other  items  that  might  be  of  import. 

REPORT  OF   COAL-TRIALS. 

In  order  that  coal-trials  may  be  similar  and  consequently 
comparative,  the  following  data  should  be  observed  (see  Arti- 
cle 343,  page  443)  : 

First. 

Dates  between  which  trials  were  conducted. 
Class  of  locomotive. 

Service  in  which  trials  were  made,  mentioning  locality  etc 
Name  of  conductor  of  trial. 

Second. 

COAL  A. 
Kind  of  coal. 

Name  of  mine  and  operator. 

Location  of  mine. 

Physical  quality  of  coal  (appearance). 

Steaming  quality  of  coal. 

Kind  of  fire  made. 

Clinkers  and  ashes. 

Cinders  in  smoke  box. 


. 

Cleaning  ash-pan  and  smoke-box. 
Labor  involved  in  firing. 

COAL  B. 
oame  as  above. 


GENERAL   REMARKS 

evaporation  (pounds  of 


§434-3  TESTING   LOCOMOTIVES.  645 

Comparison  of  coal  consumed  per  100  tons  hauled  one  mile. 

Value  coal  A,  100$. 

Value  coal  B. 

Comparative  value. 

Coal  A  is  100$  more  or  less  valuable  than  coal  B. 

A  table  of  engine-performance  and  a  table  of  general  re- 
sults of  engine-performance  for  each  coal  must  accompany  the 
report.  (See  Form  D,  page  646.) 

WATER-MEASUREMENTS. 

It  has  been  found  during  the  last  year  or  two  that  meters 
are  reliable  and  accurate  within  less  than  one  per  cent  for 
measuring  the  water  used  by  a  locomotive.  (The  experience 
of  the  author  does  not  accord  with  this  statement — see  Article 
214,  page  284.)  The  meters  should  be  specially  made  for  the 
purpose  and,  if  possible,  free  from  any  material  that  is  injured 
by  contact  with  hot  water.  They  should  be  placed  so  as  to  be 
read  from  the  cab. 

In  mounting  these  meters,  all  pipes  should  be  thoroughly 
cleaned  before  they  are  put  into  position,  and  a  sufficiently 
large  strainer  should  be  placed  between  the  meter  and  the  tank. 
A  most  essential  feature  is  to  have  a  good  flap  check-valve  be- 
tween the  injector  and  the  meter ;  otherwise  the  hot  water 
may  flow  backward  and  ruin  the  rubber  recording-disks  in  the 
meter.  As  a  check  upon  the  meter,  however,  other  means  of 
measuring  the  water  should  be  employed.  The  most  convenient 
method  is  to  use  a  float  attached  to  a  wooden  bar  which  slides 
upon  a  graduated  rod,  the  lower  end  of  which  rests  upon  the 
bottom  of  the  tank.  This  rod  is  graduated  to  show  1000  Ibs., 
and  subdivided  to  250  Ibs. 

The  method  of  graduating  the  rod  is  as  follows  :  Fill  the 
tank,  place  the  bar  and  float  in  the  proper  position  for  read- 
ing, and  mark  the  stationary  rod  zero  at  a  level  with  the  top 
of  the  float  bar.  Draw  from  the  tank  1000  Ibs.,  place  the 
measuring  device  in  position  again  and  mark  the  rod,  calling 
this  mark  i.  Again  draw  off  1000  Ibs.,  mark  the  rod  2,  and 
so  continue  until  the  water  is  all  drawn.  If  the  tank  has  a  uni- 


646 


EXPERIMENTAL   ENGINEERING. 


[§  434- 


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§  434-]  TESTING   LOCOMOTIVES.  647 

form  horizontal  section,  several  thousand  pounds  can  be  drawn 
off  at  once  and  the  rod  subdivided  accordingly. 

In  general  the  float  is  placed  in  the  man-hole  of  the  tank; 
but  as  this  is  not  in  the  centre  of  gravity  of  the  water-space,  its 
readings  are  not  quite  correct  if  the  two  ends  of  the  tank  change 
their  relative  heights.  This  can  be  overcome  by  having  a  spe- 
cial small  opening  made  at  the  centre  of  gravity  of  the  tank,  or 
as  near  it  as  possible,  and  using  a  small  float. 

Another  but  less  convenient  way  is  to  place  a  glass  tube, 
on  each  side  of  the  tank  opposite  the  centre  of  gravity  of  the 
water-space,  and  to  graduate  scales  behind  them  by  the  same 
method  as  above  described.  The  objections  to  this  method 
are  the  inconvenience  in  reading  the  scales  (especially  at  way 
stations  where  there  is  but  little  time),  their  liability  to  freezing 
in  cold  weather,  and  the  possibility  of  injuring  them  at  any 
time. 

The  float  is  always  convenient  and  serviceable. 

When  locomotive  boilers  are  being  fired  hard,  the  water 
rises  above  the  normal  level,  and  a  measurement  of  water  just' 
after  the  injectors  have  been  throwing  comparatively  cold 
water  into  the  boiler  is  not  an  accurate  one  ;  the  water  shrinks 
and  swells  according  as  the  firing  is  hard  or  as  the  locomotive 
is  being  worked.  Hence  measurements  taken  under  these  vari- 
able conditions  are  necessarily  approximations.  There  is  also 
a  continuous  movement  of  the  water  in  the  water-glass,  and  a 
mean  of  the  oscillations  is  not  quite  satisfactory.  Although 
the  amount  of  water  fed  into  the  boiler  can  be  determined  ex- 
actly by  the  use  of  meters,  yet  the  inaccuracies  of  the  location 
of  the  water-line  render  water-measurements  on  short  runs 
almost  impracticable.  The  six-hour  test  for  a  stationary  engine 
is  considered  satisfactory  when  successive  tests  will  give  the 
same  results  ;  but  in  locomotive  work,  unless  the  engine  be 
kept  quiet,  as  it  would  be  when  tested  in  a  shed,  a  short  test  is 
of  little  or  no  value.  It  may  be  accepted  that  a  determination 
of  the  water-line  by  the  sound  of  the  gauge-cocks  is  too  uncer- 
tain to  be  admissible  in  locomotive-tests  unless  the  run  is  a  long 
one.  In  such  cases  the  total  amount  of  water  used  is  so  large 


648  EXPERIMENTAL  ENGINEERING.  [§  434- 

that  any  errors  in  estimating  the  water-level  at  the  beginning 
or  the  end  of  the  trip  practically  disappear. 

A  locomotive  which  is  undergoing  a  test  should  have  a 
water-glass  on  the  boiler.  Behind  this  should  be  a  strip  of 
wood  graduated,  and  surrounding  the  glass  and  fastened  to  the 
wood  should  be  a  copper  wire  at  the  height  at  which  the  water 
should  be  left  at  the  end  of  every  trip.  The  tank-measure- 
ment should  not  be  taken  at  the  end  of  the  trip  unt.il  the  water 
in  the  boiler  is  at  the  standard  height.  The  temperature  of  the 
water  should  be  taken  as  it  enters  the  tank  at  every  station 
where  water  is  taken,  and  tank  reading  should  be  taken  before 
*nd  after  each  filling. 

Leakage  of  Boiler. — To  test  for  leakage,  keep  up  the  pres- 
sure to  be  carried,  as  nearly  as  possible,  without  blowing  off, 
and  note  the  fall  of  water  in  the  water-glass  in  a  given  time,  say 
four  hours.  Of  course  the  injector  must  not  be  applied  during 
this  interval.  The  water-meter  can  then  be  used  to  determine 
the  amount  lost  by  leakage  by  reading  the  dial,  applying  the  in- 
jector until  the  water  reaches  the  original  level,  and  then  taking 
a  second  reading.  The  difference  will  be  the  amount  of  water 
lost.  All  boilers  lose  more  or  less  from  this  cause,  and  if  the 
test  is  to  be  a  comparison  between  two  different  styles,  the 
necessity  for  this  information  is  obvious. 

******* 

Before  beginning  a  test,  the  pistons  and  the  slide  and  throttle 
valves  of  the  engine  should  be  made  tight.  The  point  of  cut- 
off for  each  notch  of  the  quadrant  should  be  ascertained,  and 
the  cut-off  should  be  painted  in  white  on  the  quadrant,  or  on 
boiler-jacket,  with  pointer  or  lever.  All  leaks  about  the  engine 
should  be  stopped. 

A  graduated  scale  and  index  should  be  attached  to  the 
throttle-rod  to  indicate  its  opening. 

A  special  steam-gauge  with  a  long  siphon  should  be  used  for 
the  boiler-pressure  and  attached  to  the  front  of  the  cab  at  the 
left  side,  so  that  it  will  not  become  incorrect  from  overheating. 
Readings  of  the  'gauge,  reverse  quadrant,  throttle-scale,  and 
boiler-height-scale  should  be  taken  frequently,  the  first  as  often 


§4340  TESTING   LOCOMOTIVES.        •  649 

as  once  in  two  and  one-half,  five,  or  ten  minutes,  depending 
on  length  and  character  of  run,  and  all  with  each  indicator- 
diagram,  if  the  latter  are  being  taken. 

Just  before  beginning  atrip  the  water  in  the  boiler  should 
be  at  the  standard  height  and  the  tank  reading  taken  in  order 
to  ascertain  the  amount  of  water  used  while  running,  or  per  in- 
dicated horse-power  per  hour. 

Extraordinary  efforts  should  be  made  to  prevent  blowing  off 
before  train  time  and  while  running.  The  number  of  times 
and  the  length  of  time  safety-valve  is  blowing  off  should  be 
recorded. 

No  water  should  be  taken  from  the  tank  for  any  purpose  ex- 
cept supplying  the  boiler,  and  the  boiler  should  not  be  blown 
off  during  a  test  if  it  can  be  avoided.  If  it  cannot  be  avoided, 
the  water  should  be  at  the  standard  height  before  and  after 
blowing. 

DYNAMOMETER  RECORDS. 

The  dynamometer  for  measuring  the  resistance  of  the  train, 
exclusive  of  the  engine  and  tender  resistance,  should  be  able  to 
record  the  following  data  : 

"  A." — The  pull  upon  the  draw-bar. 

u  B."-— The  speed  at  which  the  train  is  running. 

"  C."  — The  location  of  any  point  along  the  line  used  for  ref- 
erence stations  ;  and  possibly 

"  D." — The  wind-resistance. 

"  A." — THE   PULL   UPON  THE  DRAW-BAR. 

The  force  required  to  move  the  train  or  the  pull  upon  the 
draw-bar  should  be  registered  upon  a  strip  of  paper  travelling 
at  a  definite  rate  per  mile  of  distance  travelled  over  by  the  train. 
The  scale  upon  which  this  diagram  is  drawn  should  be  as  large 
as  is  possible  within  reasonable  limits  ;  a  scale  of  J  inch  per 
1000  Ibs.  pull  is  probably  as  suitable  as  any  that  can  be  de- 
vised, and  the  maximum  registered  pull  need  hardly  exceed 
28,000  or  30,000  Ibs.  The  height  of  the  diagram  should  be 


650  EXPERIMENTAL  ENGINEERING.  [§  434- 

measured  from  a  base-line  drawn  upon  the  paper  by  a  station- 
ary pen  so  located  that  when  no  force  is  exerted  upon  the 
draw-bar  the  base-line  should  coincide  with  zero  pull. 


"B." — THE   SPEED   AT   WHICH    THE   TRAIN   IS   RUNNING. 

This  record  should,  if  possible,  be  obtained  in  two  ways  : 

First. — By  an  accurate  time-piece,  preferably  a  chronometer 
furnished  with  an  electric  circuit-breaking  device.  It  is  of  con- 
siderable importance  that  the  time-piece  should  have  its  circuit- 
breaking  device  very  carefully  made,  to  produce  exact  intervals- 
of-time  marks,  because,  when  the  matters  of  acceleration  or  re- 
tardation of  speeds  enter  into  the  data  required,  it  is  important 
that  the  time-record  should  be  correct.  The  question  of  length 
of  intervals  of  time  required  is  open  to  discussion.  In  most 
cases  of  ordinary  work,  five-second  intervals,  or  twelve  to 
the  minute,  are  probably  as  satisfactory  as  can  be  decided 
upon ;  for  very  careful  work  it  would  probably  be  advisable  to 
have  an  auxiliary  apparatus,  something  like  the  Boyer  speed- 
recorder. 

Boyer  Speed-recorder. — This  instrument  is  constructed  in 
such  a  manner  that  its  accuracy  and  reliability  are  without 
question  when  it  is  properly  mounted  and  cared  for.  It  is  not 
a  delicate  machine,  and  only  needs  ordinary  attention.  Its 
principle  of  operation  is  as  follows :  It  consists  of  an  oil- 
pump  which  works  against  a  fixed  resistance  in  the  shape  of 
an  aperture  through  which  the  oil  flows.  The  faster  the 
pump  runs,  the  greater  is  the  pressure  in  the  oil-cylinder. 
A  piston  in  the  oil-cylinder  which  moves  against  a  spring 
rises  in  proportion  to  the  increase  of  pressure.  As  the  piston 
rises,  a  metallic  pencil  marks  the  movement  on  a  roll  of  pre- 
pared paper,  which  moves  in  proportion  to  the  longitudinal 
movement  ,of  the  engine.  In  the  cab  is  a  dial  which  indicates 
at  all  times  the  speed  of  the  engine  with  only  a  small  error. 
The  diagrams  record  all  stops  and  make  an  accurate  record  of 
the  rate  of  acceleration. 

Second. — It   would    be   well   to    have,   in   addition    to  the 


§434-]  TESTING    LOCOMOTIVES.  651 

apparatus  just  described,  another  one  which  produces  a  con- 
tinuous curve  upon  the  diagram  paper,  the  ordinate  of  which, 
measured  from  a  base-line,  would  give  the  speed  in  feet  per 
second,  or  any  other  convenient  measurement ;  this  could  be 
obtained  by  modification  of  the  Boyer  speed-indicator. 


«  C." — THE   LOCATION  OF  ANY   POINT  ALONG  THE  LINE  USED 
FOR   REFERENCE   STATIONS. 

These  location-marks  are  most  easily  produced  by  having, 
at  various  convenient  parts  of  the  car,  electric  press-buttons, 
and  having  a  pen  upon  the  dynamometer  which  will  be 
deflected  sidewise  when  the  circuit  is  made  or  broken ;  this 
pen  to  be  operated  by  an  observer  whose  special  duty  it  is  to 
attend  to  this  part  of  the  work. 

"  D."— WIND-RESISTANCE. 

Very  little  attention  has  so  far  been  given  to  measurements 
of  wind-resistance,  or  the  relation  it  bears  to  the  frictional 
resistance  of  journals  and  wheels,  and  few  experiments  on  this 
subject  are  recorded.  The  subject  is  very  complex,  owing  to 
the  fact  that  it  is  generally  supposed,  and  we  think  with  good 
reason,  that  the  train  is  so  very  largely  surrounded  by  eddies  of 
air,  and  that  it  will  be  very  difficult  to  obtain  any  reliable  data, 
especially  when  it  is  remembered  that  the  clearances  of  a  rail- 
road are  greatly  circumscribed  and  reduced  to  a  minimum,  so 
that  it  will  be  impossible  to  put  any  apparatus  which  measures 
resistance  of  this  kind  far  enough  out  from  the  car  to  get 
reliable  data.  The  apparatus  for  measuring  this  resistance 
would  probably  be  subdivided  into  three  separate  disks,  one 
facing  front  and  two  facing  toward  the  sides  of  the  car,  all 
three  connected  together  to  produce  a  single  resultant  curve 
drawn  upon  the  diagram  paper,  and  the  scale  upon  which  this 
is  drawn  could  probably  be  best  subdivided  into  ten  points,  as 
practised  by  the  United  States  Government. 


652  EXPERIMENTAL   ENGINEERING.  [§  434. 


GENERAL. 

It  is  of  very  great  advantage  to  have  more  than  one  relative 
speed  on  the  paper  upon  which  the  diagrams  are  recorded, 
and  the  length  of  the  .paper  consumed  per  mile  run  should 
bear  some  convenient  relation  to  the  distance  travelled  over. 

We  would  suggest  that  the  rates  of  travel  of  paper  per 
mile  be  such  that  I  inch  measured  upon  the  diagrams  shall 
represent  100  feet  as  the  maximum,  and  that  this  distance  be 
further  subdivided  so  that  %  mcn  shall  represent  100  feet  of 
track,  and  J  inch  shall  represent  100  feet  of  track.  It  is  of 
course  also  necessary  to  have  all  of  the  registering  pens  located 
upon  one  line  transverse  to  the  direction  of  the  movement  of 
the  paper,  as  in  that  way  only  can  simultaneous  data  be 
recorded. 

The  staff  required  to  work  the  dynamometer  is  as  follows : 

One  chief,  who  has.  general  supervision  over  the  force,  and 
Avhose  duty  it  is  to  see  that  the  records  are  properly  obtained, 
and  that  all  the  location  stations  are  properly  marked  upon 
the  diagrams. 

One  outlook,  whose  duty  it  is  solely  to  observe  the  location 
stations,  and  to  locate  them  upon  the  diagrams  by  means  of  an 
electrically  moved  pen. 

Besides  this  it  is  of  considerable  advantage  to  have  a  third 
person  who  is  familiar  with  all  the  mechanism  in  the  car,  and 
who  looks  after  the  proper  working  of  the  mechanical  parts  of 
the  apparatus,  and  assists  the  general  observer. 


TABLE   OF   ENGINE-PERFORMANCE. 

The  following  forms  are  recommended  for  tabulating  the 
results  of  a  locomotive-test,  and  in  order  to  make  the  test  com 
plete  each  test  item  should  be  entered.  It  is  particularly  im- 
portant that  the  "equivalent  evaporation  from  and  at  212°  per 
pound  of  coal "  be  entered,  as  it  is  only  by  this  that  evaporative 
comparisons  can  be  made. 


TESTING    LOCOMOTIVES. 


653 


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EXPERIMENTAL  ENGINEERING. 


[§434- 


FORM   B. 

LOCOMOTIVE-TESTS.— GENERAL  RESULTS. 

Railroad  Co. 

Tests  of  locomotive  tyo ,  between and 

Bound.  ,  18... 

Distance, miles.  Train  No. ... 

Kind  of  coal Coal  analysis Calorimetric  value  of  coal 

Date 

Left at  .  

Arrived    "    

1  Weather 

2  Mean  temperature  of  atmosphere 

3  Direction  of  wind 

4  i  Velocity  of  wind,  miles  per  hour 

§  Condition  of  rail  
Size  of  exhaust-nozzle,  single  or  double 

7  Weight  of  train  in  tons  of  2000  Ibs.,  including  locomotive,  tender,  pas- 

sengers, and  freight 

8  Weight  of  train  in  tons  of  2000  Ibs.,  exclud.  the  locomotive  and  tender. 

9  Equivalent  number  of  standard  cars  at ....  tons  each  

10  Maximum  boiler  pressure  by  gauge 

it   Minimum  k     

T2   Average  "        "       

13  Prevailing  position  of  throttle 

14  "         "  reverse-lever 

15  points  of  cut-off . 

16  Schedule  time  in  motion  . .   

17  Actual         *'      "        ''       

18  Time  made  up  in  minutes 

19  Aggregate  intermediate  stops,  minutes 

20  Time  during  which  power  was  developed,  or  throttle  open 

21  Average  speed,  miles  per  hour 

22  Maximum  number  of  revolutions  per  minute 

23  "          rate  of  speed,  miles  per  hour 

24  Minimum  number  of  seconds  per  mile 

25  Actual  weight  of  coal  used 

26  "  "        "wood" 

27  Average  weight  of  coal  burned  per  square  foot  of  grate  per  hour 

28  Number  of  miles  run  per  ton  (2000  Ibs,)  of  coal 

29  Number  of  pounds  of  coal  used  per  mile ...   

30  Weight  of  ashes  and  unconsumed  coal  in  fire-box  and  ash-pan 

3!         "        "   unconsumed  coal  in  fire-box  and  ash-pan 

32  "   cinders  (sparks)  in  smoke-box 

33  "        "   combustible  utilized K 

34  Percentage  of  ashes  and  unconsumed  coal  in  fire-box  and  ash-pan 

"  unconsumed  coal  in  fire-box  and  ash-pan 

36  "  cinders  in  smoke-box 

37  "  combustible  consumed 

38  Average  temperature  of  feed-water 

39  Weight  of  water  drawn  from  tender 

40  Waste  of  injector.  

4 1  Weight  of  water  evaporated  (39-40) 

42  Actual  evaporation  per  pound  of  total  coal 

43  Equivalent  evaporation  from  and  at  212°  per  pound  of  coal 

44  "       "    "    "      "       "       "combustible 

45  Coal  used  per  ton  of  train  per  loo  miles.  . .-... 

46  "        "       "  car-mile 

47  Water  used  per  ton  of  train  per  100  miles ; 

48  "        "        "  car  mile    

49  "  hour  while  developing  power 

c0        "        "        "      "     per  square  foot  of  heating  surface 

51  •'        "        "      "        "        "         "     "  grate  "        

52  Maximum  indicated  horse-power  developed 

53  Average  "        

54  Total  coal  per  indicated  horse-power  developed  per  hour 

55  | Water  evaporated  per  indicated  horse-power  per  hour 

56  | Dry  steam  used  per  I.  H.  P.  per  hour,  per  indicator-diagram 

57  [Percentage  of  moisture  in  steam 

58  Average  number  of  sq.  ft.  of  heating  surface  per  indicated  horse-power 

59  '-'  "        indicated  horse-power  per  sq.  ft.  of  grate  surface 

fo  Average  temperature  in  smoke-box  while  using  steam 

61    Prevailing  vacuum      "  /   **          "          "      


§434-]  TESTING    LOCOMOTIVES.  655 

STEAM    CALORIMETERS. 

There  is  little  doubt  that  the  throttling  calorimeter  will 
fulfil  all  requirements  for  testing  the  dryness  of  steam  in 
locomotives.  It  cannot  measure  quantitatively  more  than 
about  5  per  cent  of  moisture,  but  it  appears  probable  that 
locomotive  boilers  develop  steam  which  either  contains  a  frac- 
tion of  i  per  cent  of  moisture,  or  the  priming  is  a  sudden  tem- 
porary action,  causing  water  to  mix  with  the  steam  to  such  an 
extent  that  no  quantitative  measurement  of  its  amount  is 
practicable.  Under  these  circumstances  all  that  is  desired  'of  a 
calorimeter  is  to  indicate  the  temporary  occurrence  of  this  sud- 
den excessive  priming,  and  a  throttling  calorimeter  has  been 
shown  by  Mr.  D.  L.  Barnes  to  be  capable  of  doing  this,  provided 
the  thermometer  has  its  bulb  in  direct  contact  with  the  steam 
flowing  through  the  calorimeter.  Such,  an  arrangement  is 
shown  in  the  accompanying  figure,  of  which  the  following  is  a 
description  abstracted  from  the  Railroad  Gazette  of  November 
27,  1891  (see  Article  330)  : 

Calorimeter. — This  instrument  (see  Fig.  289)  consisted  of 
two  pieces  of  brass  pipe,  one  inside  of  the  other,  leaving  an  air- 
space between  the  outer  and  the  inner.  The  outer  pipe  was 
screwed  into  the  dome  and  extended  within  the  dome  to  the 
throttle.  At  this  interior  end  the  two  pipes  were  joined  together 
by  a  cap  which  had  a  perforation  -fc  of  an  inch  in  diameter. 
On  the  outer  end  of  the  inner  pipe  was  placed  a  globe-valve, 
and  next  to  this  and  outside  of  it  a  tee  in  Which  was  a 
stuffing-box  and  a  thermometer,  as  shown  in  Fig.  289.  Be- 
yond this  tee  was  another  globe-valve  and  a  short  pipe  of 
large  diameter  to  carry  the  steam-jet  away  from  the  man  in 
charge. 

With  this  device  the  point  of  most  rapid  movement  of  the 
steam  was  located  next  to  the  throttle,  and  any  water  coming 
near  it  would  immediately  pass  through  the  opening  because 
of  the  high  velocity.  The  thermometer-bulb  was  bared  to  the 
steam,  and  no  cups  were  used.  It  was  found  possible  to  shut 
off  the  outer  globe-valve  and  expose  the  thermometer  to  a  full 


EXPERIMENTAL   ENGINEERING. 


[§  435- 


boiler-pressure  without  blowing  the  thermometer  from  the  stuff. 
ing-box.  In  this  way  it  was  determined  that  the  therm  or.;  eter 
recorded  a  steam-temperature  which  corresponded  to  the 
steam-gauge  in  the  cab. 

With  this   instrument   priming   was  shown   whenever  the 


%«r 


FIG.  289. — THROTTLING  CALORIMETER  ATTACHED  TO  LOCOMOTIVE. 

boiler  was  filled  to  a  point  where  water  could  be  seen  coming 
from  the  stack.  Immediately  when  the  boiler  foamed,  the 
thermometer  in  the  second  calorimeter  dropped  to  212°.  It  is 
believed  that  this  calorimeter  is  more  accurate  for  locomotive 
work,  because  it  often  happens  that  the  locomotive  primes 
only  at  starting  and  not  for  a  sufficient  length  of  time  to  en- 
able the  throttling  instrument  to  make  a  true  record.  And 
again,  there  are  in  a  locomotive  rapid  changes  in  the  rate  of 
steam  consumption  which/  must  cause  rapid  changes  in  the 
quality  of  the  steam. 

435.  Experimental  Engines. — During  the  last  few  years 
many  of  the  engineering  schools  have  been  provided  with  en- 


§  435-]  TESTING   SPECIAL  ENGINES.  657 

gines  designed  especially  for  experimental  purposes.  These 
engines  do  not  resemble  each  other  in  any  particular  feature, 
but  they  do  generally  differ  from  the  engines  designed  for 
commercial  uses  in  the  provision  that  is  made  for  adjustment 
of  the  various  working  parts,  and  for  varying  the  conditions 
under  which  the  engine  can  be  operated.  Such  engines  are 
usually  supplied  with  all  the  known  devices  for  measuring  the 
heat  transmitted,  the  power  received  and  that  delivered  from 
the  whole  or  any  part  of  the  system. 

Space  cannot  be  spared  for  the  detailed  description  of  any 
of  these  engines,  but  the  following  are  the  principal  dimen- 
sions of  the  Sibley  College  experimental  engine,  shown  as  the 
frontispiece  of  the  present  work. 


GENERAL  DIMENSIONS  OF  SIBLEY  COLLEGE  EXPERIMENTAL 

ENGINE. 

Diameter  of  high-pressure  cylinder 9    inches 

"         "  intermediate-pressure  cylinder 16 

"         "  low-pressure  cylinder 24 

Length  of  stroke 3<> 

Revolutions  per  minute,  90. 

Diameter  of  fly-wheels 1O  feet 

Width  of  face  of  fly-wheels 17 

Number  of  fly-wheels,  3. 

Diameter  of  brake-wheels 4  feet 

Width  of  face  of  brake-wheels •  *  10 

Number  of  brake-wheels,  3. 

Diameter  of  high-pressure  crank-pin 3i 

Diameter  of  intermediate-pressure  crank-pin 7 

Diameter  of  low-pressure  crank-pin 

Length  of  crank-pin 

Length  of  connecting-rods 9  feet 

Diameter  of  main  bearings 

Length  of  main  bearings 

Length  of  pillow-block  bearings 

Distance  between  centre  lines  of  high-pressure  and  inter- 
mediate-pressure engines *4  fe 

Distance  between  centre  lines  of  intermediate-pressure  and 

12  feet     •         " 
low-pressure  engines 

Rated  horse-power,  175. 

Floor-space  occupied,  23  feet  9  inches  X  3*»*  7  inches. 


658  EXPERIMENTAL   ENGINEERING.  [§  435- 

HIGH-PRESSURE  CYLINDER. 

Steam-ports f  in.  X  12     inches 

Exhaust-ports i|  "     X  12  " 

Diameter  of  steam-valve  seats 3^  " 

Diameter  of  exhaust- valve  seats 3^  " 

Thickness  of  steam-space  in  jacket j  ' 

Diameter  of  piston-rod 2^      " 

Diameter  of  steam-inlet 3  " 

Diameter  of  exhaust-outlet 5  " 

INTERMEDIATE-PRESSURE  CYLINDER. 

Steam-ports I     in.  X  20    inches 

Exhaust-ports i£  "    X  20 

Diameter  of  steam-port 5          " 

Diameter  of  exhaust-port ..'..- 5          " 

Thickness  of  steam-space  in  jacket \\      " 

Diameter  of  piston-rod 2^-      " 

Diameter  of  steam-inlet 6 

D'  meter  of  exhaust-outlet 3 

LOW-PRESSURE  CYLINDER. 

Steam-ports , if  in.  X  28     inches 

Exhaust-ports 2-£  "     X  28  " 

Diameter  of  steam-ports 6£  " 

Diameter  of  exhaust-ports 6^  " 

Thickness  of  steam-space  in  jacket f  " 

Diameter  of  piston-rod   2T6^      " 

Diameter  of  steam-inlet 6  " 

Diameter  of  exhaust-outlet , 8  " 

All  the .  moving  parts  were  weighed  before  they  were  put 
in  place. 

The  weights  are  as  follows: 

Fly-wheels 20,807  pounds 

Brake-wheels 5,264  " 

Crank-shaft  and  eccentrics  complete 9»958  " 

Total  weight  of  crank-shaft,  fly-wheels,  brake-wheels,  and  ec- 
centrics  36,029  " 

Weight  of  high-pressure  piston  and  cross-head 378^  " 

Weight  of  intermediate-pressure  piston  and  cross-head 503  " 

Weight  of  low-pressure  piston  and  cross-head   790  " 

Weight  of  high-pressure  connecting-rod 281  " 

Weight  of  intermediate-pressure  connecting-rod 341  " 

Weight  of  low-pressure  connecting-rod 282  " 


435-] 


TESTING   SPECIAL  ENGINES. 


659 


The  connecting-rods  were   suspended  on  knife-edges,  and 
the  time  of  their  vibration  was  taken  as  follows : 

End  on  knife-edge.  Time  of  zoo  vibrations. 

j  Crank  end 4  min.  45    sec. 

"(Cross-headend 4     "     44$     " 


Low-pressure 

Intermediate-pressure. ., 
High-pressure 


\  ""'  "f  ™' 


RECEIVER  DIMENSIONS. 


HIGH-PRESSURE  RECEIVER. 

Length ' lift.    7    in- 

Diameter 14 

Number  of  tubes 15 

Diameter  of  tubes i|  " 

Receiver  volume 8.2  cu.  ft. 

•ieating  surface 62.34  sq.  ft. 


INTERMEDIATE-PRESSURE  RECEIVER. 

Length lift.    7     in. 

Diameter 20     " 

Number  of  tubes 19 

Diameter  of  tubes 2^  " 

Receiver  volume 15.8  cu.  ft. 

Heating  surface 119.8  sq.  ft. 


The  methods  of  testing  experimental  engines  do  not  differ 
in  any  essential  feature  from  those  for  testing  any  engine  of  the 
same  general  class. 


CHAPTER  XX. 

EXPERIMENTAL  DETERMINATION  OF  EFFECTS  OF 
INERTIA  ON  THE  STEAM-ENGINE. 

436.  Inertia  and  its  Effects.* — The  effect  of  inertia  of  the 
moving  parts  of  the  steam-engine  is  to  modify  to  a  consider- 
able extent  the  resultant  pressures  which  are  transmitted  by 
the  connecting-rod  to  the  crank-pin.  The  exact  solution  of 
this  problem,  including  the  effects  of  friction  and  gravity,  has 
been  accomplished  by  Prof.  Jacobus  and  is  published  in  the 
Trans.  Am.  Society  of  Mechanical  Engineers,  Vol.  XL  Com- 
plete discussions  of  the  effects  of  inertia  will  be  found  in 
various  works  devoted  to  the  steam-engine ;  also  approximate 
methods,  usually  graphical,  are  given  in  these  treatises  which 
are  sufficiently  accurate  for  practical  purposes. 

Prof.  Jacobus  gives  the  following  formula  for  the  approxi- 
mate calculation  of  the  inertia-effects  when  friction  and  gravity 
are  neglected,  and  when  the  rod  is  symmetrical  about  its  centre 
line,  and  the  path  of  motion  of  the  wrist-pin  passes  through 
the  centre  of  the  crank-shaft. 

Let  R  equal  radius  of  crank-circle ;  nR,  length  of  connect- 
ing-rod ;  0,  the  crank-angle  measured  from  its  position  when 
parallel  to  the  centre  line  of  the  cylinder;  M,  mass  of  the 
piston,  piston-rod,  and  cross  head  ;  m,  the  mass  of  the  connect- 
ing-rod ;  r,  angular  velocity  of  crank-shaft  ;  Q,  connecting-rod 
angle;  PM  and  Pc,  forces  exerted  by  the  connecting-rod  upon 
wrist-pin  and  crank-pin,  respectively;  Pa,  pressure  of  steam  on 
the  piston ;  T,  tangential  component  of  the  force  Pe  acting  on 

*  See  Thurston's  Manual /of  the  Steam-engine,  Vol.  II.,  page  425. 

660 


§437-]  DETERMINATION   OF  INERTIA.  £fa 

the  crank-pin  ;  N,  radial  component  of  the  force  Pe  acting  at 
the  crank-pin  ;  Z  and  Pb ,  auxiliary  quantities.     We  have 

2_  n*  cos2  B  —  tf  sin2  0  -f  sin4  0. 
.      Pp  =  (M+  m)r*R(cos  e  +  Z) ; 


N  =  (Pa-  Pp)  sec  ft  cos  (0  +  ft)  ; 
/>,=  (/>.-/>,)  sec  /?. 

When  the  accelerating  forces  are  not  included, 


Pc  =  Pa  sec  ft. 

In  this  work  is  discussed  only  the  experimental  method  of 
determining  the  inertia  of  an  engine  as  developed  by  Mr.  E. 
F.  Williams  of  Buffalo,  N.  Y.,  and  published  in  the  American 
Machinist  in  1884  and  '5. 

437.  The  Williams  Inertia-indicator.  —  This  instrument 
draws  a  curve  (see  Fig.  290)  closely  resembling  the  theoretical 
inertia-diagram,  and  similar  in  kind  to  an  indicator-card.  The 
horizontal  length  of  the  diagram  corresponds  to  the  stroke. 
The  abscissa  of  any  point  of  the  curve  identifies  the  position 
of  the  piston  at  a  corresponding  point  in  its  travel,  and  its  ordi- 
nate  measures  to  a  known  scale  the  force  required  to  give  to 
a  mass  of  known  weight  (one  or  two  pounds)  the  acceleration, 
positive  or  negative,  of  the  piston  at  that  point  of  its  stroke. 
The  product  of  this  force  into  the  weight  of  the  reciprocating 
parts,  in  pounds,  gives  for  that  point  of  stroke  the  positive  01 
negative  horizontal  force  at  the  crank-pin  due  to  the  inertia  of 
the  parts.  The  instrument  is  shown  in  Fig.  290  attached  to 
the  cross-head  of  an  engine,  and  in  Fig.  292  in  plan. 

The  frame  P  is  rigidly  attached  to  the  cross-head  A  by  two 
studs/  and  r,  the  former  serving  also  as  a  pivot  for  the  arrn  B. 
The  upper  end  of  B  is  pivoted  to  one  end  of  a  horizontal  bar 
y  whose  other  end  is  attached  by  a  pin  to  some  fixed  support. 
In  this  way  B  swings  back  and  forth,  its  lower  end,  together 


662 


EXPERIMENTAL   ENGINEERING. 


FIG.  »9i.— THE  WILLIAMS  INERTIA-INSTRUMENT.  PLAN 
d 


FIG.  293. — SPRING  TO  INERTIA-INSTRUMENT. 
d 


\ 


FIG.  2ga — THE  WILLIAMS  INERTIA-INDICATOR. 


§  437-]  DETERMINATION  OF  INERUA,  663 

with  the  fiame  Pand  the  parts  carried  by  it,  travelling  with 
the  cross-head.  Within  the  case  or  cage  d  (shown  in  section 
in  Fig.  292)  the  weight  h  is  free  to  slide  horizontally  on  steel 
friction  rollers,  except  as  controlled  by  the  spring.  This  spring, 
whose  tension  is  known  by  calibration,  is  the  only  means  by 
which  the  motion  of  the  cross-head  is  communicated  to  the 
weight  h,  and  it  must  therefore  be  extended  or  compressed  by 
an  amount  which  measures  the  force  needed  to  overcome  the 
inertia  of  the  weight. 

For  convenience  h  may  be  made  to  weigh,  including  the 
parts  moving  with  it,  exactly  one  pound.  It  is  joined  by  a 
light  rod  e  to  the  bent  lever  a  which  moves  a  pencil  in  a  direc- 
tion at  right  angles  to  that  of  the  cross-head  motion.  By  the 
vibration  of  the  arm  B  the  paper  is  carried  under  the  pencil 
on  the  curved  platform  b  shown  in  Figs.  290  arid  291.  This  can 
at  pleasure  be  drawn  upward  by  the  cord  m,  and  kept  in  contact 
with  the  pencil  for  one  or  more  revolutions  while  the  engine  is 
in  motion.  The  paper  is  put  in  place  while  the  engine  is  at 
rest,  and  the  neutral  line  x,  Fig.  291,  is  drawn  by  swinging  the 
arm  B  back  and  forth  by  hand.  As  soon  as  the  engine  is  run- 
ning under  the  conditions  desired,  contact  may  be  made  and 
the  diagram  drawn. 

In  using  the  instrument  so  as  to  make  a  diagram  from  2  to 
3  inches  long,  the  arm  B  may  be  varied  in  length  to  suit  the 
stroke  of  the  engine.  To  maintain  a  given  average  length  of 
ordinates  for  widely  differing  speeds,  the  scale  may  be  changed 
by  changing  the  spring,  or  the  weight,  or  both. 

For  obtaining  the  effect  per  pound  weight  of  the  recipro- 
cating masses,  determine  the  scale  as  follows:  The  force 
exerted  by  an  8o-lb.  indicator-spring  when  it  is  compressed  or 
extended  \  inch,  causing  a  pencil-movement  of  one  inch,  is  80 
Ibs.  per  square  inch  of  indicator  piston-area.  The  latter 
being  one-half  square  inch,  the  actual  force  on  the  spring 
is  40  Ibs.  If,  then,  an  8o-lb.  spring  with  a  2-lb.  weight 
be  used,  a  i-inch  ordinate,  will  mean  40  Ibs.  exerted  by  the 
spring  in  total,  or  a  force  of  20  Ibs.  per  pound  of  the  mass  it 
moves. 


664  EXPERIMENTAL   ENGINEERING.  [§  43S- 

Thus  a  scale  20  means  a  force,  for  each  inch  of  ordinate 
measured  from  the  neutral  line,  equal  to  twenty  times  the 
weight  of  the  moving  body  under  investigation.  In  other 
words,  each  twentieth  of  an  inch  in  length  of  ordinate  repre- 
sents a  force  equal  to  the  weight  of  the  reciprocating  masses. 

An  8o-lb.  spring  with  a  i-lb.  weight,  scale  40 

"     8o-lb.      "      .     "     "  2-lb.        "  "     20 

"    40-lb.      "          "     "  i-lb.        "  "     20 

"    20-lb.      "          "     "  i-lb.        "  "     10 

438.  The  Inertia-diagram  drawn  by  the  Instrument — 
In  interpreting  the  diagram  several  points  are  to  be  noted  : 

1.  The    evenness    and    general   form    of  the  diagram    are 
largely  influenced  by  the  smoothness  of  running  of  the  engine, 
which   depends  on  the  accuracy  of  bearing  surfaces,  and  the 
degree  in  which  the  weight  of  reciprocating  parts,  their  veloci- 
ties, and  the  varying  steam-pressures  are  suited  to  each  other. 

2.  The  curvature  of  the  lines  traced  depends  chiefly  on  the 
ratio    of   crank-length   to    that    of   connecting-rod ;    this  ratio 
should  be  determined  by  measurement. 

3.  In  combining  the  diagram  with  an  indicator-card  the 
ordinates  should  represent  forces  in  pounds  per  square  inch  of 
piston-area,  and  in  the  same  scale  as  that  of  the  indicator-card. 
For  this  we  determine -by  independent  measurement  (l)  the 
force  exerted  by  the  spring  for  a  given  length  of  ordinate  from 
the  neutral  line  ;  (2)  the  ratio  of  the  weight  of  the  reciprocating 
parts  of  the  engine  to  that  of  the  parts  of   the    instrument 
moved  by  the  spring.;  and  (3)  the  area  of  the  engine-piston. 

4.  The  difference  in  length  of  the  corresponding  ordinates 
in   the  inertia  and  indicator  diagrams,  the  latter  corrected  for 
back  pressure   or  compression,  represents  the  net   horizontal 
force  transmitted  to  the  crank-pin. 

For  combination  with  a  steam  indicator-card,  the  force  per 
square  inch  of  piston-area  is  required.  This  is  best  obtained 
by  getting  the  weight-ratio  or  the  weight  of  reciprocating  parts 
per  square  inch  of  piston-a/ea.  This  multiplied  by  the  scale  of 
the  inertia-diagram  gives  the  engine-scale  or  scale  of  pounds  per 


§438.] 


DETERMINATION  OF  INERTIA. 


665 


square  inch  at  the  speed  at  which  the  diagram  was  taken.  An 
example  will  make  this  clear.  The-  inertia-diagram  in  Fig.  234, 
taken  from  a  very  smooth-running  engine,  was  obtained  with  an 


Scale  4O 

285  revs,  per  tnin. 
- Allen 


FIG.  293. — INERTIA-DIAGRAM. 


Scale  4O 

265  revs,  per  min* 
4.4.16     <<        "      &eo. 


FIG.  294. — INERTIA  AND  INDICATOR  DIAGRAMS. 

So  spring  and  a  one-pound  weight.  Hence  the  diagram-scale 
is  40.  But  for  this  engine  the  weight-ratio  was  3.  Hence. 
40  X  3  =  1 20  is  the  engine-scale. 

Having,  now,  this  inertia-diagram  (Fig.  234)  whose  engine- 
scale  is  1 20,  suppose  we  are  to  combine  it  with  an  indicator, 
diagram  (Fig.  235)  from  the  same  engine  at  same  spe«..d,  and 
taken  with  a  40  spring.  The  scale  of  the  inertia-diagram  can 


666 


EXPERIMENTAL  ENGINEERING. 


[§  438 


be  changed  from  120  to  40  by  drawing  it  with  the  ordinate  of 
each  point  increased  three  times,  giving  the  curve  ab  in  Fig. 
294.  The  ordinates  to  the  compression  curve  on  the  back 
stroke  can  be  deducted  from  the  corresponding  ordinates  of  the 
inertia  curve  ab,  and  the  included  area  shaded,  thus  exhibiting 
the  modification  of  the  steam-forces  by  the  inertia  of  the 
reciprocating  parts.  By  vertical  measurement  of  the  shaded 
portion,  the  true  distribution  of  horizontal  forces  on  the  crank- 
pin  during  the  backward  stroke  may  be  obtained. 

Important  Features  of  the  Experimental  Diagram. — Sup- 
pose that  in   Fig.  295  /  and  c  are  the  positions  respectively 


FIG.  295.— REi.ATivi.  MOTION  «F  CRANK-PIN  AND  PISTON. 

of   the  cross-head  aiid  crank-pins  with  crank   on   its  centre, 
Then,  were  it  not  for  the  angle    of   the    connecting-rod,  the 
cross-head  pin  would  g.   to  /'  when  the  crank  has  moved  to 
\c",pp'  being  equal  to  oc''. 

But  its  true  place  is  at  p" :  thus  in  the  quarter-turn  of  the 
crank  from  c  to  c"  the  cross-head  has  gone  a  distance  p'p" 
past  its  mid-stroke,  and  is  then  moving  at  the  same  speed  as 
the  crank-pin,  while  its  maximum  speed  was  attained  before 
reaching  mid-stroke.  Again,  on  the  return-stroke,  when  the 
crank  is  lowest,  the  piston  has  not  gone  half-way.  This  shows 
that  the  acceleration  is  greater  when  the  piston  is  at  the  head 


438.] 


DETERMINATION  OF  INERT! 


667 


end  of  cylinder.  The  same  thing  is  shown  in  Fig  206  xv 
being  much  greater  than  *y,  while  the  fact  that  point  of 
crossing  of  yy'  and  xx'  is  at  die  left  of  the  centre  shows  that  the 


FIG.  296.— INERTIA-DIAGRAM. 


zero  of  acceleration,  which  of  necessity  corresponds  with  maxi- 
mum  velocity,  falls  where  it  should. 


Scale  1=2O  Force  Units. 
1  ft.  Stroke,  1  Rev,  per   Sec. 
Connecting  Jlod—G  Cranks. 

FIG.  297.— INERTIA-DIAGRAMS. 


All  this  is  revealed  in  the  same  way  in  the  experimental 
inei  Lia-diagram  Fig.  293,  page  665,  and  the  accuracy  of  the  dia- 


668 


EXPERIMENTAL   ENGINEERING. 


[§  438. 


gram  may  be  further  tested  by  comparing  the  area  below  the 
neutral  line  with  that  above  it  by  means  of  a  planimeter. 

In  Fig.  297  the  inertia-diagrams  for  forward  and  backward 
strokes  have  been  separated.  The  negative  and  positive  signs 
show  respectively  where  the  inertia  opposes  and  assists  the 
steam-pressures.  The  curve  y"y'"  belongs  to  the  forward 
stroke  and  y'y  to  the  return. 

In  practical  use  the  diagram  should  be  divided  into  ten  or 
more  equal  spaces,  and  the  ordinate  at  the  centre  of  each 
space  being  numbered,  the  crank-positions  corresponding,  may 
be  found  as  shown  in  Fig.  298,  and  the  relative  velocity  of 


01  2  3  4  5  6  7  8  9  10     0 

7iG.  298. —  CRANK-POSITIONS  CORRESPONDING  TO  GIVEN  PISTON-POSITIONS. 

piston  and  crank  obtained.  The  method  of  dividing  the  dia- 
gram shown  in  Fig.  297  is  convenient  in  transferring  the  curve 
to  a  steam  indicator-card  similarly  divided.  Care  being  taken 
to  draw  both  to  the  same  scale  and  in  pounds  per  square  inch 
-of  piston,  the  inertia  curves  may  be  drawn  on  an  indicator- 
•card  arranged  as  shown  in  Fig.  299.  Here  the  back-stroke 
steam-card  has  been  drawn  inverted  and  in  contact  with  the  for- 
ward card  in  its  normal  position,  the  two  back-pressure  lines 
being  made  coincident  and  used  as  the  neutral  inertia  line. 


§438.] 


DETERMINATION  OF  INERTIA. 


669 


The  ordinate  lines  are  then  produced  to  cut  the  line  X 'X ', 
which  serves  as  a  base-line  from  which  to  lay  off  ordinates  of 
the  net  horizontal  forces  at  the  crank-pin.  The  actual  forces 


S 


FIG.  299. — COMBINED  DIAGRAMS. 


at  the  crank-pin  are  thus  more  clearly  revealed  for  both  strokes, 
and  the  areas  above  and  below  X' X'  respectively,  give  the  actual 
work  on  the  crank-pin  for  forward  and  return  strokes. 


CHAPTER   XXI. 


THE  STEAM-INJECTOR-THE  PULSOMETER. 

439.  Description  of  the  Injector. — The  steam-injector  is 
an  instrument  designed  for  feeding  water  to  steam-boilers, 
although  it  can  be  and  often  is  used  as  a  pump  to  raise  water 
from  one  level  to  another.*  It  has  been  used  as  an  air-com- 
pressor, and  also  for  receiving  the  exhaust  from  a  steam-engine, 


FIG.  300. — THE  MACK  NON-LIFTING  INJECTOR. 

taking  the  place  in  that  case  of  both  condenser  and  air-pump. 
It  was  designed  by  Henri  Jacques  Giffard  in  1858. 

In  its  most  simple  form  (see  Fig.  300)  it  consists  of  a  steam- 
nozzle,  the  end  of  which  extends  somewhat  into  a  chamber 
or  converging  tube  called  the  combining  or  suction-tube  ;  this 

*See  Cassier's  Magazine,  January  and  February,  1892  ;  Thermodynamics, 
by  D.  Wood,  page  279  ;  Thermodynamics,  by  C.  H.  Peabody,  page  152. 

670 


§439-]        THE   STEAM-INJECTOR— THE  PULSOMETER.          6/1 

connects  with,  or  rather  terminates  in,  a  third  nozzle  or  tube, 
A  (Fig.  300),  termed  the  "  forcer."  At  the  end  of  the  combin 
ing  tube,  and  before  entering  the  forcer,  is  an  opening  connect- 
ing  the  interior  of  the  nozzle  at  this  point  with  the  surrounding 
area.  This  area  is  separated  from  the  outside  air  by  a  check- 
valve,  E,  opening  outward  in  the  automatic  injectors,  and  by  a 
globe  valve  termed  the  overflow-valve  in  the  non-automatic 
injector.  The  injector-nozzles  are  tubes  with  ends  rounded  to 
conform  to  the  form  of  the  "  vena  contracta  "  as  nearly  as  pos- 
sible, and  thus  receive  and  deliver  the  fluids  with  the  least  pos- 
sible loss  by  friction  and  eddies. 

Some  of  the   injectors  are  quite  complicated,  and  adjust 


FIG.  301. — THE  SELLERS  INJECTOR. 

themselves  automatically  by  varying  the  openings  through  the 
tubes  to  suit  changes  in  steam-pressure. 

Fig.  301  is  a  section  of  the  Sellers  injector  of  1876;  in  this 
injector  the  steam-nozzle  C  can  be  inserted  a  greater  or  less 
distance,  as  required,  into  the  combining-chamber  NN.  The 
overflow  P  is  closed  by  a  valve  K  operated  by  a  rod  L  con- 
nected to  the  starting-lever  T.  The  tube  NNCO  moves 


672 


EXPERIMENTAL  ENGINEERING. 


[§  440- 


automatically  to  vary  the  opening  at  C  with  change  of  steam- 
pressure. 

In  some  of  the  injectors  the  tubes  are  so  arranged  that  the 
discharge  of  one  injector  is  made  the  feed  for  a  second  injector. 
This  makes  what  is  termed  a  double  injector,  of  which  familiar 
illustrations  are  to  be  seen  in  the  Hancock,  Park,  and  World 
injectors. 


FIG.  302.— THE  HANCOCK  INSPIRATOR. 

440.   Thermodynamic  Theory  of  the  Steam-injector. — 

As  a  thermodynamic  maphine  the   injector  is  nearly  perfect, 
since  all  the  heat  received  by  it  is  returned  to  the  boiler,  ex- 


§440-]        THE   STEAM-INJECTOR—  THE  PULSOMETER.          673 

cepting  a  very  small  part  that  is  lost  by  radiation;  conse- 
quently the  thermal  efficiency  should  be  in  every  case  nearly 
IOC  per  cent.  Its  mechanical  efficiency,  or  work  done  in  lifting 
water,  compared  with  the  heat  expended,  is  small,  because  its 
heat-energy  is  principally  used  in  warming  up  the  cold  water 
as  it  enters  the  injector. 

Let  r  equal  the  heat  of  evaporation  in  B.  T.  U.  of  a  pound 
of  dry  steam  ;  x,  its  quality  ;  q,  heat  of  the  liquid  of  the 
entering  steam  in  thermal  units  above  32°  ;  q^  ,  heat  of  dis- 
charge-water in  thermal  units  above  32°  ;  h,  the  total'  heat  in 
a  pound  of  wet  steam  ;  w,  the  weight  of  steam  per  hour 
uncorrected  for  calorimeter-determinations  ;  W,  the  weight  of 
water  supplied  ;  /,  the  temperature  of  the  feed-water  ;  /',  the 
temperature  of  the  delivery.  Then  we  have,  as  the  heat  in 
one  pound  of  the  steam  supplied,  above  32°, 


(I) 


If  the  mechanical  work  consist  of  W  pounds  of  water  lifted  n 
feet  by  pressure  and  s  feet  by  suction,  the  heat  equivalent  F 
of  the  mechanical  work  is 


(2) 


if  delivered  from  the  end  of  the  discharge-pipe  without  sensible 
velocity.  In  case  there  is  a  velocity  of  z/,  feet  per  second  at 
delivery  from  discharge-pipe,  the  additional  energy  L,  in  heat- 
units,  is 

)v?  +  2g.     .....    (3) 


The  heat-units  taken  up  by  the  feed-water  are 

K=  W(tf  -t)  .........    (4) 

The  thermal  efficiency  E,  if  the  injector  is  used  for  feeding 
Boilers,  is 


w(h  -  q, 


6/4  EXPERIMENTAL  ENGINEERING.  [§44^ 

If  used  as  a  pump,  the  heat  K  received  by  the  discharge-water 
is  to  be  neglected,  and  the  efficiency  Et  is 


F+L 


441.  Mechanical  Action  of  the  Injector.  —  In  this  case  we 
consider  only  the  impact  of  the  jet  of  steam  at  high  velocity 
against  the  mass  of  water.  The  case  being  similar  to  that  of 
a  small  inelastic  ball,  moving  at  high  velocity,  impinging  on  a 
large  ball. 

Denote  the  velocity  of  the  steam  by  vt  that  of  the  water 
before  impact  by  F,,  and  after  impact  by  F;  then  by  the 
principles  of  impact  of  inelastic  bodies, 


wv  . 

7" 


When  water  is  supplied  the  injector  under  pressure,  the 
sign  of  F,  is  positive,  otherwise  it  is  negative.  The  use  of 
this  equation  requires  the  velocity  of  the  steam,  v\  that  of  the 
supply,  Vl  ;  and  of  the  discharge,  F,  to  be  given. 

The  velocity  of  the  steam,  v,  will  not  differ  essentially  from 
1400  feet  per  second  for  the  conditions  in  which  it  is  used  in 
the  injector  (see  Article  230,  page  301). 

The  velocity  of  the  water  discharged,  F,  from  the  injector 
may  be  found  by  dividing  the  volume  that  is  delivered  in  cubic 
feet  per  second,  c,  by  the  area  of  the  discharge  in  square  feet, 
A  ;  that  is, 

----^-       I44-    C  ' 
~ 


in  which  C  represents  the  discharge  in  cubic  feet  per  hour,  and 
<a  the  area  of  the  discharge-nozzle  in  square  inches. 


§441-]        THE   STEAM-INJECTOR-THE  PULSOMETER.          6? $ 

.  The  velocity  of  the  water  supplied,  V\ ,  in  the  suction-pipe 
maybe  found  by  ascertaining  the  equivalent  head,  n1 ,  that  will 
produce  the  same  velocity.  If/  be  the  absolute  pressure  per 
square  inch  in  the  combining-chamber ;  b,  the  pressure  per 
square  inch,  as  shown  by  a  barometer  or  pressure-gauge,  on 
the  water-supply ;  w" ,  the  weight  of  a  cubic  foot  of  water  at  the 
temperature  of  the  supply  ;  s,  the  suction-head  in  feet, — then 

_  1440 -/) 


V,  =  \/2gnl. 

The  velocity  of  the  suction  is,  however,  expressed  more  con* 
veniently  by  considering  a  body  of  water  with  a  head,  s,  acting 
to  accelerate  or  retard  the  whole  mass  of  water  in  the  injector. 
Let  A  be  the  smallest  section  of  the  water-jet,  w"  the  weight 
of  a  unit  of  water  ;  then  the  pressure  due  to  s  feet  of  water 
will  be  saw"  .  As  this  acts  on  a  mass  of  water  Vaw"  -j-  g,  the 
velocity  imparted  would  be 

saw"  _sg 


The  total  momentum  produced  by  the  suction  would  be 


.    (10) 

w  I  v  v 

in  which 

y  =  W-r-  W. 

The  momentum  produced  by  the  suction  would  be  negative, 
jnless  water  was  delivered  to  the  injector  under  pressure. 
As  shown  in  equation  (7)  the  momentum  of  the  suction  is 

wv  w  v,      F; 

--  -,  which  for  one  pound  of  steam  would  be  —  --  =y~- 


6/6  EXPERIMENTAL  ENGINEERING.  [§442. 

Substitute   this   value  for  the  momentum  of  the  suction  in 
equation  (7),  representing  W  -i-  w  by  y.     We  have 


or 


From  which 


The  plus  sign  to  be  employed  before  s  when  the  suction- 
water  is  supplied  under  pressure  ;  otherwise  the  negative  sign  is 
to  be  used. 

If  the  friction  in  the  pipe  be  neglected, 


and  we  have 

v 


-i (13) 


2gn  —  sg 

442.  Ltmftsof  the  Injector.—  Maximum  Amount  of  Water 
Lifted.  —  This  may  be  obtained  from  equation  (12)  or  (13),  but 
it  can  be  obtained  with  sufficient  accuracy  by  neglecting  the 

WV 
momentum  --  due  to  the  suction-water  in  equation  (7)  ;  in 

o 

this  case 


from  which 

W       v  v  1400 


§442.]        THE   STEAM-INJECTOR— THE  PULSOMETER.          6/7 

The  maximum  ratio  of  water  to  steam  is  shown  by  the  fol- 
lowing table : 


Delivery  Pressure 
above  that  on 
Injector. 

Maximum  Ratio 
of  Water  to 
Steam  by  Weight. 

Delivery  Pressure 
above  that  on  the 
Injector. 

Maximum  Ratio 
of  Water  to 
Steam  by  Weight. 

10 

36.5 

55 

15.5 

15 

29.8 

60 

14.7 

20 

25.6 

65 

14-3 

25 

23.8 

70 

13.7 

30 

20.9 

75 

13-3 

35 

19-5 

80 

12.9 

40 

17.87 

85 

12.6 

45 

17.0 

90 

12.  1 

50 

16.2 

IOO 

11,5 

I 

The  minimum  amount  of  water  required  must  be  sufficient 
to  condense  the  steam,  in  which  case 


w 


t' - 


05) 


in  which  k  is  the  heat  in  one  pound  of  entering  steam ;  q^ ,  the 
heat  of  the  liquid  in  the  delivery,  both  reckoned  from  32° ;  /', 
the  temperature  of  the  delivery ;  /,  that  of  the  feed-water,  so 
that  the  ratio  cannot  be  greater  than  shown  in  equation  (14) 
nor  less  than  that  shown  in  equation  (15). 

Temperature  of  Feed-water. — As  the  temperature  of  the 
feed-water  increases  vapor  is  given  off  which  increases  the 
pressure,  by  in  equation  (9)  on  the  surface  of  the  supply-water, 
and  reduces  the  height  through  which  the  water  can  be  lifted. 

If  the  temperature  of  the  feed-water  is  greater,  the  amount 
required  to  condense  the  steam  must  also  be  greater;  but  as 
the  amount  lifted  by  a  given  amount  of  steam  cannot  exceed 
the  approximate  value  given  in  equation  (14),  we  shall  have  at 
the  extreme  limit  at  which  the  injector  works,  the  values  of  y 
as  given  in  equations  14  and  15  equal  to  each  other,  from 
which  the  maximum  temperature  of  feed-water  becomes 


v-  V 


1400  -  \/2gn 


,  nearly. 


6;8 


EXPERIMENTAL   ENGINEERING. 


[§  442. 


The  following  table  gives  approximately  the  limiting  values 
of  suction-head  in  feet  and  temperature  of  feed-water : 


LIMIT  OF  SUCTION-HEAD   IN   FEET. 


Steam-pressure  100  Ibs.  Absolute. 

Temperature 
of  Feed-water. 
Degs.  Fahr. 

Pressure  of 
Vapor.  Pounds 
per  sq.  inch. 

Limit  of  Suction- 
head  in  case  of 
Vacuum.    Feet. 

Delivery  212°  Fahr. 
Number  of  Pounds 
of  Water  to  con- 

Delivery 180°  Fahr. 
Number  of  Pounds 
of  Water  to  con- 

dense one  of  Steam. 

dense  one  of  Steam. 

70 

80 

0.36 
0.50 

32.96 
32.6 

7.04 

7-57 

8.81 
9.61 

90 

0.69 

32.2 

8.19 

10.76 

100 

0.94 

31.4 

8.92 

12.  II 

no 

1.26 

30.9 

9.80 

13.84 

120 

1.6* 

29.7 

10.87 

16.15 

130 

2.22 

27-3 

12.  2O 

19.32 

I40 

2.87 

25-9 

13.89 

24.22 

150 

3-70 

24.8 

I6.I3 

32.3 

160 

4.72 

22.5 

19.23 

48.45 

170 

5.98 

19.6 

23.81 

96.90 

1  80 

7-50 

16.9 

3I-25 

190 

9-33 

9.9 

45.46 

200 

11.52 

9-3 

83.33 

210 

14.12 

i.r 

500.9 

MAXIMUM  TEMPERATURE  FEED-WATER. 


Gauge  Press- 

Maximum Temperature  of 
Feed-water.    Degrees  Fahr. 

Gauge  Press- 

Maximum Temperature  of 
Feed-wat;er.    Degrees  Fahr. 

ure.    Pounds 
per  sq.  inch. 

Discharge 
180°  Fahr. 

Discharge 
212°  Fahr. 

ure.    Pounds 
per  sq.  inch. 

Discharge 
i3o°  Fahr. 

Discharge 
212°  Fahr. 

20 

142 

173 

70 

I09 

139 

25 

137 

168 

75 

107 

137 

30 

133 

164 

80 

'05 

134 

35 

1  60 

90 

99 

129 

40 

126 

156 

100 

95 

125 

45 

123 

153 

110 

9i 

121 

50 

120 

150 

120 

87 

117 

55 

117 

147 

130 

83 

"3 

60 

114 

144 

140 

80 

no 

65 

III 

141 

150 

77 

107 

§444-]        THE   STEAM-INJECTOR-THE  PULSOMETER.          679 

A  series  of  carefully  conducted  experiments*  made  at  Sib- 
ley  College,  Cornell  University,  to  determine  the  efficiencies  of 
different  steam  injectors,  confirm  the  results  expressed  in  the 
preceding  computations. 

443.  Directions  for  Handling  and  Setting  Injectors.— 
Injectors  are  of  two  general  classes,  lifting  and  non-lifting.     In 
the  first  class  water  is  drawn  in  by  suction  and  then  discharged 
against  a  pressure ;   in  the  second  class  water  flows  in  under 
pressure  and  is  discharged  against  a  greater  pressure. 

As  there  is  a  limit  to  the  temperature  at  which  water  will 
be  handled  by  the  injector,  variations  in  steam-pressure  will 
affect  the  discharge  and  may  cause  it  to  stop  altogether.  This 
may  be  regulated  to  a  certain  extent  by  manipulating  the 
valves  of  the  steam  and  water  supply ;  some  injectors  are  self- 
adjusting  in  this  respect  and  are  termed  automatic. 

The  general  directions  for  starting  an  injector  are  to  open 
the  overflow,  turn  on  steam  until  the  water  appears  at  the 
overflow,  and  the  temperature  of  the  injector  is  sufficiently  low 
to  condense  the  steam.  Then  close  the  overflow  and  the -in- 
jector  should  discharge  against  a  pressure  equal  to  or  greater 
than  the  steam-pressure.  In  many  of  the  injectors  the  over- 
flow valve  will  open  whenever  the  pressure  in  the  injector 
becomes  greater  than  that  of  the  atmosphere.  In  several 
kinds  the  overflow  is  closed  by  a  valve  regulated  independ- 
ently or  connected  by  a  lever  to  the  starting  handle  so  as  to 
be  opened  and  closed  at  the  proper  time  by  the  simple  opera- 
tion of  admitting  steam. 

Injectors  will  not  work  with  oily  or  dirty  water,  and  are 
liable  to  be  stopped  by  anything  that  will  not  pass  the  nozzles. 
In  general  they  are  to  be  connected  by  pipe-fittings  made  up 
without  red  lead  and  arranged  so  as  to  deliver  water  into  a 
pipe  leading  to  the  boiler,  in  which  is  placed  a  check-valve  to 
remove  the  boiler-pressure  when  starting  the  injector. 

444.  Directions  for   Testing.— For  testing  the  injector 
use  two  tanks,  both  of  which  are  to  rest  on  weighing-scales. 

*  See  Cassier's  Magazine,  Feb.  1892. 


680  EXPERIMENTAL  ENGINEERING.  [§  444 

Fill  one  of  the  tanks  with  water,  and  locate  the  injector  any 
convenient  distance  above  or  below  this  tank,  and  arrange  it 
sc  as  to  deliver  water  into  the  second  tank. 

If  the  water  that  escapes  at  the  overflow  is  arranged  to  run 
into  the  tank  from  which  the  water  is  taken,  no  correction  will 
be  required  ;  otherwise  it  must  be  caught  and  weighed. 

Place  a  valve  in  the  delivery-pipe,  some  distance  from  the 
injector  or  beyond  an  air-chamber,  and  regulate  the  delivery 
head  by  partly  opening  or  dosing  this  valve.  The  delivery, 
pressure,  which  can  be  reduced  to  head  in  feet  of  water,  can  be 
measured  by  a  pressure-gauge  in  the  delivery-pipe  ;  the  suction- 
pressure  is  observed  in  a  similar  manner  by  using  a  vacuum- 
gauge  or  a  manometer. 

The  water  received,  W,  is  that  taken  from  the  first  tank ; 
the  amount  delivered,  W -\-  w,  is  that  weighed  in  the  second 
tank ;  the  difference  is  w,  the  steam  used. 

Arrange  thermometers  to  take  the  temperature  of  the 
water  as  it  enters  and  leaves  the  injector. 

-Make  runs  with  discharge-pressures  equal  respectively  to 
one-fourth,  one-half,  three-fourths,  once,  and  one  and  one- 
fourth  times  that  on  the  boiler.  During  each  run  take  obser- 
vations, as  required  by  the  blank  log  furnished,  once  in  two 
minutes. 

Determine  the  limits  at  which  the  injector  stops  working, 
for  temperature  of  feed-water,  suction-head  and  delivery-head. 

Careful  trials  show  that  the  thermodynamic  efficiency  of 
any  injector  is  100  per  cent ;  by  assuming  this  as  true  the  sec- 
ond tank  may  be  dispensed  with,  and  the  amount  of  steam 
computed  from  its  heating  effect  and  known  quality  on  the 
water  passing  through  the  injector. 

In  the  report,  describe  the  injector  tested,  explain  method 
of  action,  and  submit  a  graphical  log,  with  time  as  abscissa,  as 
well  as  an  efficiency  curve  for  varying  pressures  of  discharge, 
also  for  varying  temperatures  of  discharge. 

Fill  out  the  log  and  make  complete  report,  after  the  stand- 
ard form. 


§445-]        THE   STEAM-INJECTOR— THE  PULSOMETER.          68 1 

445.  Form  for  Data  and  Results  of  Injector-test 


£ 

Corrected. 

1 
!    : 

0) 

> 
«< 

1 

M 

J~ 

t? 

o 

Jf 

.- 

CO 

0       £ 

H 

}                 rt        •> 

S 

!             Q     <o 

•c 

0 

1      « 

0. 

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00 

H 

cJ          c/) 

»• 

.5      ?i       w 
Q     <       H 

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fa 
O 

« 

j 

O 

* 

S 

eo 

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H 

to 

C 

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'o 

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S             Ctf 

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]-       ii 

S, 

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C          o         S 

J       »-i        rt        w 

*3        c 

i       III 

«               S      Q      < 

S 

tftiiffil 

jMhain 

If  11  1-1  1  ill 

Temperature  of  room 
Water  supplied  
Water  delivered  
Time  of  ending  
Duration  of  run  
Barometer-gauge,  inc 

682 


EXPERIMENTAL   ENGINEERING. 


[§445- 


"> 


+      -f 

*    *! 


i  * 

* 

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:        :         :        : 

v    H' 

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j-£ 

:      a      t> 

£  "" 

H 

cc 

H 

1      1     !     *     « 

H     g 

oT 

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11^ 
u 


X 


a 


a   >    J 

111 

Wi        Wi        u 


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a.  o  > 


§446-]        THE   STEAM-INJECTOR— THE  PULSOMETER.          683 

446.  The  Pulsometer. — This  is  a  pump  consisting  of  two 
bottle-shaped  cylinders  joined  together  with  tapering  necks, 
into  which  a  ball  C  is  fitted  so  as  to  move  in  the  direction  of 
least  pressure,  with  a  slight  rolling  motion,  between  seats  formed 
in  the  passages.  These  chambers  connect  by  means  of  open, 
ings  fitted  with  clack-valves,  E  E,  into 
the  induction-chamber  D. 

The  water  is  delivered  through 
the  passage  H,  which  is  connected  to 
the  chamber  by  openings  fitted  with 
valves  G.  Between  the  chambers  is 
a  vacuum-chamber  J  which  connects 
with  the  in'duction-passage  D.  Air  is 
supplied  the  chambers  by  small  air- 
valves  moving  inward,  which  open 
when  the  pressure  is  less  than  atmos- 
pheric. 

The  method  of  working  is  as  fol- 
lows :  Conceive  the  left  chamber  full  FlG-  SOS.-THE  PULSOMETER. 
of  water,  and  a  vacuum  in  the  right  chamber ;  steam  enters 
to  the  left  of  the  valve  C,  presses  directly  on  the  surface  of  the 
water,  and  forces  it  past  the  check-valve  G  into  the  delivery- 
passage  H  and  air-chamber  J\  at  the  same  time  the  right 
chamber  is  filling  with  water,  which  rushes  in  and  by  its 
momentum  moves  the  valve  C  to  the  left.  The  steam. in  the 
left  chamber  condenses,  forming  a  vacuum,  and  the  operation 
described  is  repeated,  except  that  the  conditions  in  the  two 
chambers  are  reversed. 

All  the  steam  entering  is  condensed  and  forced  out  irith 
the  water,  increasing  its  temperature. 

The  analysis  is  very  similar  to  that  of  the  injector,  except 
that  the  steam  acts  by  pressure  instead  of  by  impact.  The 
theory  is  fully  stated  in  "  Thermodynamics,"  by  Prof.  De  Volson 
Wood,  page  293.  Thus:  if  w  equal  the  weight  of  steam,  W 
the  weight  of  water  raised,  /  the  temperature  of  the  supply,  /, 
that  of  the  delivery,  r  the  latent  heat  of  evaporation  r»f  the 


684 


EXPERIMENTAL   ENGINEERING. 


[§  447- 


steam,  T  the  temperature  of  the  steam,  n  the  delivery-head, 
n,  the  suction-head,  n  +  nl  the  total  head,—  no  allowance  being 
made  for  variation,  —  we  have 


The  heat  equivalent  of  the  mechanical  work  done, 


The  heat  expended,  in  thermal  units, 


The  efficiency, 


U 

~~  h  ~~ 


w(T-t-\-r) 
Neglecting  the  work  of  lifting  the  condensed  steam, 


E  =  - 


-—  ,  nearly. 


* 

The  following  form  for  data  and  results  of  test  is  used  by 
the  Massachusetts  Institute  of  Technology  : 

447.  Form  for  Data  and  Results  of  Test  on  Pulsometer. 

No  ............  Date  .......  .  .........  189.. 


I 
a 

s 

fc 

Total 
Av... 

8 

H 

Flow  of  Steam. 

Water. 

Heads. 

Calorimeter. 

Counter 

j  Boiler-pressure. 

1 

<u 

1 

'vn 
0 

Pressure  at  Pulsom- 
eter. 

Temp,  at  Pulsometer. 

Depth  on  Weir  in  Ins. 

(Depth  on  Weir)^' 

Q 

3 
^ 

rtfc 

ai 
ga 

iS 

a 
o 

u 
3 
C/5     . 

cfc 

sd! 

_w   0£ 

Temp,  of  Discharge, 
Degrees  F. 

Suction-gauge,  Ins.  of 
Hg. 

Discharge-gauge,  Lbs. 
per  Sq.  In. 

Actual  Suction,  in  Ft. 

Actual  Head,  in  Ft. 

u 

3 

6 
a 

V 

1 

Calorimeter-pressure. 

fc 

ex 

1 

Reading. 

Difference. 

y 

Cor.. 

§447-]        THE   STEAM-INJECTOR— THE  PULSOMETER.          685 

Diameter  suction  and  discharge  pipes „ ms> 

Transverse  area  of  pipe Sq,  f t. 

Distance  between  pressure-gauges ft. 

Barometer  (cor.). ins.;     Ibs 

Number  of  pulses  per  minute 

Width  of  weir.   ft.     Area  steam-orifice sq.  ft. 

Steam  used  in mins Ibs. 

Water  over  weir  in  , mins Ibs. 

Head  due  to  velocity  in  discharge-pipe ft. 

Total  lift  =  pressure-heads  -f-  velocity-head  -f-  distance  between  gauges ft. 

Total  work  done  by  pulsometer ft.-lbs.;     B.  T.  U. 

Total  heat  given  up  by  steam.  .* B.  T.  U. 

Efficiency per  cent. 

Duty  (ft.  Ibs.  per  1,000,000  B.  T.  U.) 


CHAPTER  XXH. 

THE   STEAM-TURBINE. 

448.  General  Principles  of  Operation. — The  steam-turbine 
has  come  into  extensive  commercial  use  for  the  production  of 
power  during  the  last  five  years,  and  for  that  reason  its  theory 
and  economic  operation  are  matters  of  considerable  importance. 

The  steam-turbine  is  defined  by  Neilson  as  a  machine  in 
which  a  rotary  motion  is  obtained  by  the  gradual  change  of 
momentum  of  the  working  fluid. 

As  constructed,  the  steam-turbine  consists  essentially  of  a 
rotating  part  carrying  buckets  against  which  the  steam  acts 
either  by  pressure  or  impulse  or  both,  as  with  water-turbines  as 
described  on  p.  316.  The  energy  of  the  moving  mass  of  steam 
is  taken  up  by  the  rotating  part  and  utilized  to  drive  machinery. 

Dry  steam  if  expanded  adiabatically,  and  without  doing  work 
on  anything  but  itself,  through  a  divergent  nozzle  or  one  which 
does  not  interfere  with  its  lateral  expansion,  will  convert  all  the 
energy  disappearing  into  velocity.  If  Q  represent  the  heat  per 
pound  of  entering,  qi  that  of  the  discharge  steam,  and  A  —  778,  the 
velocity  produced  may  be  calculated  from  the  formula 

F2 

~ 

As  an  example,  for  the  condition  in  which  the  steam  enters  at 
an  absolute  pressure  of  285  pounds  and  is  discharged  at  0.6 
pounds  absolute,  the  velocity  of  the  steam  calculated  from  the 

686 


§  449-]  THE   STEAM-TURBINE.  68/ 

preceding  formula  would  be  4370  feet  per  second.  The  cir- 
cumference of  the  rotating  part  should  move  about  one  half 
that  of  the  current  of  the  steam  which  impinges  on  it,  if  the 
steam  act  on  a  single  row  of  buckets,  in  order  that  it  may  be 
discharged  with  the  least  velocity  and  consequently  with  the 
least  energy,  which  is  a  condition  of  maximum  efficiency.  If, 
however,  there  are  a  number  of  rows  of  buckets  on  the  moving 
part  which  alternate  with  rows  of  fixed  buckets  on  the  stationary 
part  of  such  shape  as  to  deflect  the  current  of  steam  in  a  direc- 
tion to  propel  the  wheel  at  highest  velocity,  the  circumference 
of  the  rotating  part  may  move  much  slower  than  one  half  the 
velocity  of  the  current  of  steam  flowing  at  a  rate  which  produces 
maximum  efficiency. 

The  steam-turbines  of  all  types  show  a  greater  gain  due 
to  superheated  steam  than  does  the  ordinary  steam-engine;  the 
Parsons  turbine  showing  an  increase  in  efficiency  of  about  i  per 
cent,  due  to  an  increase  of  superheat  of  8  or  9  degrees  up  to  at 
least  200°  superheat.  For  best  results  the  steam-turbines  also 
require  a  high  vacuum,  and  the  specifications  for  steam-turbine 
installations  generally  require  a  high  vacuum  and  a  considerable 
degree  of  superheat. 

A  large  number  of  different  types  of  steam-turbines  *  have  been 
produced  and  many  are  in  successful  commercial  use,  but  the 
limits  of  available  space  for  this  work  permit  the  consideration 
of  only  two  or  three  types  in  a  brief  manner. 

449.  Steam-turbine  of  the  Impulse  Type. — The  De  Laval 
steam-turbine  is  an  example  of  the  impulse  type.  In  this  turbine 
a  single  wheel  carrying  a  row  of  buckets  near  its  periphery  is 
acted  upon  by  one  or  more  jets  of  steam  which  are  conveyed 
to  the  wheel  through  one  or  more  expanding  nozzles.  (See  Fig. 
304.)  The  wheel  revolves  in  a  case  which  is  maintained  at  the 
pressure  of  the  exhaust  so  that  the  steam  expands  very  nearly 
adiabatically  from  the  steam  pressure  to  the  exhaust  pressure  in 
the  diverging  nozzle,  and  before  coming  in  contact  with  the 


*  See  Steam-turbines  by  Prof.  Carl  Thomas.     New  York,  John  Wiley  &  Sons. 


688 


EXPERIMEN TA  L  ENGINEERING. 


[§449- 


buckets  of  the  wheel.     This  velocity  frequently  reaches  4000  feet 
per  second. 

The  De  Laval  turbine,  with  steam  entering  at  4000  feet  per 
second  and  with  the  nozzle  set  at  an  angle  of  20°  to  the  plane  of 


FIG.  304.— THE  DE  LAVAL  TURBINE  WHEEL  AND  NOZZLES. 

motion  of  the  buckets,  should  have  theoretically  a  peripheral 
velocity  for  maximum  efficiency  equal  to  about  47  per  cent  of  the 
velocity  of  the  steam.  The  velocity  of  discharge  for  that  condi- 


FIG.  305.— SECTIONAL  PLAN  OF  THE  DE  LAVAL  TURBINE  GENERATOR. 

tion  it  is  claimed  is  34  per  cent  of  the  initial  velocity,  and  the 
energy  absorbed  by  the  turbine  wheel  is  theoretically  88  per  cent 
of  that  expended,  making  the  steam  consumption  per  theoret- 
ical horse-power  9.1  pounds  per  hour. 


§45°-]  THE  STEAM-TURBINE.  689 

Theoretically  the  peripheral  speed  of  the  De  Laval  turbine 
for  highest  efficiency  should  be  about  1880  feet  per  second,  but 
practically  it  is  generally  operated  at  1350  feet  per  second,  for 
best  results,  giving  a  horse-power  for  a  theoretical  steam  con- 
sumption of  9.8  pounds  per  hour.  On  account  of  the  high  velocity 
of  the  steam-wheel  of  the  De  Laval  turbine,  it  is  necessary  in 
applying  the  power  to  use  a  reducing-gear  to  lessen  the  speed  of 
rotation.  The  diagram  Fig.  305  shows  a  plan,  partly  in  sec- 
tion, of  the  De  Laval  turbine  with  the  steam- wheel  near  A,  the 
reducing-gear  wheels  J  and  L,  and  couplings  at  M,  which  may 
connect  it  to  a  generator  or  other  machine  which  may  be  driven 
at  a  high  rotative  speed. 

450.  Steam-turbine  of  the  Reaction  Type. — The  Parsons 
steam-turbine,  shown  in  Fig.  307  in  section,  is  an  excellent  illus- 
tration of  a  machine  of  the  reaction  type.  In  this  turbine  the 
rotating  part  consists  of  a  steel  drum  which  carries  numerous 
rows  of  blades  which  move  between  stationary  rows  of  blades 
supported  by  the  casing  surrounding  the  rotating  part. 

The  general  arrangement  of  the  blades  is  shown  in  Fig.  306. 
The  steam  is  deflected  by  the  stationary  blades,  P,  so  as  to  strike 


ry  Blades 
Moving  Blades 
ary  Blades 
Moving  Blades 


FIG.  306. — BLADES  OF  THE  PARSONS  TURBINE. 

the  moving  blades,  PI,  at  the  most  effective  angle,  thence  the 
steam  is  deflected  to  a  row  of  stationary  blades  and  thence  again 
to  a  row  of  moving  blades  as  shown  by  the  arrows.  Steam 
enters  at  A  (Fig.  307)  and  passes  in  succession  through  the 
various  rows  of  buckets  on  the  parts  F,  G,  H,  and  K.  The  last 
series  of  buckets  are  on  an  enlarged  portion  of  the  drum,  O,  which 
increases  the  volume  and  produces  great  expansion.  From  the 
rotating  part  it  passes  into  the  chamber,  B,  connected  with  the 
condenser. 


690 


EXPERIMENTAL   ENGINEERING. 


451, 


To  take  the  lateral  thrust  off  the  bearings,  pistons  or  rotating 
collars,  P,  are  arranged  so  as  to  receive  the  steam  pressure  and 
balance  the  thrust. 

The  turbine  is  provided  with  a  governor,  L,  which  acts  to 
turn  the  steam  entirely  on  or  off  as  may  be  necessary  to  maintain 
constant  speed. 

The  driving-shaft  is  extended  for  direct  connection  for  an 


FIG.  307. — PARSONS  STEAM-TURBINE. 

electrical  generator  for  which  the  power  generated  by  the  turbine 
is  generally  used.  The  Parsons'  steam-turbine  is  built  by  the 
Westinghouse  Machine  Co.  and  by  the  Allis- Chalmers  Co. 

451.  Steam-turbine  of  Combined  Reaction  and  Impulse 
Type. — The  Curtis  turbine  as  built  by  the  General  Electric 
Co.  is  a  good  illustration  of  a  combined  impulse  and  reaction 
turbine. 

In  this  turbine  the  steam  passes  through  a  set  of  nozzles 
arranged  in  multiple;  it  then  strikes  the  first  row  of  blades, 
after  which  it  reacts  on  alternate  rows  of  moving  and  stationary 
blades  as  in  the  Parsons  turbine.  The  general  arrangement 
of  the  buckets  in  this  turbine  appears  in  Fig.  308,  which  shows 
the  valves  connecting  the  steam-chest  with  the  supply  nozzles, 
the  development  of  moving  and  stationary  blades,  and  the  nozzle 
diaphragm  through  which  the  steam  flows  against  another  set 
of  moving  blades  on  a  wheel  of  larger  diameter. 


§452.] 


THE  STEAM-TURBINE, 


69I 


The  number  of  stages  may  be  made  as  great  as  necessary, 
there  usually  being  four  stages  in  large  wheels. 

The  large-size  Curtis  turbines  are  made  of  vertical  form 
with  a  generator  above  the  turbine  and  carried  on  the  same 
vertical  shaft,  being  supported  below  by  a  rotating  collar  resting 
on  oil  or  water  under  pressure.  The  general  arrangement  is 
shown  in  Fig.  309,  the  generator  being  at  G,  the  turbine  at  T. 
The  steam-pipe  is  connected  at  S,  the  exhaust-pipe  at  E. 


Nozzle  ^ 

Moving  Blade* 
Stationary  Blades 
Moving  Blades     ! 
Stationary  Blades 
Moving  Blades 


Nozzle  Diaphragm 


Moving  Blades 
Stationary  Blades 
•  Moving  Blades 
Stationary  Blades  I 


i«j 

Moving  Blades    fM  D  BD  D  D@  D  DM)  D  D  M  Dl>  B  ^ 

i   I    I    I     I     I 

FIG.  308. — NOZZLES  AND  BUCKETS,  CURTIS 
TURBINE. 


FIG.  309. — THE  CURTIS  TURBO- 
GENERATOR. 


452.  Testing  of  Steam-turbines. — Since  there  is  a  continu- 
ous flow  of  steam  through  the  steam-turbine,  at  a  uniform  pressure 
and  temperature  for  any  one  condition,  there  is  no  opportunity 
for  taking  a  diagram  similar  to  the  indicator  card,  and  conse- 
quently there  is  no  means  for  measuring  the  mechanical  work 
done  by  the  entering  steam  on  the  rotating  part. 

There  may  be,  however,  if  the  construction  warrants,  an 
opportunity  of  measuring  the  temperature  and  pressure  at  the 


692  EXPERIMENTAL   ENGINEERING.  [§453- 

various  stages  in  a  multiple-stage  turbine,  and  these  quantities 
if  possible  should  be  observed. 

Most  of  the  steam-turbines  are  constructed  for  direct  con- 
nection to  an  electrical  generator,  and  as  usually  built  do  not 
permit  the  attachment  of  intermediate  thermometers  and  pressure- 
gauges.  The  test  for  that  reason  must  generally  consist  in  the 
measurement  of  the  total  steam  and  heat  supplied  and  the  work 
done  by  the  generator.  This  latter  is  measured  by  means  of 
various  electrical  instruments.  If  the  efficiency  of  the  generator 
is  known,  the  work  delivered  (D.H.P.)  from  the  turbine  can 
be  computed. 

From  the  heat  input  and  the  electrical  output  measured  as 
described  the  efficiency  can  be  computed  on  the  basis  of  delivered 
or  electrical  horse-power.  The  heat  (B.T.U.)  per  electrical  or. 
delivered  horse-power  supplied  per  minute  can  also  be  computed. 
These  quantities  are  usually  sufficient  for  all  commercial  require- 
ments and  serve  for  a  comparison  of  the  results  obtained  with 
those  of  reciprocating  engines,  which  are  already  well  known 
from  numerous  tests. 

453.  Log-sheets. — A  log-sheet  which  suggests  quantities  to 
be  observed  and  results  to  be  computed  in  the  test  of  a  steam- 
turbine  directly  connected  to  an  electrical  generator  is  printed  on 
the  following  page.  The  input  H.P.  is  computed  by  adding  all 
generator  losses,  reduced  to  horse-power  units,  to  the  output 
H.P.  computed  from  the  K.W.  The  thermodynamic  efficiency 
is  the  ratio  of  the  difference  of  temperature  of  steam  centering 
and  discharging,  divided  by  the  absolute  temperature  of  the 
entering  steam.  The  thermal  efficiency  is  the  ratio  of  the  work, 
expressed  in  thermal  units,  AW,  to  the  total  heat  supplied,  Q. 
A  perfect  engine  is  assumed  to  be  one  that  converts  the  differ- 
ence between  the  heat  entering,  Q,  and  that  discharging,  q,  into 
work. 


§453-1  THE   STEAM-TURBINE.  693 

REPORT  OF  DIRECT-CONNECTED  STEAM-TURBINE  TEST. 

Made  by Dale 

Kind  of  Turbine Mfg.  by 


Duration  of  run  .....................  Hours 

Revolutions  per  minute 
Temperature  of  condensing  water  cold 
Temperature  of  condensing  water  warm 
Temperature  of  condensed  steam 
Temperature  of  the  engine-room  ............ 

Steam-chest  pressure-gauge 

Barometer  ...................  inches  Hg 

Condenser  pressure  ...........     "       " 

Boiling  temp.     Exh.  pressure 

Total  steam  per  hr.  condensed  ...............  Ibs 

Total  condensing  water  per  hr  ...............  " 

Wt.  condensing  water  per  Ib.  steam  ...........  " 

Total  heat  supplied  ..............  B.T.U.  —  Q 

Total  heat  exhausted  .............     "       —  q 


Amperes  .....................................  L 

Series-field  heat  loss  ..........  .  .................  'V-. 


Shunt-field  heat  loss 

Armature  heat  loss 

Iron  and  friction  loss 

K.W.  hrs.  useful  output 

Total  generator  losses  reduced  to  B.T.U 

Total  input— H.P.  (Calculated  from  K.W.)  output . . . 

Total  D.H.P 

Efficiency  of  the  plant 

Moisture  in  steam per  cent 

Steam  per  input  H.P.  hr.  (wet) Ibs 

Steam  per  input  H.P.  hr.  (dry) '   

Steam  per  D.H.P.  hr.  (dry) " 

Thermodynamic  Eff (T-T')  +T 

Tnermal  Eff AW+Q 

Steam  per  H.P.  hr.  of  perfect  engine  (dry) Ibs.— (Q  -q)  +  2545 

Ratio  actual  to  theoretical  water  consumption 

Heat  supplied  per  minute B.T.U 

Heat  utilized  per  min 

Heat  discharged  per  min 

Heat  radiated  per  minute 


CHAPTER  XXIII. 
HOT-AIR   AND   GAS   ENGINES. 

454.  Hot-air  Engines. — Hot-air  engines  consist  of  engines 
in  which  the  piston  is  driven  backward  and  forward  by  the 
alternate  expansion  and  contraction  of  a  body  of  air  caused  by 
heating  and  cooling.  Those  now  on  the  market  are  used  prin- 


FIG.  311.  FIG.  312. 

ERICSSON  HOT-AIR  PUMPING-ENGINE. 

cipslly  for  puimping-engines,  and  are  arranged  to  use  eith 
coal  or  gas  as  fuel. 

455.   Ericsson  Hot-air  Engine. — This  engine  is  shown 
Fig,  311  in  elevation,  anjd  in  Fig.  312  in  section. 

£i  ^  * 


er 


in 


§  45 6 J  HOT-AIR  AND   GAS  ENGINES.  695 

The  method  of  operation  is  as  follows:  There  are  two 
pistons,  viz.,  A,  the  displacing  piston  or  plunger,  and  B,  the  driv- 
ing-piston. The  driving-piston  is  connected  to  the  mechanism 
as  shown.  The  displacing-piston,  A,  is  a  vessel  made  of  some 
non-conducting  substance,  and  its  office  is  to  move  a  body  of 
air  alternately  from  the  space  above  to  that  below  it.  As  shown 
in  the  figure,  the  piston  A  is  at  the  upper  end  of  its  stroke,  and 
the  piston  B  is  moving  rapidly  upward,  being  driven  by  the 
expansion  of  the  air  in  the  lower  part  of  the  receiver  d.  The 
air  in  the  upper  part  of  the  receiver  is  cooled  by  water  which 
has  been  raised  by  the  pump  r,  and  which  circulates  in  the 
annular  space  xx. 

On  the  return  stroke  of  the  piston  B  the  plunger  A  at  first 
descends  somewhat  faster,  and  thus  by  transferring  air  main- 
tains a  nearly  uniform  pressure  upon  the  piston.  When  the 
piston  B  reaches  the  position  shown  in  Fig.  312  on  its  down- 
ward stroke,  the  plunger  A  will  be  at  the  bottom  of  its  stroke, 
and  all  the  working  air  will  have  been  transferred  above  and 
its  temperature  maintained  at  its  lower  limit,  while  it  is  com- 
pressed by  the  completion  of  the  downward  stroke  of  the 
piston  B,  after  which  the  plunger  will  rise  to  the  position 
shown  in  the  figure  and  the  temperature  and  volume  are  both 
increased  at  nearly  constant  pressure.  The  mass  of  air  in  the 
engine  remains  constant. 

456.  The  Rider  Hot-air  Engine. — In  this  engine  the 
compression-piston  A  and  the  power-piston  C  work  in  sepa- 
rate cylinders,  which  are  connected  together  by  a  rectangular 
passage  D  in  which  are  placed  a  large  number  of  thin  metallic 
plates,  forming  the  regenerator,  whose  office  is  to  alternately 
abstract  from  and  return  to  the  air  the  heat  in  its  passage 
backward  and  forward.  The  same  air  is  used  continuously ;  it 
may  be  admitted  to  the  cylinders  by  a  simple  check-valve  O, 
opening  inward.  The  engine  is  used  entirely  as  a  pumping- 
engine,  and  the  water  so  raised  circulates  around  the  compres- 
'sion-chamber  B. 

The  operation  of  the  engine  is  briefly  as  follows: 

The  compression-piston  A  first  compresses  the  cold  air  in 


696  EXPERIMENTAL  ENGINEERING.  §  456-] 


FIG.  313. — THE  RIDER  HOT-AIR  PUMPING-ENGINE. 


§  458-]  HOT-AIR  AND   GAS  ENGINES.  697 

the  lower  part  of  the  compression-cylinder  B,  when,  by  the 
advancing  or  upward  motion  of  the  power-piston  C  and  the 
completion  of  the  down  stroke  of  the  compression-piston  A, 
the  air  is  transferred  from  the  compression-cylinder  B  through 
the  regenerator  D  and  into  the  heater  E  without  appreciable 
change  of  volume.  The  result  is  a  great  increase  of  pressure, 
corresponding  to  the  increase  of  temperature,  and  this  impels 
the  power-piston  up  to  the  end  of  its  stroke.  The  pressure 
still  remaining  in  the  power-cylinder  and  reading  on  the  com- 
pression-piston A  forces  the  latter  upward  till  it  reaches  nearly 
to  the  top  of  its  stroke,  when,  by  the  cooling  of  the  charge  of 
air,  the  pressure  falls  to  its  minimum,  the  power-piston  de- 
scends, and  the  compression  again  begins.  In  the  mean  time, 
the  heated  air,  in  passing  through  the  regenerator,  has  left  the 
greater  portion  of  its  heat  in  the  regenerator-plates  to  be  picked 
up  and  utilized  on  the  return  of  the  air  towards  the  heater. 

457.  Thermodynamic    Theory.  —  The    thermodynamic 
theory  of  the  hot-air  engine  will  be  found  fully  discussed  in 
Rankine's    Steam-engine    and    in    Wood's    Thermodynamics, 
from  which  it  is  seen  that  these  engines  may  work  under  the 
conditions  of  change  of  temperature  with  either  constant  press- 
ure or  constant  volume,  or  under  the  condition  of  receiving 
and  rejecting  heat  at  constant  pressure. 

The  thermodynamic  efficiency  is  found  by  dividing  the 
range  of  temperatures  of  the  fluid  by  the  absolute  temperature 
of  the  heated  fluid. 

458.  Method  of  Testing. — The  method  of  testing  hot-air 
engines  does  not  differ  essentially  from  that  for  the  steam- 
engine.     An  indicator  is  to  be  attached  so  as  to  measure  the 
pressures.      Knowing  the   pressures  and   volumes,  the  corre- 
sponding temperatures  can  be  computed  from  the  formula 

£  =  *=  53-21, 
in  which  p  is  the  pressure  in  pounds  per  square  foot,  v  the 


698 


EXPERIMENTAL   ENGINEERING. 


[§  459- 


corresponding  volume  in  cubic  feet,  and  T  the  absolute  tern- 
perature.     From  this 


T  = 


pv 
R' 


The  quantities  which  should  be  taken  in  each  test  are  shown 
OE  the  following  blank  for  data  and  results : 

459.  Forms  for  Data  and  Results  of  Test  of  Hot-air 
Engine. 


MECHANICAL  LABORATORY,   SIBLEY  COLLEGE, 
CORNELL   UNIVERSITY. 


Test  of Hot-air  pumping-engine.     Fuel. 

At 

Date 189 .. 


LOG  OF  TRIAL. 


Symbol. 

h1 

W 

p 

P 

t 

t' 

t" 

N 

G 

w 

|  Number.  I 

8 

H 

Water. 

Pressures. 

Temperatures. 

Revolutions. 

Fuel. 

Leakage 

Weir- 
reading. 

f- 

*$, 

Pressure- 
gauge. 

Suction- 
Gauge. 

\ 

o 

Cu 

W 
5 

tf 

Water  at 
Weir. 

Jacket. 

Hi 

11 

HU 

a 

Sv 

** 

1 

1 
& 

3 

£ 

Per  Hour. 

u    . 

H  be 

C  G 

M 

&*> 

3* 

Average. 

RESULTS  OF  TEST  OF  HOT-AIR   ENGINE. 

DATA  AND  GENERAL  RESULTS. 

Diameter  of  working-piston in.;  Area  of  same sq.  in. 

Diameter  of  plunger in.;  Area  of  same , sq.  in. 

Length  of  stroke,  working-piston ft.;  Displacement cu.  ft. 

Length  of  stroke,  plunger / ft.;  Displacement.. ........ .  .cu.  ft 

Distance  between  centres  of  gauges ft. ;  Zero  of  weir rt. 


§459-] 


HOT-AIR  AND    GAS  ENGINES. 


699 


Symbol. 

Determination. 

i 

3 

3 

Head  pumped  against,  feet.  

If 

h 

i 

Q'» 
X 
k 
G 
B.  T.  U. 
Duty 

M.  E.  P. 
I.  H.  P. 
D.  H.  P. 
E 
E' 

Water  delivered,  cu.  ft.  per  sec  

"             "          Ibs.  perhr  

"            "         gals,  per  24  hrs  

"            "         perhr.  plunger-displacement 

Thermal  units  per  Ib.  of  fuel  

Average  fuel-consumption  per  hour  

Duty  per  plunger-displacement  

"         indicated  H.  P  

Expenditure  of  heat  per  hour  

Indicated  work,  B.  T.  U  

Heating  jacket-water  

Total  

4 

REMARKS. 


The  indicator-diagram  obtained  from  the  hot-air  engine  will 
depend  largely  on  the  principle  of  operation.     The  form  of  the 


FIG.  314.— DIAGRAM  FROM  ERICSSON  HOT-AIR  ENGINE. 


one  obtained  from  the  Ericsson  engine  in  which  there  is  change 
of  temperature  at  constant  pressure  is  well  shown  in  Fig.  314. 


700  EXPERIMENTAL   ENGINEERING.  [§ 


SPECIAL    DIRECTIONS   FOR   EFFICIENCY-TESTS    OF  THE   RIDER 
AND  THE   ERICSSON   ENGINE. 

Rider  Engine. 

Apparatus.—  Steam-engine  indicator  with  i6-pound  spring; 
thermometers  ;  low-pressure  gauge. 

Operation.  —  Build  a  fire  in  the  heater;  fill  the  jacket  with 
water  by  priming  the  pump  ;  attach  indicator  ;  place  gauge 
behind  the  delivery-valve,  and  thermometers  to  obtain  tempera- 
tures of  water  in  supply  and  discharge  pipes  ;  open  delivery. 
valve  and  start  engine  by  hand. 

Make  five  half-hour  runs,  increasing,  the  head  five  pounds 
each  time,  and  taking  data  every  five  minutes.  To  stop  the 
engine,  open  fire-door  and  blow-off  cock. 

Submit  graphical  log  and  plot  efficiency-curve,  using  heads 
as  ordinates  and  efficiencies  as  abscissae. 

Ericsson  Engine. 

Apparatus.  —  Indicator  with  lo-pound  spring  ;  low-pressure 
gauge. 

Operation.  —  Light  the  gas  under  the  heater  ;  place  pressure- 
gauge  behind  delivery-valve,  and  attach  indicator  ;  proceed 
with  test  and  report  as  in  efficiency-test  of  Rider  compression- 
engine,  beginning  with  a  head  of  five  pounds  and  increasing 
by  five  pounds  up  to  twenty-five  pounds. 

460.  The  Gas-engine.  —  The  gas-engine  is  in  many  re- 
spects similar  to  a  hot-air  engine  in  which  the  furnace  is 
included  in  the  working-cylinder. 

There  are  many  types  of  these  engines  now  constructed, 
differing  from  each  other  in  form,  in  methods  of  igniting  the 
gas,  and  in  the  number  of  strokes  required  to  complete  a  cycle 
of  operations.  In  all  these  engines  a  mixture  of  gas  and  air,  in 
such  proportions  as  to  be  readily  exploded,  is  drawn  into  the 
cylinder  ;  this  is  then  exploded  by  firing  either  with  an  electric 
spark  or  with  a  lighted  /gas-taper,  after  which  the  piston  is  im- 
pelled rapidly  forward,  and  the  gas  expanded  ;  the  burned  gas 


4^0.]  HOT-AIR   AND    GAS  ENGINES. 


701 


is  then  expelled  from  the  cylinder  before  the  introduction  of  a 
new  charge. 

Gas-engines  are  usually  single-acting,  but  a  few  have  been 
made  that  were  double-acting  like  a  steam-engine. 

Dugald  Clerk  makes  the  following  classification  of  gas- 
engines  :  * 

A.  Engines  igniting  at  constant  volume  but  without  previous 

compression,  and  of  which  the  working  cycle  consists 
in— 

1.  Charging  the  cylinder  with  explosive  mixture. 

2.  Exploding  the  charge. 

3.  Expanding  after  explosion. 

4.  Expelling  the  burned  gases. 

Many  of  the  early  engines  were  of  this  type,  of  which  may 
be  mentioned  those  of  Lenoir,  Hugon,  and  Bisschof. 

A  type  of  gas-engine  in  which  the  cycle  is  changed  a  little 
from  that  given  was  successfully  introduced  by  Otto  and 
Langen  in  1866.  In  this  engine  the  piston  is  shot  forward  by 
the  force  of  the  explosion  in  a  long  cylinder,  while  discon- 
nected from  the  motor-shaft,  but  on  the  return  stroke  it 
engages  with  the  motor-shaft  and  completely  expels  the  burned 
gases. 

The  cycle  is  as  follows : 

1.  Charging  the  cylinder. 

2.  Exploding  the  charge. 

3.  Expanding  after  explosion  while  disconnected  from  the 

motor. 

4.  Compressing  the  burned  gases  after  some  cooling. 

5.  Expelling  the  burned  gas.     Work  is  done  only  on  the 

return  stroke. 

B.  Engines  igniting  at  constant  pressure  with  previous  com- 

pression, and  of  which  the  working  cycle  consists — 

1.  Charging  the  pump-cylinder  with  the  explosive  mixture. 

2.  Compressing  the  charge  into  an  intermediate  receiver. 

3.  Admitting  the  charge  to  the  motor-cylinder  in  the  state 

of  flame,  at  the  pressure  of  compression. 

*  The  Gas-Engine,  Dugald  Clerk  ;  N.  Y.,  J.  Wiley  &  Sons. 


7O2  EXPERIMENTAL   ENGINEERING.  [§4^0. 

4.  Expanding  after  admission. 

5.  Expelling  the  burned  gases. 

To  carry  out  this  process  perfectly  the  following  conditions 
are  required : 

(a)  No  throttling  or  heating  from  the  air  during  admission 

to  the  pump. 

(b)  No   loss   of    heat    of    compression   to   the   pump   and 

receiver-walls. 

(c)  No  throttling  as  the  charge  enters  the  motor-cylinder 

or  the  receiver. 

(d)  No  loss  of  heat  to  the  iron  of  the  motor-cylinder. 

(e)  No  back  pressure  during  the  exhaust-stroke. 

The  most  successful  engines  of  this  type  are  Brayton's  and 
Diesel's. 

C.    Engines  igniting  at  constant  volume  with  previous  com- 
pression, of  which  the  usual  cycle  of  operations  is — 

1.  Charging  the  motor-cylinder  with  the  explosive  mixture. 

2.  Compressing  the  charge  in  the  motor-cylinder. 

3.  Igniting  the  charge  after  admission  to  the  motor. 

4.  Expanding  the  hot  gases  after  ignition. 

5.  Expelling  the  burned  gases. 

To  carry  out  this  process  perfectly  the  gases  should  not  be 
heated  until  ignition,  and  they  should  not  lose  heat  to  the 
cylinder-walls  during  expansion ;  these  are  conditions  in  a 
measure  contradictory  and  impossible  to  fulfil  completely. 
The  most  successful  engines  now  in  use  belong  to  this  class, 
which  is  commonly  known  as  the  "  four-stroke-cycle  type," 
as  it  requires  four  strokes  for  each  cycle  of  operation ;  it  was 
first  proposed  by  Beau  de  Rochas  in  1860  and  first  practically 
applied  by  Otto  in  1874.  A  modified  form  of  the  above  type, 
known  as  the  "  two-stroke-cycle  engine,"  requires  but  two 
strokes  for  the  cycle  of  operation,  the  events  taking  place  in 
the  following  order:  I  (out-stroke):  Ignition;  expansion; 
commencement  of  exhaust.  2  (in-stroke) :  Completion  of 
exhaust  simultaneous  with  charging;  compression. 

Compression  engines  were  patented  by  Barnett  in  1838 
and  by  Million  in  1 840  with  a  different  cycle  from  that  described. 


§ 


HOT-AIR   AND    GAS  ENGINES. 


703 


Gas  suitable  for  use  in  gas-engines  is  manufactured  in  a 
variety  of  ways  and  from  a  considerable  number  of  substances. 
A  mixture  of  hydro-carbon  vapor  and  air  is  obtained  by 
volatilizing  some  of  the  light  hydro-carbon  oils. 

The  following  table  gives  the  composition  and  heating 
value  of  several  different  kinds  of  gases : 

COMPOSITION    AND    HEATING   VALUE   OF   GASES. 


Natural 
Gas. 
(Pa.) 

Coal  Gas. 

Water  Gas. 

Producer  Gas. 

A. 

B. 

Enriched. 

Normal. 

Anthra- 
cite. 

Bitumin- 
ous. 

CO,  percent 
H, 
CH4, 
C2H4, 
CO9  , 
N, 
0, 

0.50 
2.18 
92.6 
0.31 
0.26 
3.6l 
0.24 

8.18 
46.2 
34-0 
3-76 
8.88 
2.15 
0.65 

6.00 
46.0 
40.0 
4.0 
o.5 
i-5 
0.5 

23.6 

35-9 
20.9 

12.8 

0.3 
3-9 

O.OI 

1.5 

4.6 
688 
14900 

45-00 
45-0 
2.0 

27.0 
12.  0 
1.2 

27.0 
I2.O 

2-5 
0.4 

2-5 
56.2 

0-3 

6.59 
157 

2385 

4.0 
2.0 

0.5 

4.56 

322 
7120 

2-5 

57-0 
0.3 

6.56 
137 

2IOO 

Weight    per   100 
cu.  ft.,  Ibs  
B.T.U.percu.ft. 
B.T.U.  per  Ib... 

4.56 
IIOO 

24150 

3-2 
577 
17900 

3-2 
735 
23100 

Ignition  in  gas-engines  is  made  to  take  place  very  nearly 
at  the  time  of  greatest  compression.  The  various  methods 
in  use  are  (i)  the  open  flame,  (2)  the  hot  tube,  and  (3)  electric 
ignition  of  the  contact  and  jump-spark  variety.  The  ignition 
with  open  flame  is  accomplished  by  an  auxiliary  gas-jet  which 
is  constantly  kept  burning  in  a  chamber  adjacent  to  the 
cylinder,  and  which  is  put  in  alternate  communication  at 
suitable  intervals  with  the .  atmospheric  air  and  with  the 
cylinder  by  means  of  a  valve  actuated  by  the  engine.  This 
method  was  used  on  the  Barnett  and  the  early  Otto  engines, 
but  is  seldom  employed  at  the  present  time. 

The  ignition  with  the  hot  tube  is  performed  by  connect- 
ing a  closed  tube,  which  is  kept  hot  by  an  external  flame,  to 
the  cylinder  in  such  a  manner  that  it  will  be  filled  during 
compression  by  the  charge  in  the  clearance.  The  charge  is 


7°4 


EXPERIMENTAL   ENGINEERING., 


[§  460. 


fired  by  the  heat  communicated  through  the  tube.    Fig.     315 
illustrates  the  usual  arrangement  of  a  hot-tube  ignition  device. 

In  this  figure  A  is  the  cylinder, 
H  the  tube,  G  a  gas-jet  which 
plays  around  the  tube  H,  dis- 
charging the  products  of  com- 
bustion at  B.  In  some  con- 
structions communication  be- 
tween the  hot  tube  and  the 
cylinder  is  closed  by  a  valve 
except  at  the  time  of  ignition. 
Electric  ignition  is  of  two 
kinds :  the  contact  method,  in 
which  two  terminals  connected 
through  a  battery  and  spark 
coil  are  brought  into  contact 
within  the  cylinder  and  separ- 
ated rapidly,  causing  a  bright 
spark  by  the  self-induction  of 
,  the  coil.  One  form  of  this 

method    of   ignition  is  shown   in   Fig.    315^,   in    which    the 
igniter  terminal,  a,  is  an   arm   mounted   on  a  shaft,    b,    and 


Battery 


FIG.    315. —  IGNITION  BY  THE  HOT  TUBE. 


FIG.  3150.— WIPE-SPARK  IGNITION. 

arranged  to  be  worked  by  a  suitable  cam  rod  attached  to  the 
outer  crank  d.  The  terminal,  e,  is  stationary  and  insulated 
from  the  cylinder-wall.  The  two  terminals  may  be  mounted 


46o.l 


HOT-AIR  AND    GAS  ENGINES. 


705 


in  a  removable  plug  P.  The  extremities  of  the  terminals 
should  be  of  some  metal,  as  platinum,  that  will  resist 
the  action  of  the  electric  current.  Other  forms  of  this 
method  of  ignition  have  a  rubbing  motion  of  the  terminals 
before  ignition. 

The    other    electric-ignition    arrangement    is  illustrated 


FIG.  316. — JUMP-SPARK  IGNITION. 

by  Fig.  316.  Both  igniter  terminals  are  stationary  and 
mounted  in  a  plug  of  insulating  material,  usually  porcelain  or 
lava.  These  are  connected  to  the  secondary  terminals,  s,  s, 
of  an  induction-coil.  .  The  primary  circuit  of  this  coil  is  con- 
nected to  a  battery,  B,  at  the  proper  moment  by  a  contact 
cam  on  the  secondary  shaft,  6*. 

The  primary  circuit  of  the  coil  includes  a  vibrator,  V,  in 
many  cases.  With  this  arrangement  a  succession  of  sparks 
passes  between  the  igniter  terminals  while  the  circuit-closing 
cam  is  in  contact  with  its  brush.  In  some  cases,  however, 
the  vibrator  is  omitted,  the  circuit  being  broken  only  once, 
at  the  cam  contact. 

The  cut,  Fig.  317,  shows  the  construction  of  a  recently 
designed  four-stroke-cycle  engine  for  gas  or  hydro-carbon 
vapor.  In  this  engine,  which  is  shown  in  section,  the  gas 
and  air  enter,  through  separate  inlets,  the  mixing-chamber  M9 
from  which  the  mixture  flows  through  the  port  N  and  inlet- 
valve  J  into  the  cylinder  as  the  piston  is  beginning  a  down- 
ward stroke  at  the  commencement  of  a  cycle  of  operation. 
The  inlet-valve  is  opened  once  in  two  revolutions  by  the 
motion  of  the  cam  B,  which  makes  one  half  as  many  revo« 


706 


EXPERIMENTAL  ENGINEERING. 


[§  460. 


lutions  as  that  of  the  main  shaft  of  the  engine.     The  charge 
is  then  drawn  into  the  cylinder  by  suction.     During  the  up- 


FIG.  317. — SECTION  THROUGH  WESTINGHOUSE  ENGINE. 

stroke  of  the  piston,  the  charge  of  gas  and  air  is  compressed 
in  the  cylinder.  The  charge  is  ignited  by  an  electrical 
spark  at  about  the  time  the  compression  is  maximum  and 
when  both  inlet-  and  exhaust-valves  are  closed.  The  ignition 
is  performed  by  an  igniter-cam  arranged  so  as  to  bring  two 
igniter-terminals  into  contact,  completing  the  electric  circuit, 
and  then  suddenly  separating  them  by  the  energy  in  a  coiled 


§  46o.] 


HOT-AIR  AND    GAS  ENGINES. 


70/ 


spring  located  in  the  guide  D.    The  rise  of  pressure  following 
ignition  drives  the  piston  downward  to  the  end  of  its  stroke. 


FIG.  318. — SkcrioN  OF  LOZIER  ENGINE. 

On  its  return-stroke  the  exhaust-cam  A  opens  the  exhaust- 
valve  E  and  the  burned  gases  are  expelled  by  the  rising 
piston  into  the  exhaust-pipe  O.  One  cycle  of  operation  is 
then  complete  and  requires,  as  thus  described,  four  strokes 
of  the  piston  or  two  revolutions  of  the  engine. 

For  the  purpose  of  cooling,  a  jacket  is  provided  through 
which  water  is  made  to  circulate,  entering  at  H  and  dis- 
charging at  K.  In  the  engine  above  described  the  speed  is 
regulated  by  a  governor,  not  shown  in  the  cut,  which  throttles 
the  mixture  of  gas  and  air. 

A  two-stroke-cycle  engine  is  shown  in  Fig.  318,  in  which 
the  cycle  of  operation  is  completed  in  two  strokes  or  one  revo- 


/OS  EXPERIMENTAL    ENGINEERING.  [§  460. 

lution  of  the  engine,  although  the  number-of  operations  is  the 
same  as  in  the  case  of  the  four-stroke  cycle.  In  the  engine 
as  shown  in  the  figure,  the  mixed  charge  of  gas  and  air  is 
drawn  into  a  chamber  in  the  crank-case  through  the  opening 
A,  and  is  prevented  from  going  backward  by  a  check-valve 
opening  inward  which  is  located  on  the  pipe  supplying  the 
charge.  No  valve  other  than  the  piston  is  employed  to  con- 
trol either  the  admission-  or  the  exhaust-port.  The  admis- 
sion-port is  in  the  lower  part  of  the  cylinder,  at  C,  the 
exhaust-port  is  at  the  opposite  side  of  the  cylinder,  at  F. 
The  charge  enters  when  the  piston  is  at  the  lower  por- 
tion of  its  stroke  through  the  open  admission-port,  due 
to  the  compression  produced  by  the  downward  motion 
of  the  piston  on  the  contents  of  the  crank-chamber;  at  the 
same  instant  the  burned  gases  are  being  exhausted  through 
the  open  exhaust-port.  On  the  return-stroke  the  fresh 
charge  is  compressed  from  the  time  the  piston  has  covered 
the  exhaust-port  until  the  end  of  the  stroke.  The  ignition 
is  performed  at  about  the  time  of  greatest  compression. 
We  note  that  in  this  cycle  of  operation  admission  and 
exhaust  take  place  simultaneously  at  the  beginning  of  the 
upward  stroke,  and  compression  during  the  completion 
of  the  stroke;  ignition  takes  place  at  or  near  the  begin- 
ning of  the  downward  stroke,  expansion  during  the  down- 
ward stroke,  and  beginning  of  exhaust  near  the  end  of  this 
stroke.  The  advantages  of  this  cycle  of  operation  are 
claimed  to  be  a  greater  number  of  impulses  per  revolution 
and  a  steadier  motion  for  engines  of  the  same  weight.  The 
disadvantages  are  the  uncertainty  of  a  clean  cylinder  for  the 
explosion  and  the  probable  loss  of  unburned  gases  in  the 
exhaust.  Actual  tests  show  that  the  two-stroke-cycle  en- 
gines are  much  less  economical  than  those  of  the  four-stroke- 
cycle  type  and  fully  as  heavy  per  unit  of  power. 

A  light  hydrocarbon  oil,  termed  gasoline,  is  readily 
vaporized  by  contact  with  air,  in  which  case  it  forms  a  com- 
bustible gas  suitable  for  use  in  gas-engines.  The  gasoline  is 


§46 1.]  HOT-AIR  AND    GAS  ENGINES. 


709 


vaporized  and  mixed  with  air,  by  a  device  called  a  carburetter, 
previous  to  its  introduction  into  the  engine  cylinder.  Engines 
designed  for  the  use  of  gasolene  are  sometimes  called  "gasolene- 
engines,"  but  they  do  not  differ  in  any  essential  way  from  those 
designed  for  gas.  The  carburetter  is  always  external  to  and 
independent  of  the  engine,  and  is  equivalent  to  a  gas-machine 
in  its  results.  Gasolene  is  the  principal  source  of  fuel  for  all 
portable  or  automobile  motors,  for  which  it  is  excellently  suited, 
because  of  its  great  heating  value  per  unit  of  volume  and  because 
of  its  easy  volatilization  in  the  carburetter  without  heat.  Car- 
buretters are  designed  in  various  forms,  but  in  all  cases  they 
provide  means  for  passing  the  entering  air  over  the  necessary 
amount  of  gasolene  while  in  a  finely  divided  state.  The  regu- 
lation is  frequently  accomplished  automatically  by  a  float  or  other 
device. 

461.  Oil-engines. — This  name  is  appropriately  applied  to 
engines  designed  to  use  as  a  fuel  the  heavy  petroleum  oils  which 
are  not  readily  vaporized.  These  engines  are  internal-combus- 
tion motors,  which  differ  from  gas-engines  principally  in  the 
fuel  employed  and  in  the  means  required  for  vaporizing  and 
ignition  of  the  same.  They  may  be  either  of  the  two-stroke  or 
four-stroke  cycle  type,  but  usually  are  of  the  latter. 

The  first  oil-engines  used  flame  ignition,  but  those  now  built 
are  ignited  wholly  or  in  part  by  the  heat  of  compression  aided 
by  a  hot  tube,  hot  surface,  or  electric  spark.  The  oil-engines 
are  generally  of  the  class  which  ignite  at  constant  volume  and 
during  increase  of  pressure  and  temperature,  the  charge  having 
been  previously  compressed.  Prominent  exceptions  are  the 
Brayton,  which  is  not  now  built,  and  the  Diesel.  The  Brayton 
ignites  from  a  constantly  burning  flame  at  constant  pressure 
during  increase  of  volume  and  temperature.  The  Diesel  ignites 
from  the  heat  of  compression  at  constant  temperature  during 
increase  of  volume  and  decrease  of  pressure.  Oil-engines,  it  is 
noted,  may  be  divided  into  three  classes,  igniting,  respectively, 
(i)  at  constant  volume,  (2)  at  constant  pressure,  (3)  at  con- 
stant temperature. 


EXPERIMENTAL  ENGINEERING. 


[§  461. 


In  the  Brayton  the  oil  is  sprayed  directly  into  the  cylinder 
during  ignition,  which  takes  place  for  a  portion  of  the  forward 
stroke.  At  the  same  time  compressed  air  is  supplied  by  a  com- 
pressor, so  as  to  maintain  constant  pressure  in  the  working 
cylinder.  The  speed  is  regulated  by  a  governor  which  controls 
the  admission-valve  for  air  and  oil.  The  diagram  from  this 
engine  is  much  like  one  from  a  Corliss  steam-engine. 


FIG.  319.— THE  HORNSBY-AKROYD  OIL-ENGINE. 

o.n  the  Priestman  oil-engine  there  is  an  external  vaporizer 
heated  externally  by  the  exhaust  gases,  and  through  which  the 
entire  charge  of  oil  and  air  for  combustion  pass  on  the  way  to 
the  engine. 

In  the  Hornsby-Akroyd  engine,  shown  in  Fig.  319,  the  oil- 
charge  is  pumped  into  a  chamber  connected  to  the  working 
cylinder,  where  it  is  vaporized  by  the  heat.  The  air  is  drawn 
into  the  cylinder  through  a  separate  inlet- valve  and  forced  by  the 
compression  into  contact  with  the  oil-vapor,  causing  ignition. 
The  Priestman  and  the  Hornsby-Akroyd  in  other  respects  resem- 
bles the  Otto  gas-engine. 


§  462.] 


HOT-AIR  AND    GAS  ENGINES. 


711 


462.  Theoretical  Relations  of  Pressure,  Volume,  and 
Temperature  of  a  Gas.— The  relations  of  pressure,  p,  volume, 
v,  and  temperature,  /,  of  a  unit  of  weight  of  a  perfect  gas  during 
expansion  or  compression  may  be  expressed  by  the  following 
equations,  in  which  T  =  absolute  temperature,  a  =  coefficient  of 
expansion  per  degree  of  absolute  temperature,  a  =  number  of 
degrees  between  freezing-point  and  absolute  zero,  pQ= pressure 
at  o°,  v0  =  volume  at  o°  of  one  unit  of  weight  of  the  gas,  and 
R  =  constant  =  PQVQO.  =  poVo/a. 

From  Boyle's  and  Gay-Lussac's  laws  we  have 


pv=RT  may  be  considered  the  characteristic  equation  of  a  per- 
fect gas  since  it  shows  the  relations,  during  expansion  or  com- 
pression, of  a  unit  weight  between  the  pressure,  volume,  and  abso- 
lute temperature.  R  is  a  constant  dependent  on  the  nature  of 
the  gas,  with  values  as  follows  for  a  few  of  the  gases : 


Values 

5  Of  R. 

English  Units. 

Metric  Units. 

Hydrogen  (H)                 .... 

770.  •? 

422  .  68 

Oxvffen  (O} 

48.74 

26.475 

Carbon  dioxide  (CO2)  

7C.4I 

19.43 

Air                   

53.22 

29.20 

Expansion  and  compression  may  take  place  (i)  isothermally, 
in  which  case  there  is  no  change  of  temperature,  or  (2)  adiabat- 
ically,  in  which  case  there  is  no  increase  or  decrease  in  the  total 
heat.  For  the  first  case,  since  the  temperature  remains  constant, 

(3) 


The  curve  corresponding  to  this  equation  is  an  equilateral  hy- 
perbola asymptotic  to  the  axes  of  volume  and  pressure.     Methods 


712  EXPERIMENTAL   ENGINEENING.  [§  462 

of  drawing  this  curve  have  already  been  given  in  Art.  404,  pages 
554  and  555. 

For  the  second  case,  or  adiabatic  expansion  or  compression, 


from  which 

pvk  =  a  constant,     .....     (4) 


in  which  k  =  cp/cv.     cp  =  specific  heat  at  constant  pressure   and 
c  =  specific  heat  at  constant  volume. 

During  adiabatic  expansion  the  relations  of  temperature  and 
volume  are  shown  by  the  following  equation: 


=Y (5) 

The  relation  of  pressure  and  temperature  by 

Tp^  =  Tlp{~^ (6) 

The  following  table  (see  next  page)  from  Clausius  (Mechanical 
Theory  of  Heat)  gives  the  value  of  the  two  specific  heats  for  a 
few  of  the  gases. 

The  adiabatic  curve  may  be  drawn  when  po,  v0,  and  k  are 
known  by  assuming  values  of  v  and  calculating,  either  with  a 
table  of  logarithms  or  a  slide- rule,  corresponding  values  of  p. 

The  mechanical  work,  W,  done  during  isothermal  expansion 
between  the  volumes  v2  and  v{  is  theoretically  as  follows: 

w=    C  d  fV2^.-  !^ 

J  Jvi       V  ^  ^1  * 

The  work  done  during  adiabatic  expansion  from  v2  to  Vi  is 
as  follows: 


§  463.] 


HOT-AIR  AND    GAS  ENGINES. 


Name  of  Gas. 

Symbol 

Specific  Heat. 

!P 
cv 

k 

Constant 
Pressure. 

CP 

Constant 
Values. 

cv 

Air  

O 
N 
H 
NO 
CO 
C02 
H20 
CS2 
C2H4 
NH3 
C2H60 

°-237S 
0.2175 

0.2438 
3.4090 
0.2317 
0.2450 
0.2169 
0.4805 
0.1569 
0.4040 
0.5084 
°-4534 

0.1684 

O.ISSI 

0.1727 
2.4110 
0.1652 
0.1736 
o.  1720 
0.3700 
0.1310 

°-359° 
0.3910 
0.4100 

.406 
•403 
.416 
.414 
.402 

•413 
.261 
.298 
.198 
.125 
.300 
1.150 

Oxygen  

Nitrogen  

Hydrogen  .... 

Nitric  oxide  

Carbonic  oxide  

Carbon  dioxide.  ....'.  

Steam  

Bisulphide  carbon  

Olefiant  gas  

Ammonia  

Alcohol  

The  heat  applied  during  isothermal  expansion  or  received 
during  isothermal  compression  is  given  by  the  following  equation: 

/V2dv  i] 

--(*,-*)*-,  log, ^, 


or 


log,  ~i=Ap1v1  log,  g. 


(9) 


The  complete  derivation  of  these  equations  can  be  found 
in  any  work  on  thermodynamics;  they  are  given  here  merely  for 
convenience. 

463.  Cycle  of  Operation  of  Gas-engines. — A  body  is  said 
to  operate  in  a  closed  cycle  when  it  returns  to  its  original  state  after 
passing  through  a  series  of  physical  and  chemical  changes.  When 
a  change  of  composition  occurs,  as  is  the  case  during  combus- 
tion in  the  internal- combustion  engine,  the  body  may  return  to 
its  initial  condition  only  so  far  as  pressure  and  volume  are  con- 
cerned and  not  in  other  respects.  For  this  reason  the  gas-engine 
operates  in  a  cycle  which  is  only  approximately  closed. 

If  (3=  heat  received,  q  that  exhausted,  the  highest  possible 


714  EXPERIMENTAL   ENGINEERING.  [§4^4. 

maximum  efficiency  would  be  for  that  condition  (Q—q)/Q,  which 
ratio  has  been  called  by  A.  Witz  the  "coefficient  of  economy." 

The  Carnot  cycle  is  an  ideal  one  which  differs  materially  from 
any  actual  cycle  of  the  gas-engine,  yet  it  is  useful  as  a  basis  of 
comparison,  since  it  represents  the  maximum  return  in  work 
for  a  given  fall  of  temperature.  In  this  cycle  there  is  isothermal 
and  adiabatic  expansion  followed  by  isothermal  and  adiabatic 
compression.  For  this  case  it  can  be  shown  that 


in  which  T  is  the  absolute  temperature  during  the  isothermal 
expansion  and  Tf  that  during  isothermal  compression. 

The  thermal  efficiency  may  be  calculated  from  the  I.  H.  P. 
by  dividing  the  mechanical  work  shown  by  the  indicator  diagram, 
expressed  in  heat-units,  by  the  heat  value  of  the  fuel  consumed. 
It  may  also  be  expressed  as  the  ratio  of  the  delivered  work  in 
heat  units  to  the  heat  value  of  the  fuel.  Thus  if  W  =  the  mechan- 
ical work  delivered,  IW  the  mechanical  work  shown  by  the 
indicator  diagram,  then  will  the  efficiency  be  as  follows: 

Thermal  from  I.  H.  P.=IW/Q; 
Thermal  from  D.  H.  P.  =W/Q. 

464.  Method   of   Testing   Gas-   or   Oil-engines.— The 

method  of  testing  gas-  and  oil-engines  is  essentially  the  same,  the 
difference  being  principally  due  to  the  different  methods  of 
measuring  the  gaseous  and  liquid  fuel.  The  object  of  the  test 
in  every  case  is  to  find  the  relation  of  the  work  performed  to  the 
thermal  value  of  the  fuel  supplied,  and  the  efficiency  of  the  engine. 

To  obtain  these  results  the  amount  of  air  should  be  ascer- 
tained. This  may  be  computed  approximately  by  subtracting 
the  volume  occupied  by  the  fuel  from  the  cylinder  displacement, 
but  it  is  desirable  whenever  possible  to  meter  or  measure  the 
entering  air. 

In  attaching  the  indicator  it  will  be  found  necessary  to  use 


§  464. 


HOT- AIR  AND    GAS  ENGINES. 


a  heavy  spring  in  order  to  resist  the  effect  of  the  explosion. 
This  spring,  because  of  its  stiffness,  will  show  but  little  work  on 
the  intermediate  strokes;  for  this  reason  it  is  advisable  to  use  a 
second  indicator  with  a  light  spring,  in  which  is  placed  a  stop 
for  the  piston  so  that  the  spring  cannot  be  compressed  to  such 
an  extent  as  to  injure  it.  A  pyrometer  should  be  inserted  in 
the  exhaust,  and  a  gas-bag  placed  between  the  gas-meter  and 


FIG.  320. — PLAN  OF  ARRANGEMENT  FOR  GAS-ENGINE  TRIAL. 

the  engine.  The  proper  arrangement  of  a  gas-engine  for  trial 
i?  shown  in  Fig.  320,  from  Thurs ton's  Engine  and  Boiler  Trials. 

The  heat-units  per  cubic  foot  of  gas  used  should  be  deter- 
mined by  a  calorimetric  experiment  (see  page  451).  The  actual 
and  ideal  indicator-diagrams  are  shown  in  Fig.  321,  the  differ- 
ence being  in  great  part  due  to  losses  of  heat  in  the  cylinder. 

The  report  of  the  test  should  contain  a  description  of  the 
engine,  the  method  of  testing,  together  with  the  log  and  the  re- 


7i6 


EXPERIMENTAL   ENGINEERING. 


[§  464- 


suits  properly  tabulated.  In  connection  with  the  test  of  a  gas- 
engine,  plot  a  curve  with  cubic  feet  of  gas  per  I.  H.  P.  at  32°  F. 
and  atmospheric  pressure  as  ordinates,  and  I.  H.  P.  as  abscissae. 

In  the  test  of  gasoline-  or  oil-engines,  plot  a  similar  curve, 
using  the  weight  of  fuel  instead  of  the  volume  of  gas. 

Also  plot  a  curve  showing  the  relation  of  the  total  B.  T.  U.  in 
the  fuel  supplied  to  the  total  I.  H.  P.  and  D.  H.  P.  of  the  engine. 


Mean  pressure  68.10 

Revolutions  per  mln.  130.70 
Explosions  „  ii  78.63 
1.  H.  P.  Total 


*0»*(K1'     0.2     0.3      0.4     0.5     0.6     0.7      0.8     0.9    0.10  CuKFt. 
OTTO   ENGINE. 


0.1         0.2        0.3       0.4 
ATKINSON   ENGINE. 


FIG.  321. — ACTUAL  AND  IDEAL  INDICATOR-DIAGRAMS  FROM  GAS-ENGINES. 

In  case  the  air  cannot  be  directly  measured  it  may  be  approxi- 
mately computed  in  the  case  of  the  oil-engine  by  obtaining  the 
ratio  of  the  weight  of  oil  to  the  weight  of  air  required  for  the 
cylinder  displacement. 

In  the  test  of  the  engine  the  temperature  of  the  exhaust  gases 
is  obtained  which  is  Fess  than  the  temperature  during  the 
exhaust  stroke  existing  in  the  cylinders.  The  amount  of  this 


§  465  J 


HOT-AIR  AND   GAS  ENGINES. 


717 


difference  is  now  known.  Assume  that  it  is  50°  and  compute 
from  the  theoretical  formula  which  gives  relation  of  p,  v,  and  T, 
Art.  462,  the  temperature  at  the  beginning  and  end  of  the  stroke. 


FIG.  322. 

465.  Data  and  Results  of  Test. — The  following  form  gives 
the  data  and  results  of  test  for  a  gas-engine. 

In  case  of  the  test  of  an  oil-engine  the  items  relating  to  the 
weight,  volume,  and  thermal  value  of  gas  are  to  be  changed  for 

the    corresponding   items   respecting   the   weight,   volume,    and 
thermal  value  of  the  oil  which  is  employed  as  a  fuel. 

Fig.  322  shows  in  heavy  lines  the  actual  indicator-diagram 
from  a  four-cycle  gas-  or  oil-engine;  the  work  done  during  the  ex- 
haust and  charging  strokes  is  shown  to  a  large  scale  in  the  lower 
part  of  the  figure.  The  dotted  line  shows  the  theoretical  diagram 
for  the  same  conditions. 


718 


EXPERIMEN TA  L   ENGINEERING. 


Data  and  Results  of  Test  of Gas  Engine 

By .- 190 

Object  of  Test 


DIMENSIONS  OF  ENGINE. 

Rated  H.P.  at R.P.M.= 

Diameter  of  piston In. 

Area  of  piston Sq.  in. 

Length  of  stroke Ft. 

Piston  displacement Cu.  ft. 

Clearance Cu.  ft. 

"  Per  cent 

Diameter  piston-rod In. 

' '         crank-pin In. 

Scale  of  indicator  spring Lbs.  per  in. 


DATA. 


Run  No. 

I 

II 

Ill 

IV 

Duration  trial,  hrs  

Brake  load,  net  Ibs  

Gas,  total  cu.  ft  

*Gras  per  hour,  cu.  ft  

Air,  total  cu.  ft  

*Air  per  hour,  cu.  ft  

Ratio  air  to  gas  by  weight  

Jacket-water,  total  Ibs  

per  hour,  Ibs  

'  '              temp,  entering,  F°  

"      leaving,  F°  :  

'  '              range,  F°  

Revolutions,  total  

per  hour  

per  min  

Cycles,  per  min  

Explosions,  total  

per  hour  

per  min  

Ratio  of  explosions  to  cycles  

Temperature,  exhaust,  F°  

room,  F°  

range  

*Gas,  wt.  of  a  cu.  ft.,  Ibs  

*Air,  wt.  of  a  cu.  ft.,  Ibs  

*Mixture,  wt.  of  a  cu.  ft.,  Ibs  

Specific  heat,  gas  

air  

exhaust  gases  

*Thermal  equiv.,  cu.  ft.  gas,  B.T.U  

*  At  32°  F.  and  14/7  Ibs.  absolute  pressi 

are  per  s 

q.  in. 

§  465.] 


HOT-AIR  AND   GAS  ENGINES. 
RESULTS. 


719 


Run  No. 

I 

II 

III 

IV 

INDICATOR. 

Maximum  press,  Ibs.  sq.  in  

Compression  press,  Ibs.  sq.  in  

M.E.P.  power  stroke  

'  '          comp.        '   

I.H.P.  net  .'  

D.H.P  

Friction  horse-power  

Mechanical  efficiency,  per  cent  

Weight  of  gas  per  hr.,  Ibs  

Weight  of  air  per  hr.,  Ibs  

*Gas  per  I.H.P.,  per  hr.,  cu.  ft  

"     •  '       "            "         Ibs  

"     "  D.H.P.,    "         cu.  ft  

"     "        "          "          Ibs  

•                           HEAT  PER  HOUR. 

Supplied  B.T.U. 

'  '                                                         .              Per  cent 

Absorbed  by  jacket-water  BTU 

'  '          '  <            '  '             Per  cent 

Exhausted  B.T.U. 

"         Per  cent 

Thermal  equiv   Ind  work                                    BTU 

"             "         "         '  '         .                 .         Per  cent 

• 

Radiation  and  loss        ..        .          BTU 

"           "       "                                              Per  cent 

«           "      "    DHP      "     " 

EFFICIENCIES,   PER  CENT. 

Thermal  from  I  H  P 

"           "     DHP                          

Carnot     Tm**~Tm'm 

J.  max 

*  At  32°  F.  and  14.7  Ibs.  absolute  pressure  per  sq.  in. 


CHAPTER  XXIV. 
AIR-COMPRESSORS. 

466.  Types  of   Compressors. —  Compressed    air  is  used 
extensively   in   the   various    mechanical   arts   for   the   purposes 
of  ventilation,  operation  of  motors,  tools,  the  transmission  of 
energy,  and  refrigeration.     There  are  three  types  of  air-compres- 
sors, viz. :   (i)  the  piston,  (2)  the  rotary,  and  (3)  the  centrifugal 
blower  or  fan.     They  may  be  driven  by  any  convenient  motive 
power,  as,  for  instance,  a  steam-engine,  as  shown  in  Fig.  325, 
a  water-wheel,  an  electric  motor,  etc. 

467.  Piston    Air-compressor.  —  In  this   machine   the   air 
is  compressed  by  a  piston  moving  in  a  cylinder  which  is  pro- 
vided with  inlet-   and  exit-valves.     The  valves  are   commonly 
operated  automatically  by  the  entering  or  discharging  air,  but 
in  some  cases  they  are  positively  operated  by  mechanical  means. 
A    section    of   an    air-compressor    cylinder   with    automatically 
operated  valves  of   the  poppet-type  is  shown  in  Figs.  323  and 
324.     In  Fig.   323   the  inlet- valves  are  shown  in   the  cylinder 
walls,  in  Fig.  324  they  are  shown  in  the  piston,  which  commu- 
nicates with   the  air  by  the  hollow  inlet-pipe,  E. 

The  air  may  be  compressed  in  one  or  more  cylinders  through 
which  it  is  passed  in  succession.  When  the  compressor  has 
one  cylinder  only,  it  is  described  as  a  one-stage  or  simple  com- 
pressor; when  two  cylinders,  as  a  compound  or  two-stage  com- 
pressor; when  three  cylinders,  as  a  three-stage  compressor,  etc. 

A  section  of  a  two-stage  compressor  with  mechanically  oper- 
ated inlet-valves,  driven  by  a  direct- connected  steam-engine,  is 
shown  in  Fig.  325.  The  air  is  first  drawn  into  the  large 

720 


A  IK-  COMPRESSORS. 


721 


cylinder,  C,  compressed  to  an  intermediate  pressure,  after  which 
it  is  delivered  into  the  intercooler,  B,  thence  to  the  small  cylinder, 
C,  when  the  compression  is  completed. 


FIG.  323.— AIR-COMPRESSOR  CYLINDER. 


To  remove  the  heat  generated  during  compression,  the  cylin- 
ders are  usually  jacketed  with  water,  and  in  multiple-stage  com- 
pressors the  air  is  further  reduced  in  temperature  by  passing 


PIG.  324. — THE  INGERSOLL  AIR-COMPRESSOR. 

through  a  vessel  called  an  intercooler,  which  is  located  between 
the  cylinders,  and  through  which  water  is  made  to  circulate  in 
numerous  small  pipes. 


722 


EXPERIMENTAL   ENGINEERING. 


E§  467 


468.]  AIR-COMPRESSORS. 


723 


Water-jacket  cooling  is  very  inefficient,  and  for  that  reason 
water  is  sometimes  sprayed  directly  into  the  cylinder.  This 
method  of  cooling  is  objectionable  because  of  the  moisture 
added  to  the  air  which  may  be  converted  into  steam  by  the  heat 
of  compression. 

The  clearance  space  in  the  air-compressor  cylinders  should 
be  as  small  as  possible,  since  this  will  be  filled  during  the  for- 
ward stroke  with  compressed  air  at  full  pressure,  which  will 
expand  to  atmospheric  pressure  on  the  return  stroke  of  the  pis- 
ton, and  thus  reduce  the  space  available  for  the  entering  charge. 

Air-cooling  is  sometimes  employed  for  removing  the  extra 
heat  where  the  compressor  cylinders  are  exposed  to  a  draught 
of  air,  as,  for  instance,  those  used  on  locomotives  for  operating 
the  air-brakes. 

Piston  air- compressors  are  employed  when  high  air  pressures 
are  required,  but  in  some  cases  are  used  for  low  pressures,  as,  for 
instance,  for  blowing-engines  for  supplying  the  necessary  air  for 
steel  furnaces.  These  are  usually  of  the  piston  type,  although 
the  pressures  rarely  exceed  20  pounds  per  square  inch. 

468.  Rotary  Blowers.  —  Rotary  blowers  consist  of  two 
revolving  blades,  or  pistons,  of  such  form  as  to  drive  the  air  for- 


FIG.  326. 

ward  and  maintain  contact  with  the  walls  of  the  surrounding 
case  and  with  each  other  so  as  to  prevent  leakage  and  a  back- 
ward flow  of  the  compressed  air.  A  great  variety  of  forms  are 


724 


EXPERIMENTAL   ENGINEERING. 


[§ 


made,  one  of  which  is  shown  in  Fig.  326.    These  blowers  are  suited 

for  a  pressure  which  does  not  exceed  20  pounds  per  square  inch. 
469.  Centrifugal   Fans,  or   Blowers. — In  the  centrifugal 

fan,  or  blower,  particles  of  air  are  moved  radially  by  the  centrifugal 

force  set  up  by  the  blades  of  a  revolving  wheel,  which  produces 
a  pressure  head  proportional  to  the 
square  of  the  velocity  of  the  circumfer- 
ence. Two  types  are  in  commmon  use: 
(i)  the  propeller  or  disc  form  shown  in 
Fig.  327,  in  which  the  current  of  air 
travels  through  the  fan  parallel  to  the 
axis,  and  (2)  the  blower  type  shown  in 
Fig.  328,  in  which  the  air  is  received  at 
the  center  of  the  wheel  and  discharged 

at  the  periphery  into  a  casing  or  chamber  from  which  it  may 

be  conveyed  by  pipes. 

The  disc  fan  is  not  adapted  to  move  air  against  any  sensible 

pressure,  and  is  generally  employed  for  circulating  large  volumes 

of  air. 


FIG.  327. 


FIG.  328. 


The  blower  type  of  fan  is  well  adapted  for  pressures  which 
do  not  exceed  J  pound  per  square  inch.  By  arranging  blower 
fans  in  series,  so  that  a  fan  working  at  low  pressure  supplies 
air  to  one  working  at  higher  pressure,  the  air  can  be  compressed 
economically  to  a  pressure7  of  several  pounds  per  square  inch. 


§  47°-]  AIR-COMPRESSORS. 


725 


470.    Measurement    of    Pressure    and  Velocity.—  The 

pressure  of  compressed  air  is  measured  by  a  suitable  type  of 
pressure  gauge  or  manometer  as  described  in  Chapter  XI.  When 
the  pressure  is  high  it  is  usually  expressed  in  pounds  per  square 
inch  or  in  atmospheres;  when  low  it  is  usually  expressed  in 
fractions  of  a  pound,  or  in  ounces  per  square  inch,  or  in  inches 
of  water  or  mercury.  The  relations  of  these  units  are  shown 
in  the  table  on;,  page  336. 

The  velocity  of  air  may  be  measured  directly  by  use  of  the 
anemometer  described  in  Art.  233,  or  indirectly  by  use  of  the 
Pitot  tube  described  in  Arts.  222  and  223.  The  velocity  may 
be  computed  from  the  formula 


in  which  v  =  velocity  in  feet  per  second  of  the  air  impinging 
against  the  Pitot  orifice,  h,  the  reading  of  the  anemometer,  r,. 
the  ratio  of  the  density  of  the  liquid  in  the  manometer  to  that 
of  the  air,  c,  a  coefficient  to  be  found  by  calibration. 

When  the  air  is  at  32°  F.  and  under  a  barometric  pressure 
of  29.92  inches,  and  dry,  one  inch  of  water  column  will  balance 
60.2  feet  of  air,  consequently  for,  that  case  r  =  6o.2. 

The  density  of  air  increases  directly  with  the  absolute  pres- 
sure, and  inversely  as  the  absolute  temperature,  it  varies  also 
with  moisture  so  that  corrections  are  required  for  pressure,  tem- 
perature, and  the  amount  of  moisture. 

An  extended  use  of  the  Pitot  tube  by  the  author  has  shown 
its  accuracy  for  measurements  of  the  velocity  of  air  currents. 
The  coefficient  c  will  vary  with  the  shape  of  the  openings;  with 
a  tube  of  the  form  shown  in  Fig.  144,  having  an  internal  diam- 
eter of  about  J  inch  and  an  opening  at  C  of  TV  inch,  c  will  be 
unity  without  sensible  error.  A  straight  tube  with  an  opening 
in  the  side  will  give  the  same  results  as  the  bent  nozzle  shown 
in  Fig.  144  and  is  much  easier  made. 

The  Pitot  tube,  shown  in  Fig.  146,  may  be  arranged  to  give 
a  value  of  c  considerably  higher  than  unity;  for  instance,  if  the 


726  EXPERIMENTAL   ENGINEERING.  [§  470. 

end  of  the  straight  tube  D  is  closed,  and  an  opening  made  about 
J  inch  above  the  lower  end  at  right  angles  to  the  directions  of 
the  current,  the  value  of  c  may  reach  1.4.  With  the  opening 
in  one  tube  pointing  down-stream  and  in  the  other  up-stream 
the  value  of  c  will  equal  about  1.25. 

In  case  the  Pitot  tube  is  used  for  determining  the  velocity 
in  a  pipe  or  channel,  readings  should  be  taken  at  regular  intervals 
of  depth.  The  mean  velocity  may  be  determined  with  little 
error  by  multiplying  the  velocity,  which  corresponds  to  each 
reading,  by  the  area  of  section  of  which  it  forms  the  center,  and 
dividing  the  sum  of  these  products  by  the  area  of  section.  By 
constructing  a  velocity  diagram,  by  laying  off  the  velocities  as 
abscissa  to  ordinates  corresponding  to  depths,  the  mean  velocity 
can  also  be  obtained  by  dividing  the  area  as  obtained  with  a 
planimeter  by  this  total  depth  or  diameter. 

The  velocity  of  air  can  be  computed  with  accuracy  by  measur- 
•  ing  the  amount  of  heat  required  to  warm  it  through  an  observed 
range  of  temperature,  as  follows: 

Let  W  represent  the  weight  of  air  flowing  in  a  given  time, 
v  its  volume  in  cubic  feet,  d  its  weight  per  cubic  foot  or  density, 
s  its  specific  heat  (which  is  constant  and  equals  0.238),  V  its 
velocity,  F  the  area  of  section  of  moving  air  in  square  feet,  t 
its  initial  temperature,  tr  its  temperature  after  being  heated, 
and  H  the  heat  of  known  amount  in  heat-units  applied  to  warm 
the  air  from  temperature  /  to  tf. 

Since  the  heat  absorbed  by  air  is  equal  to  the  product  of 
its  weight,  into  its  specific  heat,  into  its  rise  of  temperature, 


but  since 

v=FV, 


from  which  the  velocity 

H 


V 


F3s(t'-t)- 


§47IJ-  AIK-COMPKESSORS. 

A  method  of  making  the  measurements  as  above  is  illus- 
trated in  Fig.  329,  in  which  the  air  enters  the  pipe  or  channel 
at  A  and  is  discharged  at  D.  Means  for  heating  the  air,  which 
may  be  either  a  steam  or  electric  radiator,  is  to  be  supplied.  If 
a  steam  radiator,  the  heat  discharged  is  computed  from  measure- 
ments of  the  weight  and  temperature  of  the  condensed  steam, 
the  heat  entering  from  measurements  of  pressure,  quality,  and 
weight  by  methods  already  explained.  The  heat  taken  up  by 
the  air  is  the  difference  of  that  entering  and  discharged.  If  an 
electric  heater  is  used,  the  electric  energy  disappearing  is  measured 
and  reduced  by  computation  to  heat-units.  The  means  for 
heating  should  be  of  such  form  as  to  heat  the  air  uniformly,  which 
can  often  be  accomplished  by  adopting  a  suitable  form  of  heater. 


FIG.  329.— DIAGRAM  OF  METHOD  OF  MEASURING  VELOCITY  OP  AIR. 

The  temperature  of  the  entering  and  discharge  air  should 
be  taken  at  sufficiently  numerous  points  in  the  cross-section  to 
make  the  average  results  accurate,  and  the  thermometers  should 
be  protected  from  radiant  heat.  The  average  temperature  should 
also  be  measured  at  the  section  where  the  velocity  is  to  be  com 
puted.  It  may  be  desirable,  in  case  extreme  accuracy  is  required, 
to  compute  the  weight  of  moisture  in  the  air  from  observations 
with  the  dry-  and  wet-bulb  thermometer. 

Direct-reading  instruments,  as  the  anemometer  or  Pitot  tube, 
can  be  calibrated  by  comparison  of  numerous  readings  in  a 
section  with  the  velocity  obtained  as  explained  above. 

471.  Effect  of  Clearance.— The  effect  of  clearance  in 
reducing  the  effective  volume  of  the  compressor  cylinder  may 


728  EXPERIMENTAL   ENGINEERING.  [§  472- 

be  worked  out  from  the  relations  of  pressure,  volume,  and  tem- 
perature, as  given  in  equation  (4)  of  Art.  462. 
It  is  readily  shown  from  equation  (4)  that 


Vl="2Vft 

in  which  -v2  is  the  clearance  volume  in  cubic  feet,  which  is  filled 
with  air  compressed  to  a  pressure  of  p2  pounds  per  square  foot 
at  each  stroke,  Vi  is  the  volume  after  the  same  air  has  expanded 
to  a  pressure  of  pi  pounds. 

The  loss  expressed  in  percentage  of  the  cylinder  displace- 
ment can  be  obtained  by  subtracting  the  volume  at  end  of  com- 
pression stroke  from  that  at  the  beginning,  which  was  occupied 
by  the  same  mass  of  air,  and  dividing  by  the  volume  of  piston 
displacement.  If  c  =  per  cent,  of  clearance,  and  100  =  piston 
displacement,  then  will 


**      M  x  „     r-          /A  \  i 

\Pl  I  C  I  p2\ 

percentage  loss  of  volume = — : = 1  i  —  (  j-  ) 

L  Vjt*/ 

472.  Loss  of  Work  Due  to  the  Rise  of  Temperature. — 

The  increase  of  temperature  in  adiabatic  compression  causes  a  loss 
of  work.  It  can  be  computed  by  equation  (6),  Art.  462.  The 
cooling  of  the  air  by  the  water-jacket  is  so  slight  that  the  actual 
compression  curve,  as  shown  on  an  indicator  diagram,  is  usually 
very  nearly  coincident  with  the  adiabatic  curve.  This  causes 
a  decided  loss  of  work  which  is  shown  clearly  by  the  diagram 
Fig.  330,  which  represents  the  work  performed  in  compressing 
air  in  various  ways. 

Thus  the  area  of  the  diagram  ABCFG  represents  the  work 
of  compressing  a  given  volume  of  air  isothermally,  from  o  pressure 
by  gauge  (14.7  pounds  absolute)  to  120  pounds  by  gauge  (134.7 
pounds  absolute).  The  area  of  the  diagram  ADEFG  represents 
in  a  similar  manner  the  /work  done  in  compressing  the  same 
volume  of  air  through  the  same '  pressures  adiabatically.  The 


§  473-] 


A IR-  COMPRESSORS. 


729 


difference  in  these  areas  shows  the  loss  in  work  due  to  the  rise 
of  temperature  during  adiabatic  compression. 

The  diagram  ADBHFG  represents  the  compression  of  the 
same  volume  in  a  two-stage  or  compound  compressor,  with  an 
intercooler.  In  this  case  the  air  is  compressed  adiabatically 


E   H    C 


from  A  to  D  in  the  first  cylinder,  the  excess  of  heat  is  removed 
by  the  intercooler,  reducing  the  volume  from  D  to  B;  it  is  then 
compressed  adiabatically,  B  to  H,  in  the  second  cylinder.  The 
difference  in  area  DBHE  represents  the  saving  in  work  by  the 
two- stage  or  compound  compressor  as  compared  with  the 
single  compressor. 

473.  Theory  of  the  Centrifugal  Blower. — In  the  opera- 
tion of  the  centrifugal  blower  the  air  is  compressed  so  slightly 
that  the  change  in  pressure,  volume,  or  temperature  may  be 
neglected  in  ordinary  cases  without  producing  sensible  error. 

For  this  condition  the  volume  Q  recorded  will  be  directly 
proportional  to  the  number  of  revolutions,  n\  the  pressure  pro- 


73°  EXPERIMENTAL   ENGINEERING.  [§  474. 

duced,  p,  to  the  square  of  the  number  of  revolutions;  the  work 
required,  W,  to  the  cube  of  the  number  of  revolutions. 

A  full  discussion  of  this  theory  will  be  found  in  the  author's 
work  on  "  Heating  and  Ventilating  of  Buildings." 

The  following  formulae  are  nearly  correct: 

Pressure  producedy 

h, 


3600 


in  which  ^2  =  pressure  produced  in  inches  of  water,  u=  velocity 
of  tips  of  blades,  ft.  per  min.,  F=  area  of  outlet,  -Fi  =  area  of 
inlet. 

Volume  discharged, 

Q=KDdbn, 

in  which  D  =  outer  diameter  of  fan-  wheel,  d  =  inner  diameter 
of  fan-  wheel  in  feet,  b  =  breadth  of  fan  at  tips  in  feet,  n  =  num- 
ber of  revolutions,  K  =  a  constant  for  a  given  pressure. 

When  db  =  o.2$  D2t  which  is  the  usual  proportion,  K  =  0.6 
when  h2=%,  ^  =  0.5  when  /*3  =  i,  #=0.4  when  &2  =  2,  approxi- 
mately. 

The  'Work  required. 


In  which  K'  is  a  coefficient  which  decreases  as  the  pressure 
increases. 

474.  Test  of  Air-compressor.  —  The  following  tables 
suggest  the  observations  that  are  needed  for  a  complete  test 
of  an  air-compressor. 

Air  -compressor  built  by  ...................................  at  ............... 

Tested  at  ..........................................  Date  ..............  190 

Cards  integrated  by  ...........  /  .................  Checked  by  ................ 

Scale  of  springs.  .  .  .Steam,  left.  .  .  .Steam,  right..  .Air  high  press.  .  .  Air  low  press. 


§  474-1  AIR-COMPRESSORS.  73! 


DIMENSIONS. 

STEAM-CYLINDERS. 
£«/'•  Right. 

Dia.  in  inches Dia.  in  inches 

Area  in  sq.  in Area  in  sq.  in 

Dia.  piston  rod  in  in Dia.  piston  rod  in  in.  . . . 

Area  in  sq.  in Area  in  sq.  in 

Length  of  stroke  in  feet Length  of  stroke  in  feet. 


Piston  Displacement  in  Cubic  Feet. 
Head Crank Head. .  .  .Crank.. 


Volume  in  Clearances  Per  Cent. 

Head Crank Head Crank., 

Barometer  inches Tempt,  room 

Per  cent,  moisture  in  air  . . 


AIR-CYLINDERS. 
High  Pressure.  Low  Pressure. 

Dia.  in  inches Dia.  in  inches 

Area  in  sq.  in Area  in  sq.  in 


Diameter  of  Piston-rods  in  Inches. 
Head..  ..Crank..  Head..  ..Crank., 


Area  of  Piston-rods  in  Square  Inches. 

Head Crank Head Crank.. . 

Length  of  stroke  in  ft Length  of  stroke  in  ft 


Piston  Displacement  in  Cubic  Feet. 
Head Crank Head Crank.. . 

Volume  of  Clearances  per  cent. 
Head.  .  ..Crank..  Head Crank... 


Revolutions: 

Continuous  counter 

Per  minute 

Boiler  or  steam -chest  pressure. 

Reservoir  pressure,  air 

Nozzle  pressure,  air 


732  EXPERIMENTAL   ENGINEERING.  [§  475' 

Temperatures: 

Entering  low-pressure  cylinder,  air 

Leaving  low-pressure  cylinder,  air 

Entering  high-pressure  cylinder,  air 

Leaving  high-pressure  cylinder,  air 

Nozzle,  air 

Outside,  air 

Calorimeter,  steam 

Jacket-water: 

Entering  cooler 

Leaving  cooler  or  entering  low-pressure  cylinder 

Leaving  low-pressure  cylinder  or  entering  high-pressure  cylinder. 

Leaving  high -pressure  cylinder 

Weight  of  jacket-water,  pounds 

Weight  of  condensed  steam,  pounds. 

Heat  absorbed  by  jacket-water: 

From  cooler 

From  low-pressure  cylinder 

From  high-pressure  cylinder 

Total 

Quality  of  steam,  per  cent 

Mechanical  efficiency,  per  cent 

Pounds  of  steam  per  I.H.P.  per  hour 

Cubic  feet  of  air  per  piston  displacement  at  standard  conditions 

Cubic  feet  of  air  delivered  as  per  nozzle  at  standard  conditions 

Per  cent  slip 

Pounds  of  air  compressed  per  hour,  standard  conditions 

Efficiency  of  compressor 

Volumetric  efficiency 

Total  efficiency  of  machine 

475.  Test  of  Centrifugal  Blower.— The  following  table 
suggests  the  quantities  to  be  observed  for  a  test  of  a  centrifu- 
gal blower  driven  through  a  transmission  dynomometer: 

TEST  OF  CENTRIFUGAL  BLOWER. 


Kind " Date 

Form  of  blades Discharge  area 

Diameter  of  fan Temperature  of  room 

Width  of  fan Barometer 

Form  of  inlet Anemometer  diameter 

Inlet  area coefficient .... 

Formula Weight  of  air  per  cubic  foot. 

Maker Moisture  in  air,  per  cent.  .  . 

Made  by 


§  475-] 


A IR-  COMPRESSORS. 


733 


No.  of  Run  

j 

Time  begun  

Time  ended  

Length  of  run  

Duration  in  minutes  

Tachometer  

R.P.M.  of  fan  

Air  pressure  per  square  inch,  ounces  

Pressure  head  in  water,  inches  

Anemometer  readings,  inlet  

Temperature  entering  heating-box  

'  '            leaving                        

Heat  units  absorbed 

Weights  discharged  per  second       .  .        ... 

Velocity  of  air  feet  oer  second     .              .  . 

CHAPTER  XXV. 
MECHANICAL  REFRIGERATION. 

476.  Introduction.  —  Systems  of  mechanical  refrigeration 
are  extensively  employed,  either  for  maintaining  a  low  tempera- 
ture or  for  the  manufacture  of  ice,  and  some  practical  acquaint- 
ance with  the  processes  successfully  employed  is  of  importance 
to  the  mechanical  engineer. 

The  refrigerating  machine  is  a  species  of  heat-engine,  in 
which,  by  means  of  mechanical  work,  heat  is  transferred  from 
one  substance  to  another,  the  effect  being  to  reduce  or  lower 
one  temperature  and  increase  the  other.  The  ideal  machine 
for  this  work  is  the  reversible  engine  operating  in  a  Carnot 
cycle  in  a  reverse  or  backward  direction  from  that  of  the  steam- 
engine,  the  hot-air  engine,  and  other  heat-engines. 

The  following  illustrations  will  render  this  statement  clear. 
Carnot's  reversible  engine,  when  working  as  a  heat-engine, 
takes  from  the  source  of  heat  a  quantity,  H,  of  which  it  changes 
a  part,  AW,  into  mechanical  energy,  and,  as  there  are  no  losses, 
rejects  the  remainder,  He,  to  the  refrigerator,  b.  We  have  for 
the  efficiency,  since  H  —  He  =  AW, 

AW    H-He     T-T, 


If  the  engine  be  run  backward  so  as  to  describe  its  cycle  in  the 
reverse  order,  it  takes  heat  from  the  refrigerator,  adds  to  it  the 
heat  equivalent  of  the  work  of  the  cycle,  and  delivers  the  same 
to  the  source  of  heat  and  thus  becomes  a  refrigerating  machine. 

734 


UNIVERSITY 

OF 


§477-]  MECHANICAL   REFRIGERATION.  735 

Th_-  efficiency  becomes  for  this  case 


(ft) 


~7hich  is  called  the  "  Thermodynamic  Efficiency." 

In  a  heat-engine  operating  in  a  Carnot  cycle  the  working 
substance  is  first  compressed  adiabatically,  in  which  case  its  tem- 
perature rises;  second,  it  is  compressed  isothermally,  in  which 
case  the  temperature  remains  constant,  which  requires  that  the 
heat  generated  be  absorbed  and  removed  ;  then  it  is  allowed  to 
expand,  adiabatically  and  isothermally,  until  the  working  sub- 
stance is  in  its  orginal  condition.  During  the  last  operation 
heat^  must  be  supplied  the  working  substance  to  maintain  a  con- 
stant temperature. 

The  equations  expressing  the  relations  between  pressure, 
volume,  and  temperature  during  compression  and  expansion  of 
a  perfect  gas  are  given  in  Art.  462,  and  should  be  referred  to 
in  connection  with  the  investigation  of  the  refrigerating  machine. 

477.  Relation  of  Mechanical  Work  to  Heat  Transfer.— 
The  cycle  of  heat  exchanges  for  a  refrigerating  machine  of  any 
class  can  be  written  for  one  unit  of  weight  as  follows: 

Let  H  =the  original  heat  of  the  working  substance;  Hl  =the 
heat  at  end  of  compression,  were  none  removed  by  cooling  or 
loss;  H2  =  the  heat  at  end  of  compression  after  cooling;  H3  = 
the  heat  at  end  of  expansion,  supposing  none  removed  for  cool- 
ing purposes  ;  K  =  the  heat  taken  up  by  the  cooling  liquid  during 
compression  and  condensation  ;  KI  =  the  heat  taken  up  by  the 
substance  during  refrigeration  ;  A  Wc  =  the  mechanical  work  of 
compression;  AWe  =  the  mechanical  work  done  during  expansion. 
We  have  then  the  following  equations,  expressed  in  heat-units, 
supposing  no  radiation  or  cylinder  losses  to  exist: 

During  compression,         H  +AWc=Hi]      .    .     .  (i) 

Cooling  or  condensation,  Hi  —  K=H2',     ....  (2) 

During  expansion,            H2-AWf=H3;      ...  (3) 

Refrigeration,                    H3-{-Ki=H  .....  (4) 


736  EXPERIMENTAL   ENGINEERING.  [§  478. 

In  the  above  equations  K±  is  the  measure  of  the  refrigerating 
value,  since  it  is  the  heat  absorbed  at  the  lowest  temperature, 
and  by  substituting  in  the  above  equations  we  find  that 


-We).      .     (5) 

That  is,  the  possible  heat  transfer  or  refrigeration  in  the 
perfect  machine  is  equal  to  the  heat  carried  off  by  the  cool- 
ing and  condensing  water,  K,  diminished  by  the  difference  of 
the  heat  equivalent  of  the  work  done  in  compression  and  in 
expansion. 

By  transposing  in  equation  (5), 

A(Wc-We)=K-K1  .......     (6) 

That  is,  the  mechanical  work  in  the  perfect  refrigerating 
machine  is  equivalent  to  the  heat  removed  by  cooling  and 
condensing  less  that  transferred  from  refrigerator  to  source  of 
heat. 

478.  The  Efficiency  of  the  Refrigerating  Machine.—  It 
has  previously  been  shown,  by  equation  (5),  that,  supposing  no 
losses  in  the  machine,  the  heat,  KI,  received  from  the  refrigera- 
tor, increased  by  the  heat  equivalent  of  the  mechanical  work 
(AWC  —  We),  equals  the  heat  discharged,  K.  That  is,  represent- 
ing the  net  mechanical  work  by  A  Wt 

AW=A(Wc-We)=K-Kl.     \     ....     (7) 

If    the   heat   carried  off  in  the  condensing  water  cannot  be 
utilized,  the   highest   possible    efficiency   of   the    system  is    the 
'ratio  of  the  refrigeration  K±  to  the  work  A(Wc  —  We)\    that  is, 
the  possible  efficiency  E  becomes,  for  that  case, 


___  xov 

A(W-  wyK-Ki      '    '    *    '    * 


§478-]  MECHANICAL   REFRIGERATION.  737 


If  W  is  expressed  in  foot-pounds,  A  =T|^;   if  W  is  expressed  in 
horse-power,  A  =42.42. 

The  actual  refrigerating  machine  not  being  perfect,  the 
mechanical  work  expended,  AW,  is  less  than  the  increase  in 
the  heat  transferred,  and  we  should  have  for  the  actual  machine 


AW<K-K1 


The  amount  of  refrigeration  or  cold  produced  is  the  quantity 
KI,  since  that  is  the  heat  taken  from  the  colder  body  and  trans- 
ferred to  the  hotter.  The  object  of  the  refrigerating  process 
is  the  removal  of  the  heat  K^  so  that  this  may  be  considered 
the  useful  work.  The  total  energy  supplied  is  the  mechanical 
work  of  compression.  The  efficiency  of  the  actual  machine 
is  the  ratio  of  the  useful  work  to  the  total  energy  expended, 
and  consequently  is 


The  thermodynamic  efficiency  of  a  refrigerating  machine 
operating  in  a  Carnot  cycle,  as  given  in  equation  (6),  is  the  abso- 
lute temperature  (I1!  =  460  +  *),  divided  by  the  rise  in  temperature 
(T  —  Ti).  The  ratio  of  the  actual  efficiency  to  this  quantity,  often 
called  the  "  Coefficient  of  performance,"  E3,  is  a  valuable  standard 
of  comparison: 


The  thermodynamic  efficiency  of  an  engine  working  in  a 
Carnot  cycle  is  less  than  one,  hence  that  in  the  refrigerator  cycle 
must  in  every  case  be  correspondingly  greater  than  one.  It 
mil0*,  reach  its  limit,  as  noted  by  discussion  of  equation  (9),  when 
T-Ti  has  the  least  value,  or  when  this  value  approaches  o, 
in  which  case  the  limiting  value  of  the  efficiency  approaches 
infinity. 


738  EXPERIMENTAL  ENGINEERING.  [§  479- 

The  expression  asserts  what  is  certainly  true,  that  for  a  given 
expenditure  of  work  the  output  or  energy  discharged  is  much 
greater  than  that  put  in,  or,  from  such  a  standpoint,  the  machine 
has  a  greater  efficiency  than  unity.  (See  test,  page  747.) 

Considering  the  refrigerating  machine  as  the  heat-engine 
reversed,  it  is  noted  that  in  the  heat-engine  the  amount  discharged 
by  the  exhaust  is  very  great.  In  the  case  of  a  refrigerating  machine 
heat  is  received  at  the  lower  temperature;  in  other  words,  flows 
in  at  the  exhaust-pipe,  is  increased  by  the  mechanical  equiva- 
lent of  the  work  done,  and  the  total  is  discharged  at  a  higher 
temperature. 

There  is  no  reason  why  KI  should  not  be  many  times  greater 
than  AW\  in  fact  they  stand  in  no  closer  relation  in  a  theoretical 
way  than  the  heat  discharged  in  the  exhaust  does  to  that  trans- 
formed into  work  in  the  steam-engine. 

479.  Negative  Heat  Losses. — In  the  case  of  the  steam- 
engine,  heat  is  taken  from  the  steam  to  warm  up  the  cylinder 
and  keep  it  warm,  giving  rise  to  the  loss  known  as  cylinder  con- 
densation;   in  addition,  heat   is   radiated  into  the  surrounding 
space.     These  losses  reduce  the  working  value  of  the  steam  20 
to  50  per  cent.     In  the  refrigerating  machine  similar  losses  of  an 
opposite  and  negative  character  exist. 

The  effect  of  the  negative  heat  losses  would  be  as  follows:  In 
the  compression  the  cylinder  becomes  heated,  and  this  heat  is  only 
partially  discharged  to  the  condenser;  the  remainder  keeps  the 
cylinder  warmer  than  it  otherwise  would  have  been  even  at  the 
end  of  expansion.  This  heat  in  the  cylinder  walls  warms  and 
expands  the  entering  gas  as  it  flows  in,  and  has  the  effect  of 
reducing  its  capacity,  being  thus  exactly  opposed  in  character, 
but  otherwise  similar  to  the  loss  of  heat  which  occurs  with  a 
heat-engine.  During  a  great  part  of  the  revolution  the  tem- 
perature in  the  cylinder  is  below  that  of  the  room,  in  which  case 
heat  will  flow  from  the  surrounding  room  into  the  working 
cylinder. 

480.  The    Working    Fluid.  — The    working    fluids    are 
usually  selected  among  the  fixed  gases,  or  from  liquids  whose 


§480.]  MECHANICAL   REFRIGERATION. 


739 


boiling-point  is  very  low.  The  principal  freezing  machines 
use  either  air,  ammonia,  or  carbon  dioxide,  but  water-vapor 
or  steam  may  be  employed.  The  properties  desirable  in  a  vapor 
or  gas  to  be  used  for  refrigeration  purposes  are: 

First,  latent  heat  of  vaporization  large,  which  will  permit 
the  use  of  a  small  amount  of  working  substance,  since  the  capacity 
of  a  given  weight  to  transfer  heat  is  proportional  to  this  quantity. 

Second,  freezing-point  low;  as  the  capacity  to  absorb  heat 
is  a  function  of  difference  of  temperature,  the  lower  the  tem- 
perature at  which  a  given  substance  will  remain  liquid,  the 
greater  the  capacity  for  a  given  weight,  and  also  the  lower  the 
temperature  which  can  be  attained.  It  is  hardly  necessary  to 
mention  that  a  solid  body  cannot  be  pumped,  and  that  as  soon 
as  it  solidifies  it  becomes  useless  for  refrigeration. 

Third,  considerable  change  in  temperature  for  moderate 
increase  of  pressure.  In  addition,  commercial  considerations 
render  it  necessary  that  the  liquid  shall  be  reasonable  in  cost, 
and  shall  be  one  that  will  not  attack  or  destroy  the  machinery  used. 

Water  Vapor. — A  steam-engine,  run  backward  or  as  a  com- 
pressor, with  steam  as  a  working  substance,  would  convey  heat 
from  a  lower  to  a  higher  temperature  at  the  expense  of  the  net 
work  of  compression.  In  this  case,  however,  the  lower  limit 
of  temperature  could  not  be  much  less  than  that  of  the  freezing- 
point  of  water.  In  any  case,  when  expansion  occurred,  an 
amount  of  heat  equivalent  to  the  latent  heat  of  liquefaction 
would  be  absorbed  from  the  surrounding  medium. 

While  steam  or  vapor  of  water  has  a  very  high  latent  heat, 
it  becomes  solid  at  a  comparatively  high  temperature  (32°  F.), 
and  (onsequently  is  not  well  suited  for  use  in  a  refrigerating 
machine. 

In  a  pressure  below  that  of  the  atmosphere  considerable 
vapor  is  given  off,  and  practical  ice-making  machines  have  been 
built  to  work  under  such  conditions.  These  machines  are  known 
as  water-vapor  vacuum  machines. 

Air.— An  air-compressor  would  transfer  heat,  as  already 
explained,  by  the  mechanical  work  of  compression. 


740 


EXPERIMENTAL   ENGINEERING 


[§  480. 


Anhydrous  Ammonia. — This  material  is  produced  as  a  waste 
product  in  various  industries  in  an  impure  form,  and  it  •  needs 
only  to  be  purified  and  separated  from  water  to  fit  it  for  refrig- 
eration purposes. 

The  material  exerts  r  o  corrosive  action  on  iron,  and  for  this 
reason  does  not  affect  in  any  degree  the  ordinary  machinery 
for  conveying  or  compressing  it. 

It  will,  however,  attack  brass  or  copper  and  must  be  kept 
from  contact  with  these  metals. 

Its  important  properties  are  given  in  the  following  table: 

At  atmospheric  pressure  boiling-point  is  28.6°  F.  Weight 
at  32°  F.,  combined  with  water,  is  0.6364,  or  39.73  pounds  per 
cubic  foot,  or  5.3  pounds  per  gallon.  Specific  heat  is  0.50836. 
Latent  heat  at  32°  F.  is  about  560  B.T.U. 

The  following  table,  giving  the  principal  properties  for  each 
10  degrees  of  temperature  on  the  Fahrenheit  scale,  is  taken 
from  Professor  Wood's  Thermodynamics. 


PROPERTIES  OF  SATURATED  ANHYDROUS  AMMONIA. 


Degrees 
F. 

Pressure 
Absolute 
per 
Sq.  Inch. 

Total 
Latent 
Heat. 

External 
Latent 
Heat. 

Internal 
Latent 
Heat. 

Volume  of 
i  Pound 
of  Vapor 
Cu.  Ft. 

Volume  of 
i  Pound 
of  Liquid 
Cu.  Ft. 

Weight  of 
i  Cu.  Ft. 
in  Pounds. 

r 

apw 

5 

-40 

10.69 

579-67 

48.25 

S31  -42 

24.38 

0.0234 

0.0411 

-3° 

14.13 

573-69 

48.85 

524-84 

18.67 

0.0237 

0-0535 

—  20 

18.45 

567.67 

49.44 

518.23 

14.48 

o  .  0240 

o  .  0690 

—  10 

23-77 

561.61 

5°-°5 

5ri-56 

11.36 

o  .  0243 

o  .  0880 

o 

3°-37 

555-5 

51-38 

504.12 

9.14 

0.0246 

o.  1094 

IO 

38.55 

549-4 

S*-*3 

498.22 

7.20 

o  .  0249 

0.1381 

20 

47-95 

543  -IS 

51-65 

49I-5° 

5-82 

0.0252 

o.  1721 

30 

59-4i 

536.92 

52.02 

484.90 

0.0254 

O.2III 

40 

73.00 

530-63 

52.42 

478.21 

3.88 

0.0257 

0.2577 

5° 

88.96 

524-3 

52.82 

471.44 

3-21 

0.0260 

°-3II5 

60 

107.60 

5*7.93 

53-21 

464.76 

2.67 

0.0265 

0-3745 

70 

129.21 

5H-52 

53-67 

457-95 

2.24 

0.0268 

0.4664 

80 

154.11 

504.66 

53-96 

45°  -75 

1.89 

0.0272 

0.5291 

9° 

182.8 

498  .  i  i 

54.28 

443  •  7° 

1.61 

0.0274 

0.6211 

100 

215.14 

491*5 

54-54 

437-35 

1-36 

0.0279 

0-7356 

§  481.]  MECHANICAL   REFRIGERATION.  74! 

481.  The  Air-refrigerating  Machine.— In  this  case  air 
is  compressed  by  mechanical  means,  and  the  heat  which  is 
generated  is  removed  by  a  water-jacket,  so  that  the  temperature 
after  compression  is  approximately  the  same  as  at  the  beginning. 
It  is  then  permitted  to  expand  adiabatically  against  a  resistance 
so  as  to  perform  mechanical  work,  and  in  so  doing  falls  in  tem- 
perature. It  can  afterward  take  up  heat  from  the  surrounding 
bodies.  It  was  experimentally  demonstrated  by  Joule  that  the 
temperature  of  air  remains  constant  if  it  expands  without  doing 
external  work. 

For  the  air-refrigerating  machine  We  in  equation  (5),  the 
mechanical  work  done  during  expansion,  is  considerable;  for 
the  ammonia  machine  it  is  usually  small  and  often  zero.  The 
heat  capacity  of  any  gas  which  does  not  change  its  state  is  small, 
and  is  equal  to  the  product  of  specific  heat,  into  weight,  into 
change  of  temperature.  On  the  other  hand,  when  vapors  are 
employed  which  are  converted  into  liquids  during  the  process 
of  compression  and  cooling,  and  then  changed  into  vapors  during 
expansion,  the  heat  capacity  of  a  given  weight  is  increased  because 
of  its  latent  heat,  which  is  always  comparatively  large.  It  becomes 
quite  evident  from  the  latter  consideration  alone  that  the  air 
machine  must  for  a  given  capacity  be  many  times  greater  in  size 
than  the  ammonia  machine. 

Two  of  the  more  successful  machines  of  this  type  are  described 
as  follows:  The  Windhausen  machine,  which  was  operated 
during  the  Vienna  Exposition,  had  a  capacity  of  30  cwt.  of  ice 
per  hour.  In  its  construction  it  consisted  of  a  single  cylinder, 
each  end  of  which  was  alternately  a  compressed-air  engine  and 
a  pump  for  compressing  the  air.  The  compressed  air  was  de- 
livered to  a  cooling  vessel,  and  from  thence  to  one  end  of  the 
cylinder,  being  admitted  by  a  valve  motion,  and  acting  in  its 
expansion  to  move  the  piston  and  help  to  compress  the  air  drawn 
in  at  the  other  end.  The  exhaust  air  after,  being  deprived  of 
its  heat  by  the  work  of  expansion,  was  passed  to  the  cooling 
vessels,  and  utilized  in  lowering  the  temperature  of  a  quantity 
of  brine,  or  directly  discharged  for  refrigeration  purposes.  The 


742 


EXPERIMENTAL   ENGINEERING. 


[§  482. 


power  required  over  and  above  that  provided  by  the  compressed 
air  was  supplied  by  an  engine. 

The  Bell-Coleman  machine,  which  is  extensively  used  on 
shipboard  for  refrigeration  purposes,  is  constructed  in  much 
the  same  manner  as  the  Windhausen,  but  the  operations  of 
compressing  and  expanding  are  performed  in  separate  cylinders. 
The  machine  consists  of  three  tandem  cylinders,  and  three  pis- 
tons fixed  to  a  common  piston-rod.  One  cylinder  is  the  air- 
compressor,  the  other  the  air-engine,  while  a  third  is  a  steam- 
engine  which  supplies  the  excess  of  power  needed  to  move  the 
pistons. 

The  amount  of  work  required  and  the  change  of  temperature 
produced  in  the  expansion  and  compression  of  air  have  been 
discussed  quite  fully  in  Art.  462. 

482.  The  Ammonia  Compressor. — A  general  outline 
of  an  ammonia  compression  system  is  shown  in  Fig.  331.  It 


Ammonia 


Water  Supply 
11  Condenser  C 


Compression 

Refrigerating 

Apparatus 

Three  Parts 


EXPANSION 

Brine  Tank  or  Congealer  A.    ' 


FIG.  331. — OUTLINE  DRAWING  OF  MECHANICAL  COMPRESSION  SYSTEM. 

consists  of  a  compressor  or  pump,  B,  which  draws  the  ammonia 
vapor  from  the  brine-tank  or  congealer,  A,  compresses  it,  and 
then  delivers  it  to  the  large  condenser,  C,  where  it  is  cooled  by 
water  and  is  liquefied.  The  liquid  ammonia  under  pressure 
is  then  permitted  to  flow  through  the  expansion-valve  shown 


§  482-]  MECHANICAL  REFRIGERA  TION.  743 

between  the  condenser  and  the  brine- tank.  In  passing  through 
the  expansion-valve  and  into  the  expansion-pipe  shown  in  the 
brine- tank,  the  liquid  ammonia  is  vaporized  by  expansion,  and 
the  heat  required  is  taken  up  from  the  material  surrounding 
the  coil. 

The  apparatus  as  shown  consists  of  three  parts:  (i)  the 
expansion- valve  and  coil,  in  which  the  liquid  is  vaporized,  (2)  the 
compressor,  in  which  the  vapor  is  compressed;  and  (3)  the  con- 
denser, in  which  the  vapor  is  reduced  to  a  liquid.  If  there  were 
no  other  heat  losses,  it  is  evident  that  the  heat  given  off  in  the 
condenser  would  equal  that  drawn  from  the  medium  surrounding 
the  expansion-coils. 

In  the  apparatus  illustrated  ,  the  expansion-coils  are  shown 
surrounded  by  brine.  In  many  cases  the  expansion  coils  are 
in  contact  with  the  air  of  the  room  which  is  to  be  lowered  in  tem- 
perature. In  some  instances  the  brine,  after  being  cooled  by  the 
expansion  of  ammonia,  is  circulated  to  the  places  where  a  low 
temperature  is  required. 

The  compression  cylinder  for  the  ammonia  refrigeration 
machine  should  be  made  with  as  small  a  clearance  as  possible, 
for  the  reasons  which  have  already  been  given  in  the  discussion 
of  the  air-compressor.  Fig.  332  shows  an  enlarged  view  of  a 
single-acting  ammonia- compression  cylinder  surrounded  with  a 
water-jacket  for  removing  heat  during  compression.  In  some 
instances  ammonia  compressors  have  been  provided  with  means 
for  keeping  the  clearance  spaces  filled  with  oil.  In  such  cases 
an  oil-separator  is  employed  between  the  compressor  and  the 
condenser,  which  is  arranged  to  take  the  oil  out  of  the  ammonia 
pipes  and  return  it  to  the  compressor. 

Refrigerating  machines  are  used  for  the  cooling  of  buildings 
and  also  for  the  manufacture  of  ice.  For  the  manufacture  of 
ice  a  brine-tank  is  usually  employed  which  is  maintained  at  low 
temperature  by  the  expansion  of  ammonia  in  coils  inserted  in 
the  tank  substantially  as  shown  in  Fig.  331.  The  ice  is  usually 
made  by  freezing  distilled  water  in  cans  of  the  desired  shape. 
In  nearly  all  ice-plants  of  this  character,  apparatus  is  required 


744 


EXPERIMEN TA  L  ENGINEERING. 


[§  483. 


not  only  for  the  ammonia  system  but  also  for  supplying  and 
purifying  the  water.  Fig.  333  shows  a  section  of  an  ice-making 
plant  with  all  the  principal  parts  named.  The  operation  of 
the  plant  can  be  understood  from  a  study  of  the  drawing. 


FIG.  332. — AMMONIA  COMPRESSION  CYLINDER. 

Ice  is  also  made  by  directly  freezing  water  in  contact  with 
the  expansion  system.  In  such  case  the  ice  is  frozen  in  large 
plates,  and  is  usually  removed  by  discharging  hot  ammonia  liquid 
directly  into  the  expansion  system,  which  loosens  it  from  the 
expansion  plates.  It  is  in  such  cases  usually  cut  into  small 
pieces  by  the  use  of  jets  of  steam. 

483.  Relations  of  Pressure  and  Volume.  —  In  the 
compression  of  ammonia  the  relations  of  pressure,  volume,  and 
temperature  are  essentially  as  those  given  in  equation  in  Art.  462. 
The  compression  is  usually  very  nearly ,  adiabatic,  as  indicated 
by  the  diagrams  taken  with  an  indicator.  For  the  adiabatic 
curve  of  ammonia  vapor, 


k 


§  4830 


MECHANICAL   REFRIGERATION. 


745 


746 


EXPERIMENTAL   ENGINEERING. 


[§  483- 


In  Fig.  334  is  shown  a  series  of  adiabatic  curves  for  different 
pressures  and  volumes  drawn  by  Mr.  R.  L.  Shipman,  which  will 
be  found  extremely  useful  in  making  a  comparison  of  the  com- 
pression line  obtained  on  an  indicator  diagram  with  an  adia- 
batic curve  corresponding  to  the  same  pressure  and  volume. 


VOLUME  OR  LENGTH  OF  STROKE 
FIG.  334. — ADIABATIC  CURVES  FOR  DIFFERENT  PRESSURES  AND  VOLUMES. 

The  following  table  gives  the  result  of  a  series  of  tests  on 
ammonia  compression  machines,  made  by  C.  Linde  of  Munich, 
and  are  of  interest  as  showing  the  amount  and  character  of  the 
various  quantities  described  The  table  is  copied  from  a  paper 
read  before  the  American  Society  of  Mechanical  Enigneers,  at 
the  Chicago  meeting,  1893.  Tne  units  were  reduced  to  one] 


484.] 


MECHANICAL  REFRIGERATION. 


747 


minute  of  time  instead  of  one  hour.  It  is  noted  that  in  every 
case  AW  is  less  than  K-K1}  and  it  should  also  be  further  noted 
that  the  smaller  this  difference  the  greater  the  economical  per- 
formance of  the  machine. 


Number  of  Test  

4 

5 

Temp,  of  brine:  Inlet,  deg.  F.  . 
Temp,  of  brine:  Outlet,  deg.  F. 
Specific  heat  of  brine-  per  unit  o 
volume  

43-2 
37-o 

o  86 

28.3 
22.9 

o  8? 

13-9 
8.7 

o   RA 

-0.3 

-5-9 

r>   R-JT 

28.3 
23-1 

Quantity  of  brine  per  hr.,  cu.  ft.  . 
Cold  produced,  B.T.U.  per  min. 
KI.     ... 

1039.4 

908.8 

615-4 

97$  T      1 

0.837 
915.0 

0.051 
800.9 

Temp,  of  cooling  water:    Inlet 
degs.  F.  . 

48  8 

4v5uy  •  i 

2701.3 

2024.5 

3671-  4 

Temp,  of  cooling  water:   Outlet 
degs.  F  

66  7 

4V  •  3 
68  o 

49.  I 
67     I 

49.  I 

67    1 

49-2 

Quan.  of  cooling  water  per  hr. 
cu  ft 

3^8  i 

260  8 

**/  •  i 

18*7     A 

°7-3 

93-4 

ni    8 

Heat  removed  by  condenser  per 
minute,  B.T.U.,  K  
Increase  in  heat,  K—K\  

00°  •  / 

63°5-9 
^qo.8 

5°23-4 
724.  •? 

iOy  .4 

35°9-5 

728    2 

2648.7 

624    2 

97-0 

45J8-9 

8/17    C 

I.H.P.  in  comp.  cyl.,  W  
Heat  equivalent  of  work,  AW. 
I.H.P.  in  steam-engine  cylinder.  . 
Consumption  of  steam  per  hour, 
Ibs. 

13.82 
586.2 
15.80 

•211     < 

14.29 
606.2 
16,47 

336  o 

13.84 
587 

J5-45 
-206  8 

11.98 
508.2 
14.24 

278  8 

°4/  -5 

J9-75 
837-i 

21  .6l 

Consumption  of  steam  per  min- 
ute, Ibs.  .  .    . 

o^-1  -o 
ir    IQ 

oo"-'-' 
«;  6 

5i  i 

A  6c 

Cold    produced    in    B.T.U.    per 
minute  per  I.H.P.  in  comp.  cyl. 
Cold    produced    in    B.T.U.    per 
minute    per    I.H.P.    in    steam 
cylinder. 

4I3-5 
361    7 

3°7-7 
267  i 

200.9 

180  7 

169.0 

142    2 

'    */ 

185.9 

160  7 

Cold    produced    in    B.T.U.    per 
minute  per  pound  of  steam.  .  .  . 
Thermodvnamic  efficiency  (460  + 
t}~(tc-t)=El  
Actual  efficiency  Kl+AW  =  E2.  . 
Ratio  of  actual  to  thermodynamic 
efficiency  

100 

17.2 

9-75 
o.  <6 

785-6 

10.65 
7.26 

0.68 

543-9 

8.04 
4-73 

o.  159 

435-8 

6.2 

4-03 
0.667 

512.1 

6.86 
4-38 

0.637 

AW-(K-Ki)  

-4.6 

-118.1 

—  141.2 

—  116.0 

-10.4 

*  Lbs.  of  ice  melted  per  Ib.  of 
steam   . 

7.  <2 

5.66 

3.85 

3-  l 

3.64 

Lbs.  of  ice  melted  per  Ib.  of  coal.  . 

75-2 

56.6 

38-5 

31.0 

36-4 

*  Latent  heat  of  ice  taken  as  141  B.T.U. 


484.   The  Absorption  System  of  Refrigeration.— This 

system  was  invented  by  M.  Carre,  and  dispenses  with  the  ammo- 


EXPERIMENTAL  ENGINEERING.  [§  484. 

ma  compressor.  Instead  of  compressing  the  ammonia  by  pres- 
sure, water  strongly  impregnated  with  ammonia  gas  is  heated 
by  steam.  The  heat  vaporizes  the  ammonia  and,  because  of 
the  low  boiling  temperature  of  the  ammonia,  causes  as  much 
pressure  as  required.  The  compressed  ammonia  is  treated 
as  in  the  other  processes,  that  is,  it  is  first  passed  through  a  con- 
denser and  liquefied,  thence  to  expansion-coils,  where  it  takes 
up  heat  from  the  surrounding  material.  Instead  of  being  pumped 
tack  as  in  the  first  system,  it  is  absorbed  by  water  and  the  dilute 
liquid  is  pumped. 

Fig.  335  shows  a  view  of  an  absorption  system  with  all  the 
principal  parts  named.  It  is  worthy  of  a  close  study,  as  showing 
the  economy  practiced  in  the  use  of  the  heat  employed. 

The  strong  ammonia  liquid  from  the  absorber  is  pumped 
through  a  heater,  where  it  is  surrounded  by  weak  ammonia 
liquor  which  had  been  previously  heated  in  the  gene  ator.  It 
then  flows,  partially  heated,  to  the  analyzer,  where  it  exposes 
a  large  surface  to  the  heat.  The  principal  part  of  the  ammonia 
gas  under  pressure  passes  off  above,  the  weak  ammonia  liquor 
falls  to  the  bottom  of  the  generator.  The  ammonia  gas  under 
the  pressure  due  to  its  temperature  is  received  in  the  condensing 
coil.  In  this  coil  the  pressure  is  maintained,  but  the  tempera- 
ture is  lowered  by  the  use  of  condensing  water,  so  that  the  ammo- 
nia gas  is  converted  into  liquid  anhydrous  ammonia. 

The  anhydrous  ammonia  is  used  as  in  the  other  systems;  it 
may  be  allowed  to  expand  in  a  tank  filled  with  brine,  or  it  may 
be  carried  to  the  rooms  where  refrigeration  is  needed  and  then 
permitted  to  expand.  In  the  figure  the  brine  system  is  shown, 
the  expansion  taking  place  in  the  cooler,  in  which  a  circulation 
of  brine  is  maintained  by  a  pump. 

The  weak  ammonia  from  the  generator,  after  parting  with 
some  of  its  heat  in  the  heater,  is  brought  in  contact  with  the 
ammonia  in  a  vessel  called  the  absorber.  The  ammonia  gas 
has  a  strong  affinity  for  water,  and  is  absorbed  readily,  convert- 
Ing  the  weak  ammonia  liquor  into  strong  ammonia  liquor.  This 
is  pumped  to  the  heater  and  completes  the  cycle.  The  exhaust 


484.] 


MECHANICAL  REFRIGERA  TION. 


749 


75°  EXPERIMENTAL   ENGINEERING.  [§  484, 

steam  from  the  pumps  is  utilized  in  heating  under  ordinary 
conditions,  so  that  all  the  heat  wastes  are  carried  off  in  the  coa- 
densing  water  and  in  the  drip  from  the  generator. 

When  a  low  back  pressure  is  wanted,  such  as  is  required 
in  production  of  ice,  this  system  succeeds  well,  and  is  somewhat 
more  economical  than  the  compression  system.  For  purposes 
of  refrigeration  where  a  high  back  pressure  is  maintained  the 
compression  system  is  more  economical  in  its  operation. 

The  following  sheets  indicate  the  observations  which  are 
necessary  for  a  complete  test  of  an  ammonia  refrigerating  machine : 


LOG  A. 

Test  of  Refrigerating  Machine    built  by Style 

Tested  at ' Date 

Size  o)  Ammonia  Cylinder — Diam Stroke Scale  of  Ind.  Spring. 

Capacity  of  Expansion  Valve ....  Specific  gravity  of  Brine ....  Barometer. .  . 

Test  made  by 

No 

Time 

Speed-counter 

Revolutions  per  minute 

Temperature,  room 

Temperature,  external  air 

Condenser: 

Temperature,  entering  gas 

Temperature,  injecting  water 

Temperature,  discharging  water 

Weight  water Ibs 

•Compression  gauge " 

Expansion  Coils: 

Temperature,  entering  gas Deg.  F.    

Temperature,  discharging  gas "      

Suction  gauge Ibs 

Brine  Tank: 

Temperature,  entering  brine 

Temperature,  discharging  brine 

Meter  reading 

Cubic  feet,  brine 

Weight  of  brine,  pounds 

Revolutions  of  expansion  valve 

Temperature,  liquid  NH3,  at  expansion  valve. . 


484-]  MECHANICAL   REFRIGERATION.  751 


LOG   B. 


Test  of  Refrigerating  Machine  built  by 

Tested  at Date 

Tested  by \ 

Specific  gravity  of  NH3 Specific  heat  of  NH3. 

Specific  gravity  of  brine Specific  heat  of  brine. 

Number 

Brine: 

Pounds,  circulated 

Range,  temperature 

B.T.U.  discharge 

Condenser: 

Pounds,  water 

Range,  temperature 

B.T.U.  discharge 

Gain  B.T.U 

Compression  cylinder: 

Absolute  pressure  admitted 

Absolute  pressure  discharged 

M.E.P 

D.H.P 

Work,  B.T.U 

Ammonia: 

Pounds,  circulated 

Heat  of  vaporizion,  suction  pressure 

Heat  of  vaporizion,  condenser  pressure 

Temperature  due  to  pressure  in  refrigerating  coils 

Absolute  pressure  in  refrigerating  coils 


SPECIFIC   HEAT   OF   BRINE. 

Specific  Gravity 1.187     1.170     1.103     1.072     1.044     1.023     LO" 

Specific  Heat 0.791        .805        .863        .895        .931        .962       .978 


SPECIFIC   HEAT   CHLORIDE  OF   CALCIUM   SOLUTION. 

Specific  Gravity 1.0255  1.163 

SpecificHeat °-957  °-827 


752 


EXPERIMENTAL   ENGINEERING. 


[§  484. 


REPORT. 


Test  of  Refrigerating  Machine  built  by 

Tested  at Date Latent    heat 

Tested  by 


ice    142.2 


No. 

Sym- 
bols. 

Formulae. 

I 

Pounds  of  condensing  water  per  hour     

o 

2 

Ran^e  of  temperature  of  condensing  water  

to, 

Pounds  of  brine  per  hour   

o, 

th 

o« 

1 

Pounds  of  condensing  water  per  pound  of  NH,  

Average  temperature  outlet  of  brine   

2o 

8 

Average  temperature  outlet  of  cooling  water  

tn 

Temperature  of  NH,  entering  brine  tank  

tl 

10 

ii 

12 

Corresponding  sensible  heat  liquid  above  32  in  B.T.U.  .  . 
Total  heat  NH3  gas  B.T.U.  at  suction  pressure  
Temperature  of  gas  leaving  brine  tank 

?1 
^ 

I 

13 
14 

j  ^ 

Temperature  of  gas  corresponding  to  suction  pressure. 
Superheating  of  gas  in  degrees  Fahrenheit  
Cooling  per  pound  of  ammonia  in  B.T.U  

I 

K* 

t-t3 
X%  —  ^1  +  0.51  d\ 

16 

17 
18 
10 

Temperature  of  gas  entering  condenser  
Heat  carried  off  by  condensing  H2O  per  hour  B.T.U.  .  .  . 
Heat  taken  from  brine  per  hour  B.T.U.  (Refrigeration) 
D  JJ  p   ammonia  cylinder                                

tc 
K 
Kv 

QT 
QiFiX  Spe.  ht. 

20 

Foot-pounds  of  work  per  hour  no  friction  

W 

21 
22 

23 
24. 

Heat  equivalent  of  work  per  hour  B.T.U  
Heat  carried  from  brine  per  pound  NH3  circulated.  .  .  . 
Heat  carried  off  by  cond.  H2O  per  pound  NH,  cir  
Heat  gained  by  system  per  hour  B.T.U.  . 

AW 
K-K} 

2< 

Thermodynamic  efficiency  

Fi 

2+461 

26 

Actual  efficiency  

Eo 

tc-t 
K}+AW 

27 

Ratio  actual  to  thermal  efficiency  

£3 

Ei  +  E 

28 

Ice-melting  capacity  pounds  24  hours  at  100  revolutions 

LIST    OF  TABLES. 


I.  U.  S.  STANDARD  AND  METRIC  MEASURES 754 

II.  NUMERICAL  CONSTANTS 756 

III.  LOGARITHMS  OF  NUMBERS 769 

IV.  LOGARITHMIC  FUNCTIONS  OF  ANGLES 771 

V.  NATURAL  FUNCTIONS  OF  ANGLES 777 

VI.  COEFFICIENTS  OF  STRENGTH  OF  MATERIALS 781 

VII.  STRENGTH  OF  METALS  AT  DIFFERENT  TEMPERATURES 782 

VIII.  IMPORTANT  PROPERTIES  OF  FAMILIAR  SUBSTANCES 783 

IX.  COEFFICIENT  OF  FRICTION 784 

X.  HYPERBOLIC  OR  NAPERIAN  LOGARITHMS 784 

XI.   MOISTURE  ABSORBED  BY  AIR 785 

XII.  RELATIVE  HUMIDITY  OF  THE  AIR 785 

XIII.  TABLE  FOR  REDUCING  BEAUME'S  SCALE-READING  TO  SPECIFIC 

GRAVITY 786 

XIV.  COMPOSITION  OF  VARIOUS  FACTS  OF  THE  UNITED  STATES 787 

XV.  BUEL'S  STEAM -TABLES 788 

XVI.  ENTROPY  OF  WATER  AND  STEAM 794 

XVII.  DISCHARGE  OF  STEAM  :    NAPIER  FORMULA 795 

XVIII.  WATER  IN  STEAM  BY  THROTTLING  CALORIMETER 795 

DIAGRAM  FOR  DETERMINING  PER  CENT  OF  MOISTURE  IN  STEAM.  796 

XIX.  FACTORS  OF  EVAPORATION 797 

XX.  WROUGHT-IRON  WELDED  PIPES 798 

XXI.  WEIGHT  OF  WATER  AT  VARIOUS  TEMPERATURES 799 

XXII.  HORSE-POWER  PER  POUND  MEAN  PRESSURE 800 

XXIII.  WATER  COMPUTATION  TABLE .801 

XXIV.  WEIRS  WITH  PERFECT  END  CONTRACTION 803 

XXV.  WEIRS  WITHOUT  END  CONTRACTION. 803 

XXVI.  ELECTRICAL  HORSE-POWER  TABLE. 803 

XXVII.  HORSE-POWER  OF  SHAFTING 804 

XXVIII.  HORSE-POWER  OF  BELTING 804 

SAMPLE-SHEET  OF  PAPER 8°4 

753 


754 


EXPERIMEN  TA  L   ENGINEERING. 


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U.  S.  STANDARD   AND   METRIC  MEASURES.  755 


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II  II  II  II  II  II  II  II  II 

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Kilometres 
to  Miles. 


Metres  to 
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apportioned  to  the 


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the 
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In 
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The  litre  is  equal  to  a 
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756 


EXPERIMENTAL  ENGINEERING. 


II. 

NUMERICAL  CONSTANTS. 


n 

MT 

«»? 
.  « 

»* 

«3 

Vn 

a 
V» 

.0 

3.142 

0.7854 

1.  000 

1.  000 

.0000 

.OOOO 

.1 

3.456 

0.9503 

I.2IO 

1.331 

.0488 

.0323 

.2 

3-770 

1.1310 

1.440 

1.728 

.0955 

.0627 

.3 

4.084 

1.3273 

1.690 

2.197 

.1402 

.0914 

•4 

4.398 

1-5394 

1.960 

2.744 

.1832 

.1187 

.5 

4.712 

1.7672 

2.250 

3.375 

.2247 

•  1447 

.6 

5-027 

2.0106 

2.560 

4.096 

.2649 

.1696 

.7 

5.341 

2.2698 

2.890 

4.913 

.3038 

.1935 

1.8 

5-655 

2.5447 

3.240 

5-832 

.3416 

.2164 

1.9 

5-969 

2.8353 

3.6IO 

6.859 

.3784 

.2386 

2.0 

6.283 

3-1416 

4.000 

8.000 

.4142 

.2599 

2.1 

6.597 

3.4636 

4.410 

9.261 

.4491 

.2806 

2.2 

6.912 

3.8013 

4.840 

10.648 

.4832 

.3006 

2-3 

7.226 

4.1540 

5.290 

12.167 

.5166 

.3200 

2.4 

7-540 

4.5239 

5.760 

13.824 

.5492 

.3389 

2.- 

7-854 

4.9087 

6.250 

15.625 

.5811 

.3572 

2.6 

8.168 

5.3093 

6.760 

17.576 

.6125 

•3751 

2.7 

8.482 

5.7256 

7.290 

19.683 

.6432 

.3925 

2.8 

8.797 

6.1575 

7.840 

21.952 

.6733 

•4095 

2.9 

9.111 

6.6052 

8.410 

24.389 

.7029 

.4260 

3.0 

9-425 

7.0686 

9-00 

27.000 

.7321 

•  4422 

3-1 

9-739 

7-5477 

9.61 

29.791 

.7607 

.458! 

3.2 

10.053 

8.0425 

IO.24 

32.768 

.7889 

•4736 

3-3 

10.367 

8.5530 

10.89 

35-937 

.8166 

.4888 

3-4 

10.681 

9.0792 

11.56 

39-304 

.8439 

.5037 

3-5 

10.996 

9.6211 

12.25 

42-875 

.8708 

.5183 

3-6 

11.310 

10.179 

12.96 

46.656 

.8974 

•5326 

3-7 

11.624 

10.752 

13.69 

50-653 

.9235 

.5467 

3.8 

H.938 

11.341 

14.44 

54.872 

•9494 

.5605 

3-9 

12.252 

11.946 

15.21 

59-3I9 

.9748 

•5741 

4.0 

12.566 

12.566 

16.00 

64.000 

2.0000 

.5874 

4-i 

12.881 

13.203 

16.81 

68.921 

2.0249 

.6005 

4.2 

13.195 

13.854 

17.64 

74-088 

2.0494 

.6134 

4-3 

13  509 

14.522 

18.49 

79-507 

2.0736 

.6261 

4-4 

13.823 

15-205 

19.36 

85.184 

2.0976 

.6386 

4-5 

14  137 

I5-9Q* 

20.25 

91.125 

2.1213 

.6510 

4.6 

I4-45I 

16.619 

/2I.I6 

97.336 

2  .  1448 

.6631 

,4-7 

14.765 

17.349 

22.09 

103.823 

2.1680 

I  6751 

NUMERICAL   CONSTANTS. 
CONSTANTS— Continued. 


757 


* 

nn 

*i? 

4 

»« 

»* 

V~n 

fc 

4.8 

15.080 

18.096 

23.04 

110.592 

2.1909 

.6860 

4.9 

15.394 

18.857 

24.01 

117.649 

2.2136 

.6985 

5-0 

15.708 

I9.635 

25.00 

125.600 

2.2361 

.7IOO 

5-i 

16.022 

20.428 

26.01 

132.651 

2.2583 

.7213 

5.2 

16.336 

21.237 

27.04 

140.608 

2  .  2804 

•7325 

5-3 

16.650 

22.062 

28.09 

148.877 

2  .  3022 

•7435 

5-4 

16.965 

22.902 

29.16 

157.464 

2.3238' 

•7544 

5-5 

17.279 

23.758 

30.25 

166.375 

2.3452 

.7652 

5-6 

17-593 

24.630 

3I.36 

175.616 

2  .  3664 

.7758 

5-7 

17.907 

25.518 

32.49 

185-193 

2.3875 

.7863 

5.8 

18.221 

26.421 

33.64 

I95.H2 

2.4083 

.7967 

5-9 

18-535 

27  .  340 

34.81 

205.379 

2.4290 

.8070 

6.0 

18.850 

28.274 

36.00 

216.000 

2-4495 

.8171 

6.1 

19.164 

29.225 

37-21 

226.981 

2.4698 

.8272 

6.2 

19.478 

30.191 

38.44 

238.328 

2.4900 

-8371 

6.3 

19.792 

31.173 

39-69 

250.047 

2.5100 

.8469 

6.4 

2O.IO6 

32.170 

40.96 

262.144 

2.5298 

.8566 

6.5 

20.420 

33.183 

42.25 

274.625 

2-5495 

.8663 

6.6 

20.735 

34-212 

43.56 

287.496 

2.5691 

.8758 

6.7 

21.049 

35.257 

44.89 

300.763 

2.5884. 

.8852 

6.8 

21.363 

36.317 

46.24 

314.432 

2.6077 

.8945 

6.9 

21.677 

37.393 

47.61 

328.509 

2.6268 

.9038 

7.0 

21.991 

38.485 

49.00 

343-000 

2.6458 

.9129 

7-1 

22.305 

39.592 

50.41 

357-9" 

2.6646 

.9220 

7.2 

22.619 

40.715 

51.84 

373-248 

2.6833 

.9310 

7-3 

22.934 

41.854 

53.29 

389.017 

2.7019 

•9399 

7-4 

23.248 

43.008 

54.76 

405.224 

2  -  7203 

.9487 

7-5 
7.6 

23.562 
23.876 

44.179 
45.365 

56.25 
57.76 

421.875 
438.976 

2.7386 
2.7568 

•  9574 
.9661 

7-7 

24.190 

46.566 

59-29 

456.533 

2-7749 

•  9747 

7.8 
7-9 

24.504 
24.819 

47.784 
49.017 

60.84 
62.41 

474.552 
493.039 

2  .  7929 
2.8107 

.9832 
.9916 

8.0 
8.1 

8.2 

8.3 
8.4 

25.133 
25.447 
25.761 
26.075 
26.389 

50.266 
51.530 

52.810 

54.106 
55.418 

64.00 
65.61 
67.24 
68.89 
70.56 

512.000 

53L44I 
55L468 
57I-787 
592.704 

2.8284 
2.8461 
2.8636 
2.8810 
2.8983 

2.0000 
2.0083 
2.0165 
2.0247 
2.0328 

8.5 
8.6 

8-7 

8.8 

8.9 

26.704 
27.018 
27.332 
27.646 
27.960 

56.745 
58.088 

59-447 
60.821 
62.211 

72.25 
73.96 
75.69 
77-44 
79.21 

614.125 
636.056 
658.503 
681.473 
704.969 

2.9155 
2.9326 
2.9496 
2.9665 
2.9833 

2.0408 
2.0488 
2.0567 
2.0646 
2.0724 

758 


EXPERIMENTAL  ENGINEERING. 
CONSTANTS — Continued. 


n 

nit 

*'? 

4 

«• 

«> 

tfn 

ft 

9  ° 

28.274 

63.617 

81.00 

729.000 

3.OOOO 

2.0801 

9.1 

28.588 

65.039 

82.81 

753.571 

3.0166 

2.0878 

9.2 

28.903 

66.476 

84.64 

778.688 

3  0332 

2.0954 

9-3 

29.217 

67.929 

86.49 

804.357 

3-0496 

2  .  1029 

9.4 

29-531 

69.398 

88.36 

830.584 

3.0659 

2.II05 

9-5 

29.845 

70.882 

90.25 

857.375 

3.0822 

2.II79 

9.6 

30.159 

72.382 

92.16 

884.736 

3-0984 

2.1253 

9-7 

30-473 

73.898 

94.09 

912.673 

3."45 

2.1327 

9.8 

30.788 

75.430 

96.04  . 

941.192 

3-1305 

2.1400 

9-9 

31  .  102 

76.977 

98.01 

970.299 

3.1464 

2.1472 

10.  0 

3I.4r6 

78  .  540 

IOO.OO 

1000.000 

3.1623 

2.1544 

10.  1 

31.730 

80.119 

102.01 

1030.301 

3.1780 

2.1616 

10.2 

32.044 

81.713 

104.04 

1061.208 

3-1937 

2.1687 

10.3 

32.358 

83.323 

106.09 

1092.727 

3  •  2094 

2.'i757 

IO.4 

32.673 

84.949 

108.16 

1124.863 

3.2249 

2.1828 

10.5 

32.987 

86.590 

110.25 

1157.625 

3-2404 

2.1897 

10.6 

33-301 

88.247 

112.36 

1191.016 

3-2558 

2.1967 

10.7 

33.615 

89.920 

114.49 

1225.043 

3.2711 

2  .  2036 

10.8 

33.929 

91.609 

116.64 

1259.712 

3-2863 

2.2104 

10.9 

34-243 

93.313 

118.81 

1295.029 

3-30I5 

2.2172 

II.  0 

34-558 

95-033 

121.00 

1331.000 

3-3166 

2.2239 

li.  i 

34.872 

96.769 

123.21 

1367.631 

3.33I7 

2.2307 

II.  2 

35-186 

98.520 

125-44 

1404.928 

3.3466 

2.2374 

"•3 

35  •  500 

IOO.29 

127.69 

1442.897 

3-3615 

2.2441 

11.4 

35.814 

102.07 

129.96 

1481.544 

3.3764 

2.2506 

II-  5 

36.128 

103.87 

132.25 

'1520.875 

3-39T2 

2.2572 

II.  6 

36.442 

105.68 

134.56 

1560.896 

3-4059 

2.2637 

II.  7 

36.757 

107.51 

136.89 

1601.613 

3.4205 

2.2702 

11.8 

37-071 

109.36 

139.24 

1643.032 

3-4351 

2.2766 

11.9 

37.385 

III.  22 

141.61 

1685.159 

3.4496 

2.2831 

12.0 

37.699 

II3.IO 

144.00 

1728.000 

3-4641 

2.2894 

12.  1 

38.013 

114.99 

146.41 

1771.561 

3.4785 

2.2957 

12.2 

38.327 

116.90 

148.84 

1815.848 

3.4928 

2.3021 

12.3 

38.642 

118.82 

151.29 

1860.867 

3-507I 

2.3084 

12.4 

38.956 

120.76 

153.76 

1906.624 

3-5214 

2.3146 

12.5 

39-270 

122.72 

156.25 

1953.125 

3-5355 

2  .  32O8 

12.6 

12.7 

39.584 
39.898 

124.69 

126.68 

158.76 
161.29 

2000.376 
2048.383 

3-5496 
3.5637 

2.3270 
2.3331 

12.8 

40.212 

128.68 

163.84 

2097.152 

3-5777 

2.3392 

12.9 

40.527 

130.70 

166.41 

2146.689 

3.5917 

2-3453 

13.0 

40.841 

132.73 

169.00 

2197.000 

3-6056 

2.3513 

13-1 

41.155 

134.78 

/I7i.6i 

2248.091 

3-6194 

2-3573 

13.2 

41.469 

136-85 

174.24 

2299.968 

3-6332 

2.3633 

NUMERICAL   CONSTANTS. 
CONSTANTS— Continued. 


759 


n 

nir 

4 

„ 

" 

r. 

ft 

13-3 
13.4 

4L783 
42.097 

138.93 
I4L03 

176.89 
179.56 

2352.637 
2406.104 

3.6469 
3.6606 

2.3693 
2.3752 

13.5 

42.412 

143.14 

182.25 

2460.375 

3-6742 

2.3811 

13.6 

42.726 

145.27 

184.96 

2515.456 

3.6878 

2.3870 

13.7 

43.040 

147.41 

187.69 

257L353 

3.7013 

2.3928 

13-8 

43-354 

149-57 

190.44 

2628.072 

3.7148 

2  .  3986 

13.9 

43.668 

I5L75 

193.21 

2685.619 

3.7283 

2.4044 

14.0 

43-982 

153-94 

196.00 

2744.000 

3.7417 

2.4IOI 

14.1 

44.296 

156.15 

198.81 

2803.221 

3-7550 

14.2 

44.611 

158.37 

201  .  64 

2863.288 

3.7683 

2.4216 

14.3 

44-925 

160.61 

204.49 

2924.207 

3.7^15 

2.4272 

14.4 

45-239 

162.86 

207  .  36 

2985.984 

3-7947 

2.4329 

14.5 

45.553 

165.13 

210.25 

3048.625 

3.8079 

2.4385 

14.6 

45.867 

167.42 

2I3.I6 

3112.  136 

3.8210 

2.4441 

14.7 

46.181 

169.72 

216.09 

3176.523 

3.8341 

2-4497 

14.8 

46.496 

172.03 

219.04 

324L792 

3.847I 

2-4552 

14.9 

46.810 

174-37 

222.01 

3307-949 

3.8600 

2.4607 

15.0 

47.124 

176.72 

225.00 

3375-000 

3.8730 

2.4662 

;  15-1 

47.438 

179.08 

228.01 

3442.951 

3.8859 

2.4717 

15.2 

47-752 

181.46 

231.04 

3511.808 

3.8987 

2.4772 

15-3 

48.066 

183.85 

234.09 

3581.577 

3-9"5 

2.4825 

15.4 

48.381 

186.27 

237.16 

3652.264 

3.9243 

2.4879 

15.5 

48.695 

188.69 

240.25 

3723.875 

3.9370 

2-4933 

15-6 

49.009 

191.13 

243.36 

3796.416 

3.9497 

2.4986 

49-323 

193.59 

246.49 

3869.893 

3.9623 

2.5039 

is's 

196.07 

249.64 

3944-312 

3-9749 

2.5092 

1  15-9 

49-951 

198.56 

252.81 

4019.679 

3-9875 

2.5146 

16.0 

50.265 

201.06 

256.00 

4096.000 

4.0000 

2.5198 

16.1 

50.580 

203.58- 

259-21 

4173.281 

4-0125 

2.5251 

16.2 

50.894 

206.12 

262.44 

4251.528 

4.0249 

2.5303 

16.3 

51.208 

208.67 

265.69 

4330.747 

4.0373 

2.5355 

16.4 

5I-522 

211.24 

268.96 

4410.944 

4.0497 

2.5406 

16.5 

51-836 

213.83 

272.25 

4492.125 

4.0620 

2.5458 

16.6 

52.150 

216.42 

275.56 

4574.296 

4-0743 

2.5509 

16.7 

52.465 

219.04 

278.89 

4657.463 

4.0866 

2.5561 

16.8 
16.9 

52.779 
53-093 

221.67 
224.32 

282.24 
285-61 

4741.632 
4826.809 

4.0988 
4.1110 

2.5612 
2.5663 

17,0 

53-407 

226  98 

289.00 

4913.000 

4.1231 

2.5713 

17.1 
17.2 

17.3 
17.4 

53.721 

54-035 
54-350 
54.664 

229.66 

I32-35 
235.06 

23^.79 

292.41 
295.84 
299.29 
302  .  76 

5000.211 

5088.448 

5177.717 
5268.024 

4.I352 
4-1473 
4.1593 
4.1713 

2  •  5763 
2.5813 
2.5863 
2.5913 

760 


EXPERIMENTAL  ENGINEERING. 
CONSTANTS— Continued. 


If 

««r 

n*"- 
4 

n* 

«8 

V~» 

h 

17.5 

54-978 

240.53 

306.25 

5359-375 

4.1833 

2.5963 

17.6 

'  55-292 

243.29 

309.76 

545L776 

4.1952 

2.6012 

17.7 

55.606 

246.06 

313.29 

5545-233 

4.2071 

2.6061 

17.8 

55-920 

248.85 

316.84 

5639.752 

4.2190 

2.6109 

17.9 

56.235 

251.65 

320.41 

5735-339 

4.2308 

2.6158 

18.0 

56.549 

254-47 

324.00 

5832.000 

4.2426 

2  .  62O7 

18.1 

56.863 

257.30 

327.61 

5929.741 

4.2544 

2.6256 

18.2 

57-177 

260.16 

33L24 

6028  .  568 

4.2661 

2.6304 

18.3 

57-491 

263.02 

334.89 

6128.487 

4.2778 

2.6352 

18.4 

57-805 

265.90 

338.56 

6229  .  504 

4.2895 

2.64OI 

18.5 

58.119 

268.80 

342.25 

6331-625 

4.3012 

2  .  6448 

18.6 

58.434 

271.72 

345.96 

6434.856 

4-3128 

2.6495 

18.7 

58.748 

274-65 

349.69 

6539.203 

4-3243 

2-6543 

18.8 

59.062 

277-59 

353-44 

6644.672 

4-3359 

2.6590 

18.9 

59-376 

280.55 

357-21 

6751.269 

4-3474 

2.6637 

19.0 

59-690 

283.53 

361.00 

6859.000 

4.3589 

2.6684 

19.1 

60.004 

286.52 

364.81 

6967.871 

4.3703 

2.6731 

19-2 

60.319 

289.53 

368.64 

7077.888 

4.3818 

2.6777 

19-3 

60.633 

292.55 

372-49 

7189.057 

4-3932 

2.6824 

19-4 

60.947 

295-59 

376.36 

7301.384 

4.4045 

2.6869 

19-5 

61.261 

298.65 

380.25 

7414.875 

4-4T59 

2.6916 

19.6 

6i.575 

301.72 

384.16 

7529-536 

4.4272 

2.6962 

19-7 

61.889 

304.31 

388.09 

7645.373 

4-4385 

2.7008 

19.8 

62  .  204 

307-91 

392.04 

7762.392 

4-4497 

2.7053 

19-9 

62.518 

3".03 

396.01 

7880.599 

4-4609 

2.7098 

20.0 

62.832 

314.16 

400.00 

8000.000 

4-4721 

2.7144 

20.1 

63.146 

317.31 

404.01 

8120.601 

4.4833 

2.7189 

20.2 

63.460 

320.47 

408.04 

8242.408 

4.4944 

2.7234 

20.3 

63.774 

323.66 

412.09 

8365.427 

4.5055 

2.7279 

20.4 

64.088 

,  326  85 

416.16 

8489.664 

4-5166 

2.7324 

20.5 

64.403 

330.06 

420.25 

8615.125 

4-5277 

2.7368 

20.6 

64.717 

333.29 

424.36 

8741.816 

4.5387 

2.7413 

20.7 

65.031 

336.54 

428.49  . 

8869.743 

4-5497 

2-7457 

20.8 

65.345 

339-80 

432.64 

8989.912 

4.5607 

2.7502 

20.9 

05.659 

343.07 

436.81 

9129-329 

4.5716 

2-7545 

21.  0 

65.973 

346.36 

441.00 

9261.000 

4.5826 

2.7589 

21.  1 

66.288 

349-67 

445.21 

9393-931 

4-5935 

2.7633 

21.2 

66.602 

352.99 

449.44 

9528.128 

4-6043 

2.7676 

21.3 

66.916 

356.33 

453.69 

9663.597 

4-6152 

2.7720 

21.4 

67.230 

359-68 

457-96 

9800.344 

4.6260 

2.7763 

21-5 

67.544 

363.05 

462.25 

9938.375 

4.6368 

2.7806 

21.6 

67.858 

366.44 

466.56 

10077.696 

4.6476 

2.7849 

31.7 

68.173 

369-  84  / 

470.89 

10218.313 

4.6583 

2.7893 

NUMERICAL   CONSTANTS. 
CONSTANTS — Continued. 


n 

nit 

"'4 

»a 

«» 

Vi 

h 

21.8 
21.9 

68.487 
68.801 

373.25 
376.69 

475.24 
479.61 

10360.232 
10503.459 

4.6690 
4.6797 

2.7935 
2.7978 

22.0 

69.115 

380.13 

484.00 

10648.000 

4  •  6904 

2  .  8O2I 

22-1 
22.2 

69.429 
69.743 

383.60 
387.08 

488.41 
492.84 

10793.861 
10941.048 

4-7011 
4.7117 

2.8063 
2.8IO5 

22.3 

70.058 

39°-  57 

497.29 

11089.567 

4.7223 

"j 

2.8147 

22.4 

70.372 

394.08 

501.76 

11239.424 

4.7329 

2.8189 

22.5 

70.686 

397.61 

506.25 

11390.625 

4-7434 

2.8231 

22.6 

71.000 

401.15 

510.76 

11543.176 

4.7539 

2.8273 

22.7 

7L3I4 

404.71 

5I5.29 

11697.083 

4.7644 

2.8314 

22.8 

71.268 

408.28 

519.84 

11852.352 

4-7749 

2.8356 

22.Q 

71.942 

411.87 

524.41 

12008.989 

4.7854 

2.8397 

23.0 

72.257 

415.48 

529.00 

12167.000 

4.7958 

2.8438 

23.1 

72.571 

419.10 

533.61 

12326.391 

4.8062 

2  .  8479 

23-2 

72.885 

422.73 

538.24 

12487.168 

4.8166 

2.8521 

23-3 

73.199 

4-26.39 

542.89 

12649.337 

4.8270 

2.8562 

23-4 

73.513 

430.05 

547-56 

12812.904 

4.8373 

2.8603 

23.5 

73.827 

433-74 

552.25 

12977.875 

4.8477 

2.8643 

23.6 

74.142 

437.44 

556.96 

13144.256 

4.8580 

2.8684 

23-7 

74.456 

44I.I5 

561.69 

13312.053 

4.8683 

2.8724 

23.8 

74.770 

444.88 

566.44 

13481.272 

4.8785 

2.8765 

23-9 

75.084 

448.63 

571.21 

13651.919 

4.8888 

2.8805 

24.0 

75.398 

452.39 

576.00 

13824.000 

4.8990 

2.8845 

24.1 

75.712 

456.17 

580.81 

I3997.52I 

4.9092 

2.8885 

24-2 

76.027 

459.96 

585-64 

14172.488 

4.9I93 

2.8925 

24-3 

76.341 

463.77 

590.49 

14348.907 

4-9295 

2.8965 

24-4 

76.655 

467.60 

595.36 

14526.784 

4.9396 

2.9004 

24-5 

76.969 

471.44 

600.25 

14706.125 

4-9497 

2.9044 

24.6 

77-283 

475.29 

605  .  16 

14886.936 

4.9598 

2.9083 

24.7 

77.597 

479.16 

610.09 

15069.223 

4.9699 

2.9123 

24.8 

77-9" 

483-05 

615.04 

15252.992 

4-9799 

2.9162 

24.9 

78.226 

486.96 

620.01 

15438.249 

4.9899 

2.Q20I 

25.0 

78.540 

490.87 

625.00 

15625.000 

5.0000 

2.9241 

25.1 

78.854 

494.81 

630.01 

15813-251 

5-0099 

2.9279 

25.2 

79.168 

498.76 

635-04 

16003.008 

5.0199 

2.9318 

25-3 

79-482 

502.73 

640.09 

16194.277 

5-0299 

2.9356 

25  4 

79.796 

506.71 

645.16 

16387.064 

5-0398 

2.9395 

25-5 

80.  in 

510.71 

650.25 

16581.375 

5-0497 

2-9434 

25.6 

80.425 

514-72 

655-36 

16777.216 

5.0596 

2.9472 

25-7 

80.739 

518.75 

660.49 

16974.593 

5-0695 

2.9510 

25.8 

81.053 

522.79 

665.64 

17173.512 

5-0793 

2-9549 

25-9 

81.367 

526.85 

670.81 

17373-979 

5.0892 

2.9586 

762 


EXPERIMENTAL  ENGINEERING. 
CONSTANTS— Continued. 


ff 

Hit 

"'4 

«» 

«* 

*« 

h 

26.0 

81.681 

530.93 

676.00 

17576.000 

5.0990 

2.9624 

26.1 

81.996 

535-02 

681.21 

17779.581 

5.1088 

2.9662 

26.2 

82.310 

539-13 

686.44 

17984.728 

5.1185 

2.9701 

26.3 

82.624 

543-25 

691.69 

18191.447 

5.1283 

3.9738 

26.4 

82.938 

547-39 

696.96 

18399.744 

5.1380 

2.9776 

26.5 

83.252 

551-55 

702.25 

18609.625 

5.1478 

2.9814 

26.6 

83.566 

555.72 

707.56 

18821.096 

5.1575 

2.9851 

26.7 

83.881 

559.90 

712.89 

19034.163 

5.1672 

2.9888 

26.8 

84.195 

564.10 

718.24 

19248.832 

r.i768 

2.9926 

26.9 

84.509 

568.32 

723.61 

19465  .  109 

5.1865 

2.9963 

27.0 

84.823 

572.56 

729.00 

19683.000 

5.1962 

3.0000 

27.1 

85.137 

576.80 

734.41 

I9902.5II 

5-2057 

3.0037 

27.2 

85.451 

581.07 

739.84 

2OI23.648 

5-2153 

3.0074 

27-3 

85.765. 

585.35 

745.29 

20346.417 

5.2249 

3.0111 

27.4 

86.080 

589.65 

750.76 

205/0.824 

5.2345 

3.0147 

37*5 

86.394 

593.96 

756.25 

20796.875 

5.2440 

3.0184 

27.6 

86.708 

598.29 

761.76 

21024.576 

5.2535 

3.0221 

27-7 

87.022 

602.63 

767.29 

21253-933 

5.2630 

3.0257 

27.8 

87.336 

606.99 

772.84 

21484.952 

5.2725 

3.0293 

27-9 

87.650 

611.36 

778.41 

21717.639 

5.2820 

3.0330 

28.0 

87.965 

615.75 

784.00 

21952.000 

5-2915 

3.0366 

28.1 

88.279 

620.16 

789.61 

22I88.O4I 

5.3009 

3.0402 

28.2 

88.593 

624.58 

795-24 

2242  L.  768 

5.3103 

3-0438 

28.3 

88.907 

629.02 

800.89 

22  65.187 

5.3I97 

3.0474 

28.4 

89.221 

633.47 

806.56 

22906.304 

5.3291 

3.0510 

28.5 

89-535 

637.94 

812.25 

23149.125 

5.3385 

3.0546 

28.6 

89.850 

642.42 

817.96 

23393.656 

5.3478 

3.0581 

28.7 

90.164 

646.93 

823.69 

23639.903 

5-3572 

3.0617 

28.8 

90.478 

651.44 

829.44 

23887.872 

5.3665 

3.0652 

28.9 

90.792 

655.97 

835.21 

24137.569 

5-3758 

3.0688 

29.0 

91  .  106* 

660.52 

841.00 

24389.000 

5.3852 

3.0723 

29.1 

91.420 

665.08 

846.81 

24642.171 

5  •  3944 

3-0758 

29.2 

91-735 

669.66 

852.64 

24897.088 

5.4037 

3-0794 

29.3 

92.049 

674  .  26 

858.49 

25153.757 

5.4129 

3.0829 

29-4 

92.363 

678.87 

864.36 

25412.184 

5.4221 

3  .  0864 

29  5 

92.677 

683.49 

870.25 

25672.375 

5.43I3 

3-0899 

29.6 

92.991 

688.13 

876.16 

25934.336 

5.4405 

3.0934 

29.7 

93.305 

692.79 

882.09 

26198.073 

5-4497 

3.0968 

29.8 

93.619 

697.47 

888.04 

26463  .  592 

5.4589 

3.1003 

29.9 

93.934 

702.15 

894.01 

26730.899 

5.4680 

3.1038 

30.0 

94.248 

706.  867 

900.00 

27000.000 

5.4772 

3.1072 

30.1 

94-562 

711.58 

906.01 

27270.90! 

5.4863 

3-1107 

30.2 

94.876 

716.32 

912.04 

27543.608 

5-4954 

3.1141 

NUMERICAL   CONSTANTS. 
CONSTANTS — Continued. 


763 


n 

nit 

««T 

4 

«» 

«* 

*n 

h 

30.3 
30-4 

95.190 
95-505 

721.07 
725.83 

9I8.O9 
924.16 

278I8.I27 
28094.464 

5  •  5045 
5.5136 

—  —    

3-1176 
3.1210 

30-5 
30.6 

95.819 
96.133 

730.62 
735-42 

930.25 
936.36 

28372.625 
28652.616 

5.5226 
5.5317 

3.1244 

a  1278 

30.7 
30.8 

96.447 
96.761 

740.23 
745.06 

942.49 
948.64 

28934.443 
292I8.II2 

5.5407 
5-5497 

J  .  A  ^  /  U 
3-I3I2 
3.1346 

30.9 

97-075 

749.91 

954-81 

29503.629 

5.5587 

3.1380 

31.0 

97.389 

754-77 

96I.OO 

297QI.OOO 

5-5678 

3.I4I4 

$1.1 

97  .  704 

759.65 

967.21 

30080.231 

5.5767 

3.1448 

31.2 

98.018 

764.54 

973-44 

3037L328 

5-5857 

3.  I48l 

31-3 

98.332 

769.45 

979.69 

30664.297 

5  .  5946 

3.I5I5 

31-4 

98.646 

774-37 

985.96 

30959.144 

5-6035 

3.1548 

31-5 

98.960 

779.31 

992.25 

31255.875 

5.6124 

3.1582 

31.6 

99.274 

784.27 

998.56 

31554.496 

5.6213 

3.I6I5 

31-7 

99.588 

789.24 

IOO4.89 

31855.013 

5.6302 

3.1648 

31.8 

99.903 

794.23 

IOII.24 

32157.432 

5-6391 

3.I68I 

31.9 

100.22 

799.23 

IOI7.6I 

32461.759 

5.6480 

.3.1715 

32.0 

100-53 

804.25 

1024.00 

32768.000 

5-6569 

3.1748 

32.1 

100.85 

809.28 

IO3O.4I 

33076.161 

5-6656 

3.1781 

32.2 

101.  16 

814.33 

1036.84 

33386.248 

5.6745 

3.1814 

32.3 

101.47 

819.40 

1043.29 

33698.267 

5-6833 

3-I847 

32-4 

101.79 

824.48 

1049.76 

34012.224 

5.6921 

3.1880 

32-5 

IO2.  IO 

829.58 

1056.25 

34328.125 

5.7008 

3-I9I3 

32.6 

102.42 

834-69 

1062.75 

34645.976 

5.7096 

3-1945 

32.7 

102.73 

839.82 

1069.29 

34965  .  783 

5-7183 

3.1978 

32.8 

103.04 

844.96 

1075.84 

35287.552 

5.7271 

3.2010 

32.9 

103.36 

850.12 

1082.41 

35611.289  « 

5.7358 

3-2043 

33-o 

103.67 

855.30 

loSg.OO 

35937.000 

5.7446 

3-2075 

33-1 

103.99 

860.49 

I095.6I 

36264.69! 

5.7532 

3.2108 

33-2 

104  .  30 

865.70 

IIO2.24 

36594.368 

5.7619 

3.2140 

33-3 

104.62 

870.92 

II08.89 

36926.037 

5.7706 

3.2172 

33-4 

104.93 

876.16 

1II5-56 

37259.704 

5-7792 

3-2204 

33-5 

105.24 

88I.4I 

1122.25 

37595-375 

5.7879 

3.2237 

33-6 

105.56 

886.68 

1128.96 

37933.056 

5.7965 

3.2269 

33-7 

105.87 

891.97 

1135-69 

38272.753 

5.8051 

3.2301 

33-8 

106.19 

897.27 

1142.44 

38614.472 

5.8137 

3.2"32 

33-9 

106.50 

902.59 

1149.21 

38958.219 

5-8223 

3^364 

34-0 

106.81 

907.92 

II56.OO 

39304.000 

5-8310 

3.2396 

34-i 

107.13 

913.27 

II62.8I 

39651.821 

5.8395 

3.2428 

34-2 

107.44 

918.63 

1:69.64 

40001.683 

5  .  8480 

3.2460 

34-3 

107.76 

924.01 

1176.49 

40353.607 

5.8566 

3.2491 

34-4 

108.07 

929.41 

Il83o6 

40707  .  584 

5-8651 

3  2522 

EXPEKIMEN  TA L  ENGINEERING. 
CONSTANTS — Contin  ued. 


n 

rnt 

^l 

«* 

«« 

tf* 

fa 

34-5 

108.38 

934.82 

1190.25 

41063.625 

5.8730 

3.2554 

34-6 

108.70 

940.25 

1197.16 

41421.736 

5.8821 

3.2586 

34-7 

IOQ.OI 

945.69 

1204.09 

41781.923 

5.8906 

3.2617 

34-8 

109.33 

95I-I5 

1211.04 

42144.192 

5.8991 

3  •  2648 

34-9 

109.64 

956.62 

1218.01 

42508.549 

5.9076 

3.2679 

35-o 

109.96 

962.11 

1225.00 

42875.000 

5.9161 

3-2710 

35-1 

110.27 

967.62 

1232.01 

43243.551 

5.9245 

3.2742 

35-2 

110.58 

973.14 

1239-04 

43614.208 

5.9329 

3.2773 

35-3 

IlO.gO 

978.68 

1246.09 

43986.977 

5-9413 

3-2804 

35-4 

III.  21 

984.23 

1253.16 

44361.864 

5-9497 

3-2835 

35-5 

"1-53 

989.80 

1260.25 

44738.875 

5.9581 

3.2866 

35-6 

111.84 

995.38 

1267.36 

45118.016 

5-9665 

3.2897 

35-7 

112.15 

1000.98 

1274.49 

45499.293 

5-9749 

3-2927 

35-8 

112.47 

IOO6  .  6O 

1281.64 

45882.712 

5.9833 

3.2958 

35-9 

.  112.78 

1012.23 

1288.81 

46268.279 

5.9916 

3-2989 

36.0 

113.10 

1017.88 

1296.00 

46656  .  ooo 

6.0000 

3-3019 

36.1 

113.41 

1023.54 

1303.21 

47045.881 

6.0083 

3-3050 

36.2 

113-73 

1029.22 

1310.44 

47437.928 

6.0166 

3  .  3080 

36.3 

114.04 

I034.9T 

1317-69 

47832.147 

6.0249 

3-3"! 

36.4 

H4.35 

1040.62 

1324-96 

48228.544 

6.0332 

3.3141 

39-5 

114.67 

1046.35 

1332.25 

48627.125 

6.0415 

3.3I7I 

36.6 

114.98 

1052.09 

I339-56 

49027.896 

6.0497 

3  •  3202 

367 

115-30 

1057.84 

1346.89 

49430.863 

6.0580 

3-3232 

36.8 

115.61 

1063.62 

1354.24 

49836.032 

6.0663 

3.3262 

36.9 

115.92 

1069.41 

1361.61 

50243.409 

6.0745 

3-3292 

37-o 

116.24 

1075.21 

1369.00 

50653.000 

6.0827 

3-3322 

37-1 

116.55 

I08l.03 

1376.41 

51064.811 

6.0909 

3-3352 

37-2 

116.87 

1086.87 

1383.84 

51478.848 

6.0991 

3-3382 

37-3 

117.18 

1092.72 

1391.29 

51895.117 

6.1073 

3-3412 

37-4 

117.50 

1098.58 

1398-76 

52313.624 

6.1155 

3-3442 

37-5 

117.81 

1104.47 

1406.25 

52734.375 

6.1237 

3-3472 

37-6 

118.12 

IIIO.36 

1413.76 

53157-376 

6.1318 

3-3501 

37-7 

118.44 

1116.28 

1421.29 

53582.633 

6.1400 

3-3531 

37-8 

118.75 

1122.21 

1428.84 

54010.152 

6.1481 

3.356r 

37-9 

119.07 

1128.15 

1436.41 

54439.939 

6.1563 

3-3590 

38.0 

119-38 

H34.II 

1444.00 

54872.000 

6.1644 

3.3620 

38.1 

119.69 

1140.09 

1451.61 

55306.341 

6.1725 

3.3649 

38.2 

120.01 

1146.08 

1459.24 

55742.968 

6.1806 

3.3679 

38.3 

120.32 

1152.09 

1466.89 

56181.887 

6.1887 

3.3708 

38.4 

120.64 

1158.12 

1474.56 

56623.  104 

6.1967 

3-3737 

38-5 

120.95 

1164.  i6/ 

1482.25 

57066.625 

6.2048 

3.3767 

38.6 

121.27 

1170.21 

1489.96 

57512.456 

6.2129 

3-3796 

.38-7 

121.58 

1176.28 

1497.69 

57960.603 

6.2209 

3-3825 

NUMERICAL   CONSTANTS. 
CONSTANTS— Continued. 


765 


« 

«JT 

4 

- 

* 

* 

h 

38.8 
38-9 

121.89 

122.21 

H82.37 
1188.47 

1505.44 
1513.21 

58411.072 
58863.869 

6.2289 
6.2370 

3-3854 
3-3883 

39-o 

122.52 

1194.59 

1521.00 

59319.000 

6.2450 

3.3912 

39-i 

122.84 

I2OO.72 

I528.8I 

59776.471 

6.2530 

7  .  -304.1 

39-2 

123.15 

1206.87 

1536.64 

60236  .  288 

6.2610 

j  jy^t1 
3.397O 

39-3 

123.46 

1213.04 

1544-49 

60698.457 

6.2689 

3  .  3999 

39-4 

123.78 

1219.22 

1552.36 

61162.984 

6.2769 

3-4028 

39-5 
39-6 

124.09 
124.41 

1225.42 
1231.63 

1560.25 
1568.16 

61629.875 
62099.136 

6.2849 
6.2928 

3.4056 
3.4085  v 

39-7 

124.72 

1237.86 

1576.09 

62570.773 

6.3008 

3.4114 

39-8 

125.04 

1244.10 

1584.04 

63044.792 

6.3087 

3.4142 

39-9 

125.35 

1250.36 

1592.01 

63521.199 

6.3166 

3.4I7I 

40.0 

125.66 

1256.64 

I6OO.OO 

64000.000 

6.3245 

3.4200 

40.1 

125.98 

1262.93 

I  608.  01 

64481.201 

6.3325 

3.4228  i 

40.2 

126.29 

1269.23 

l6l6.O4 

64964  .  808 

6.3404 

3.4256 

40-3 

I26.6I 

1275.56 

1624.09 

65450.827 

6.3482 

3.4285 

40.4 

126.92 

I28I.90 

1632.16 

65939.264 

6.3561 

3.4313 

40.5 

127.23 

1288.25 

1640.25 

66430.125 

6.3639 

3-4341 

4O.6 

127.55 

1294.62 

1648.36 

66923.416 

6.3718 

3-4370 

40.7 

127.86 

1301.00 

1656.49 

67419.143 

6.3796 

3  •  4398 

40.8 

I28.I8 

1307.41 

1664.64 

67911.312 

6.3875 

7  - 

3  .  4426 

40.9 

128.49 

1313.82 

l672.8l 

68417.929 

6.3953 

3-4454 

4i.o 

I28.8I 

1320.25 

1681.00 

68921.000 

6.4031 

3.4482 

4i.  i 

129.12 

1326.70 

1689.21 

69426.531 

6.4109 

3-4510 

41.2 

129.43 

1333.17 

1697.44 

69934.528 

6.4187 

41.3 

129.75 

1339.65 

1705-69 

70444.997 

6.4265 

3.4566 

41.4 

130.06 

1346.14 

1713.96 

70957.944 

6-4343 

3-4594 

41-5 

130.38 

1352.65 

1722.25 

71473.375 

6.4421 

3  .  4622 

41.6 

130-69 

1359.18 

1730.56 

71991.296 

6.4498 

3.4650 

41.7 

131.00 

1365.72 

1738.89 

72511.713 

6-4575 

3.4677 

41.8 

I3L32 

1372.28 

1747.24 

73034.632 

6.4653 

3.4705 

41.9 

131.63 

1378.85 

I755.6I 

73560.059 

6.4730 

3-4733 

42.0 

131-95 

1385.44 

1764.00 

74088.000 

6.4807 

3.4760 

42.1 

132.26 

1392.05 

1772.41 

74618.461 

6.4884 

3.4788 

42.2 

132.58 

1398.67 

1780.84 

75151.448 

6.4961 

3-4815 

42.3 

132.89 

1405.31 

1789.29 

75686.967 

6.5038 

3.4843 

42.4 

133.20 

1411.96 

1797.76 

76225.024 

6.5H5 

3-4870 

42.5 

I33-52 

1418.63 

1806.25 

76765.625 

6.5192 

3-4898 

42.6 

133.83 

1425.31 

1814-76 

77308.776 

6.5268 

3*4925 

42.7 

134.15 

1432.01 

1823.29 

77854.483 

6.5345 

3  4952 

42.8 

134.46 

1438.72 

1831.84 

78402.752 

6.5422 

3-4080 

42.9 

134-77 

1445.45 

1840.41 

78953.569 

6.5498 

3.5007 

766 


EXPERIMENTAL  ENGINEERING. 
CONSTANTS — Continued. 


n 

nit 

"'4 

«' 

*• 

fa 

h 

43-0 

135-09 

1452.20 

1849.00 

79507.000 

6-5574 

3-5034 

43-i 

135-40 

1458.96 

1857.61 

80062.991 

6.5651 

3-5061 

43-2 

135.72 

1465.74 

1866.24 

80621.568 

6.5727 

3-5088 

43-3 

136-03 

1472.54 

1874.89 

81182.737 

6.5803 

3.5II5 

43-4 

136.35 

1479-34 

1883.56 

81746.504 

6.5879 

3.5H2 

43-5 

136.66 

1486.17 

1892.25 

82312.875 

6-5954 

3.5169 

43-6 

136.97 

1493-01 

1900.96 

82881.856 

6.6030 

3-5I96 

43-7 

137.29 

1499.87 

1909.69 

83453.453 

6.6ic6 

3-5223 

43-8 

137.60 

1506.74 

1918.44 

84027.672 

6.6182 

3-5250 

43-9 

137.92 

1513.63 

1927.21 

84604.519 

6.6257 

3.5277 

44.0 

138.23 

1520.53 

1936.00 

85184.000 

6.6333 

3.5303 

44.1 

138.54 

1527.45 

1944.81 

85766.121 

6.6408 

3-5330 

44.2 

138.86 

1534-39 

I953-64 

86350.888 

6.6483 

3-5357 

44-3 

139-17 

1541-3* 

1962.49 

86938.307 

6.6558 

3-5384 

44-4 

139-49 

1548.30 

1971.36 

87528.384 

6.6633 

3-54^0 

44  5 

139.80 

1555.28 

1980.25 

88121.125 

6.6708 

3-5437 

44.6 

140.12 

1562.28 

1989.16 

88716.536 

6.6783 

3-5463 

44-7 

140.43 

1569.30 

1998.09 

89314.623 

6.6858 

3-5490 

44-8 

140.74 

1576.33 

2007.04 

89915.392 

6.6933 

3.55i6 

44-9 

141.06 

1583.37 

2OIO.OI 

90518.849 

6  .  7007 

3-5543 

45-0 

I4L37 

1590.43 

2O25.OO 

91125.000 

6.7082 

3.5569 

45-i 

141.69 

I597-5I 

2034.01 

91733-851 

6.7156 

3-5595 

45-2 

142.00 

1604.60 

2043.04 

92345.408 

6.7231 

3-5621 

45-3 

142.31 

1611.71 

2052.09 

92959-677 

6.7305 

3-5648 

45-4 

142.63 

1618.83 

2061.  16  ' 

93576.664 

6.7379 

3-5674 

45-5 

142.94 

1625.97 

2070.25 

94196.375 

6.7454 

3-5700 

45-6 

143-26 

1633.13 

2079.36 

94818.816 

6.7528 

3-5726 

45-7 

143-57 

1640.30 

2088.49 

95443-993 

6  .  7602 

3-5752 

45.8 

143-88 

1647.48 

2097.64 

96071.912 

6.7676 

3-5778 

45-9 

144.20 

1654.68 

2106.  8r 

96702.579 

6.7749 

3.5805 

46.0 

144.51 

1661.90 

2116.00 

97336.000 

6.7823 

3-5830 

46.1 

144.83 

1669.14 

2125.21 

97972.181 

6.7897 

3-5856 

46.2 

I45-I4 

1676.39 

2134.44 

98611.128 

6.7971 

3-5882 

46.3 

145.46 

1683.65 

2143.69 

99252.347 

6.8044 

3-5908 

46.4 

145-77 

1690.93 

2152.96 

99897.344 

6.8117 

3-5934 

46.5 

146.08 

1698.23 

2162.25 

100544.625 

6.8191 

3.5960 

46.6 

146.40 

1705.54 

2171.56 

101194.696 

6.8264 

3-5986 

46-7 

146.71 

1712.87 

2180.89 

101847.563 

6.8337 

3.6011 

46.8 

147.03 

1720.21 

2190.24 

102503.232 

6.8410 

3.6037 

46.9 

147-34 

1727.57 

2199.61 

103161.709 

6.8484 

3.6063 

47.0 

147.65 

1734.94 

2209.00 

103823.000 

6.8556 

3.6088 

47.1 

147-97 

1742.34 

2218.41 

104487.111 

6.8629 

3  6114 

,47-2 

148.28 

1749.74  j 

2227.84 

105154-048  1 

6.8702 

3.6139 

NUMERICAL   CONSTANTS. 
CONSTANTS — Contin  ued. 


767 


n 

nit 

4 

.. 

ft* 

« 

* 

47-3 

148.60 

1757.16 

2237.29 

105823.817 

6.8775 

3.6165 

47-4 

148.91 

1764.60 

2246.76 

106496.424 

6.8847 

3-6190 

47-5 

149.23 

1772.05 

2256.25 

I07I7I.875 

6.8920 

3.6216 

47.6 

149-54 

1779.52 

2265.76 

107850.176 

6.8993 

3.6241 

47-7 

149.85 

1787.01 

2275.29 

108531.333 

'  6.9065 

3-6267 

47-8 

150.17 

1794-51 

2284.84 

109215.352 

6.9137 

3.6292 

47-9 

150.48 

1802.03 

2294.41 

109902.239 

6  .  9209 

3.6317 

48.0 

150.80 

1809.56 

2304.00 

110592.000 

6.9282 

3-6342 

48.1 

I5I.H 

1817.  II 

23I3.6I 

111284.641 

6-9354 

3.6368 

48.2 

151.42 

1824.67 

2323.24 

III980.I68 

6  .  9426 

3-6393 

48.3 

I5I-74 

1832.25 

2332.89 

112678.587 

6.9498 

3.6418 

48.4 

152.05 

1839.84 

2342.56 

"3379-904 

6.9570 

3-6443 

48.5 

152.37 

1847.45 

2352.25 

II4084.I25 

6  .  9642 

3.6468 

48.6 

152.68 

1855.08 

2361.96 

II479I.256 

6.9714 

3-6493 

48.7 

153.00 

1862.72 

2371.69 

II550I.303 

6.9785 

3.6518 

48.8 

I53.3I 

1870.38 

2381.44 

II62I4.272 

6.9857 

3-6543 

48.9 

153.62 

1878.05 

2391.21 

116930.169 

6.9928 

3-6568 

49.0 

153.94 

1885.74 

24OI.OO 

117649.000 

7.0000 

3-6593 

49.1 

154.25 

1893.45 

24I0.8I 

H8370.77I 

7.0071 

3.6618 

49-2 

154-57 

1901.17 

2420.64 

119095.488 

7.0143 

3-6643 

49-3 

154.88 

1908.90 

2430.49 

II9823.I57 

7.0214 

3.6668 

49-4 

155.19 

1916.65 

2440.36 

120553.784 

7.0285 

3.6692 

49-5 

155-51 

1924.42 

2450.25 

121287.375 

7.0356 

3-6717 

4Q-6 

155.82 

1932.21 

2460.16 

122023.936 

7.0427 

3-6742 

*T7 

49-7 

156.14 

I94O.OO 

2470.09 

122763.473 

7.0498 

3.6767 

49-8 

156.45 

1947.82 

2480.04 

I23505-992 

7.0569 

3.6791 

49-9 

156.77 

I955.65 

249O.OI 

124251.499 

7.0640 

3.6816 

50.0 

I57-08 

1963.50 

25OO.OO 

125000.000 

7.0711 

3.6840 

51.0 

160.22 

2042.82 

26OI.OO 

132651.000 

7.1414 

3.7084 

52.0 
53.o 

163.36 
166.50 

2123.72 
2206.19 

27O4.OO 
2809.00 

140608.000 
148877.000 

7.2111 
7.2801 

3-7325 
3-7563 

54-0 
55-0 
56.0 

169  .  64 

172.78 
175  93 

229O.22 

2375.83 
2463.01 

2916.00 
3025.00 
3136.00 

157464.000 
166375.000 
175616.000 

7.3485 
7.4162 

7.4833 

3.7798 
3.8030 

3.8259 

57-o 
58.0 

179.07 
182.21 

255I-76 
2642.08 

3249.00 
3364.00 

185193.000 
I95II2.0CO 

7^6158 

3.8485 
3.8709 

60.0 

I85-35 
188.49 

2733-^7 
2827.44 

3481.00 
3600.00 

205379.000 
216000.000 

7.6811 
7.7460 

3.8930 

3-9M9 

61.0 
62.0 
63.0 
64.0 
65.0 
66.0 

191-63 

194-77 
197.92 
201.06 
204  .  20 
207.34 

2922.47 
3019.07 
3II7-25 
3216.99 
3318.31 
3421.20 

3721.00 
3844.00 

3969.00 
4096.00 
4225.00 
4356.00 

226981.000 
238328.000 
250047.000 
262144.000 
274625.000 
287496.000 

7.8102 
7.8740 

7-9373 
8.OOOO 
8.0623 
8.1240 

3-9579 
3-97QI 
4.0000 
4.0207 
4.0412 

7  68 


EXPERIMENTAL   ENGINEERING. 
CONSTANTS — Continued. 


m 

nit 

*? 

4 

«» 

«8 

Vn 

h 

67.0 

210.48 

3525.66 

4489.00 

300763.000 

8.1854 

4-0615 

68.0 

213.63 

3631-69 

4624  .  oo 

314432.000 

8.2462 

4-0817 

69.0 

216.77 

3739-29 

4761  .00 

328509.000 

8.3066 

4.1016 

70.0 

219.91 

3848.46 

4900  .  oo 

343000  .  ooo 

8.3666 

4.1213 

71.0 

223.05 

3959-20 

5041.00 

357911.000 

8.4261 

4-1408 

72.0 

226.19 

4071.51 

5184.00 

373248.000 

8.4853 

4.1602 

73-o 

229.33 

4185-39 

5329.00 

389017.000 

8.5440 

4.1793 

74.0 

232.47 

4300.85 

5476.00 

405224.000 

8.6023 

4.1983 

75-o 

235.62 

4417.87 

5625.00 

421875.000 

8.6603 

4.2172 

76.0 

238.76 

4536.47 

5776.oo 

438976.000 

8.7178 

4-2358 

77.0 

241.90 

4656.63 

5929.00 

456533.000 

8.7750 

4-2543 

78.0 

245.04 

4778.37 

6084.00 

474552.000 

8.  318 

4.2727 

79.0 

248.18 

4901.68 

6241.00 

493039.000 

8.8882 

4.2908 

80.0 

251.32 

5026.56 

6400.00 

512000.000 

8.9443 

4.3089 

81.0 

254.47 

5I53.0I 

6561.00 

531441.000 

9.0000 

4.3267 

82.0 

257.61 

5281.03 

6724.00 

551368.000 

9-0554 

4.3445 

83.0 

260.75 

5410.62 

6889.00 

571787.000 

9.1104 

4-3621 

84.0 

263.89 

554I-78 

7056.00 

592704.000 

9.1652 

4-3795 

85.0 

267  .  03 

5674.50 

7225.00 

614125.000 

9-  "195 

4-3968 

86.0 

270.17 

5808.81 

7396.00 

636056.000 

9.2736 

4.4140 

87.0 

273.32 

5944.69 

7569.00 

658503.000 

9.3274 

4.4310 

88.0 

276.46 

6082.13 

7744.00 

681472.000 

9.3808 

4.4480 

89.0 

279.60 

6221.13 

7921.00 

704969.000 

9.4340 

4.4647 

90.0 

282.74 

6361.74 

8100.00 

729000.000 

9.4868 

4.4814 

91.0 

285.88 

6503.89 

8281.00 

753571.000 

9-5394 

4.4979 

92.0 

289.02 

6647.62 

8464.00 

778688.000 

9-5917 

4.5144 

93-o 

292.17 

6792.92 

8649  .  oo 

804357.000 

9-6437 

4.5307 

94.0 

295.31 

6939.78 

8836.00 

830584.000 

9.6954 

4.5468 

95-0 

298.45 

7088.23 

9025.00 

857375.000 

9.7468 

4-5629 

96.0 

301.59 

7238.24 

9216.00 

884736.000 

9.7980 

4-5789 

97.0 

304.73 

7389.83 

9409  .  oo 

912673.000 

9.8489 

4-5947 

98.0 

307.87 

7542.98 

9604  .  oo 

941192.000 

9.89Q5 

4.6104 

99.0 

3II.O2 

7697.68 

9801.00 

970299  .  ooo 

9.9499 

4.6261 

100.  0 

3I4.I6 

7854.00 

IOOOO.OO 

lOOOOOO.OOO 

10.0000 

4.6416 

LOGARITHMS  OF  NUMBERS. 


769 


III. 

LOGARITHMS   OF   NUMBERS. 


No, 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

0000 

0043 

0086 

0128 

0170 

0212 

0253 

0294 

°334 

°374 

ii 

0414 

0453' 

0492 

0531 

0569 

0607 

0645 

0682 

0719 

°755 

12 

0792 

0828 

0864 

0899 

0934 

0969 

1004 

1038 

1072 

*  ***J 

1106 

13 

"39 

'"73 

1206 

1239 

1271 

1303 

1335 

1367 

1399 

143° 

*4 

1461 

1492 

1523 

'553 

1584 

1614 

1644 

1673 

1703 

1732 

15 

,1761 

1790 

1818 

1847 

1875 

1903 

1931 

1959 

1987 

2014 

16 

2041 

2068 

2095 

2122 

2148 

2175 

2201 

2227 

2253 

2279 

*-7 

2304 

2330 

2355 

2380 

2405 

2430 

2455 

2480 

2504 

2529 

IB 

2553 

2577 

2601 

2625 

2648 

2672 

2695 

2718 

2742 

2765 

19 

2788 

2810 

2833 

2856 

2878 

2900 

2923 

2945 

2967 

2989 

20 

3010 

3032 

3054 

3075 

3096 

3Il8 

3139 

3160 

3181 

3201 

21 

3222 

3243 

3263 

3284 

3304 

3324 

3345 

3365 

3385 

3404 

22 

3424 

3444 

3464 

3483 

3502 

3522 

3541 

3560 

3579 

3598 

23 

3617 

3636 

3655 

3674 

3692 

3711 

3729 

3747 

3766 

3784 

24 

3802 

3820 

3838 

3856 

3874 

3892 

3909 

3927 

3945 

3962 

25 

3979 

3997 

4014 

4031 

4048 

4065 

4082 

4099 

4116 

4133 

26 

415° 

4166 

4183 

4200 

4216 

4232 

4249 

4265 

4281 

4298 

27 

43H 

4330 

4346 

4362 

43/8 

4393 

4409 

4425 

4440 

4456 

28 

4472 

4487 

4502 

4518 

4533 

4548 

4564 

4579 

4594 

4609 

2Q 

4624 

4^39 

4654 

4669 

4683 

4698 

47U 

4728 

4742 

4757 

30 

4771 

4786 

4800 

4814 

4829 

'4843 

4857 

4871 

4886 

4900 

31 

4914 

4928 

4942 

4955 

4969 

4983 

4997 

5011 

5024 

5038 

32 

5°65 

5°79 

5092 

5^5 

51  19 

5*32 

5H5 

5  '59 

5172 

33 

5°85 

5198 

5211 

5224 

5237 

525° 

5263 

5276 

5289 

5302 

34 

5315 

5328 

5340 

5353 

5366 

5378 

5391 

5403 

54l6 

5428 

35 
36 
37 

544i 
55^3 
5682 

5453 

5575 
5694 

5465 
5587 
57°5 

5478 
5599 
57J7 

5490 
5611 

5729 

55°2 
5623 

5740 

SS'4 
.5635 
5752 

5527" 
5647 
5763 

5539 
5658 

5670 
5786 

38 

5798 

5809 

5821 

5832 

5843 

5855 

5866 

5877 

5888 

5899 

39 

59" 

5922 

5933 

5544 

5955 

5966 

5977 

5988 

5999 

6010 

4° 

6021 

6031 

6042 

6053 

6064 

6075 

6085 

6096 

6107 

6117 

41 

6128 

6138 

6149 

6160 

6170 

6180 

6191 

6201 

6212 

6222 

42 

6232 

6243 

6253 

6263 

6274 

6284 

6294 

6304 

63H 

6325 

43 

6335 

6345 

6355 

6365 

6375 

6385 

6395 

6405 

6415 

6425 

44 

6435 

6444 

6454 

6464 

6474 

6484 

6493 

6503 

6513 

"6522 

45 
46 

47 
48 

6532 
6628 
6721 
6812 

6542 

6637 
6730 
6821 

655  1 
6646 

6739 
6830 

6561 
6656 
6749 
6839 

6571 
6665 
6758 
6848 

6580 
6675 
6767 
6857 

6590 
6684 
6776 
6866 

6599 
6693 
6785 
6875 

6609 
6702 
6794 
6884 

6618 
6712 
6803 
6893 

49 

6902 

6911 

6920 

6928 

6937 

6946 

6955 

6964 

6972 

6981 

5° 

6990 

6998 

7007 

7016 

7024 

7°33 

7042 

7050 

70591 

7067 

52 
53 
54 

7076 
7160 
7243 

7324 

7084 
7168 

7251 
7332 

7093 
7177 

7259 
7340 

7101 

7267 
7348 

7110 
7J93 

7275 
7356 

7118 
7202 
7284 
7364 

7126 
7210 
7292 
7372 

7*35 
7218 
7300 
7380 

7  '43 
7226 

7308 
7388 

7'52 
7235 
73i6 
7396 

No, 

O 

1 

2 

3 

4 

5 

6 

7 

3 

9 

770 


EXPERIMEN  TA  L   ENGINEERING. 
LOGARITHMS  OF  NUMBERS — Continued. 


No, 

O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

55 

7404 

7412 

7419 

7427 

7435 

7443 

745' 

7459 

7466 

7474 

56 

7482 

7490 

7497 

75°5 

75'3 

7520 

7528 

7536 

7543 

755i 

57 

7559 

7566 

7574 

7582 

7589 

7597 

7604 

7612 

-7619 

7627 

58 

7634 

7642 

7649 

7657 

7664 

7672 

7679 

7686 

7694 

7701 

59 

7709 

7716 

7723 

773i 

7738 

7745 

7752 

7760 

7767 

7774 

60 

7782 

7789 

7796 

7803 

7810 

7818 

7825 

7832 

7839 

7846 

61 

7853 

7860 

7868 

7875 

7882 

7889 

7896 

7903 

7910 

7917 

62 
63 

7924 
7993 

793i 
8000 

7938 
8007 

7945 
8014 

7952 
8021. 

7959 
8028 

7966 
8035 

7973 
8041 

7980 
8048 

7987 
8055 

64 

8062 

8069 

8075 

8082 

8089 

8096 

8102 

8109 

8116 

8122 

65 

8129 

8136 

8142 

8149 

8156 

8162 

8169 

8176 

8182 

8189 

66 

8i95 

8202 

8209 

8215 

8222 

8228 

8235 

8241 

8248 

8254 

67 

8261 

8267 

8274 

8280 

8287 

8293. 

8299 

8306 

8312 

8319 

68 

8325 

8331 

8338 

8344 

8351 

8357 

8363 

8370 

8376 

8382 

69 

8388 

8395 

8401 

8407 

8414 

8420 

8426 

8432 

8439 

8445 

70 

8451 

8457 

8463 

8470. 

8476 

8482 

8488 

8494 

8500 

8506 

7* 

8513 

8519 

8525 

8531 

8537 

8543 

8549 

8555 

8561 

8567 

72 

8573 

8579 

8585 

8591 

8597 

8603 

8609 

8615 

8621 

8627 

73 

8633 

8639- 

8645 

8651 

8657 

8663 

8669 

8675 

8681 

8686 

74 

8692 

8698 

8704 

8710 

871.6 

8722 

8727 

8733 

~8739 

8745 

75 

8751 

8756 

8762 

8768 

8774 

8779 

8785 

8791 

8797 

8802 

76 

8808 

8814 

8820 

8825 

8831 

8837 

8842 

8848 

8854 

8859 

77 

8865 

8871 

8876 

8882 

8887 

8893 

8899 

8904 

8910 

8915 

78 

8921 

8927 

8932 

8938 

8943 

8949 

8954 

8960 

8965 

8971 

79 

8976 

8982 

8987 

8993 

8998 

9004 

9009 

9015' 

9020 

9025 

80 

9031 

9036 

9042 

9047 

9°53 

9058 

9063 

9069 

9074 

9079 

81 

9085 

9090 

9096 

9101 

9106 

9112 

9117. 

9122 

9128 

9133 

82 

9138 

9H3 

9149 

9154 

9159 

9165 

9170 

9175 

9180 

9186 

83 

9191 

9196 

9201 

9206 

9212 

9217 

9222 

9227 

9232 

9238 

B4-. 

9243 

9248 

9253 

9258 

9263 

9269 

9274 

9279 

9284 

9289 

85 

9294 

9299 

9304 

9309 

93*5 

9320 

9325 

'9330 

9335 

9340 

86 

9345 

935° 

9355 

9360 

9365 

937° 

9375 

9380 

9385 

9390 

87 

.9395 

9406 

9405 

9410 

9415 

9420 

9425 

9430 

9435 

9440 

88 

9445 

945° 

9455 

9460 

9465 

9469 

9474 

9479 

9484 

9489 

85 

9494 

9499 

95/H 

95°9^ 

95'3 

95l8 

9523 

9528 

9533 

9538 

go 

9542 

"9547 

9552 

9557 

9562 

9566 

9571 

9576 

958i 

9586 

9i 

9590 

9595 

9600 

9605 

9609 

9614 

9619 

9624 

9628 

9633 

92 

9638 

9643 

9647 

9652 

9657 

9661 

9666 

9671 

9675 

9680 

93 

9685 

9689 

9694 

9699 

97°3 

9708 

97I3 

9717 

9722 

9727 

94 

9731 

9736 

9741 

9745 

9750 

9754 

9759 

9763 

9768 

9773 

95 

9777 

9782 

9786 

979i 

9795 

9800 

9805 

9809 

9814 

9818 

96 

9823 

9827 

9832 

9836 

9841 

9845 

9850 

9854 

9859 

9863 

97 

9868 

9872 

9877 

9881 

9886 

9890 

9894 

.9899 

9903 

9908 

98 

9912 

9917 

9921 

9926 

9930 

9934 

9939 

9943 

9948 

9952 

99 

9956 

9961 

9965 

9969 

9974 

9978 

9983 

9987 

9991 

9996 

No, 

O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

LOGARITHMIC  FUNCTIONS  OF  ANGLES. 


771 


IV. 

LOGARITHMIC    FUNCTIONS   OF   ANGLES. 


Angle. 

Sin. 

D.I'. 

Cos. 

D.  1'. 

Tan. 

D.I'. 

Cot. 

0°    O' 

•—oo 

0.0000 

•  —  oo 

00 

9O°0' 

0°    I07 
0°    20' 

o°  30' 
o°  40' 
o°  50* 

7$S 

.9408 
8.0658 

.1627 

30I.I 
1  76.0 
125.0 
96.9 
70.2 

.0000 

.0000 
.0000 

.0000 
.0000 

.O 
.0 
.0 
.0 
.1 

74637 
.7648 
.9409 
8.0658 
.1627 

3OI.I 
176.1 
124.9 
96.9 
70  2 

2.5363 
.2352 
.0591 
1.9342 
•8373 

89°  50* 
89o40' 
8.9°  30' 

89°  20' 

89°  lo' 

1°    0' 

8.2419^ 

669 

9-9999 

.0 

8.2419 

67.O 

1.7581 

89°  0' 

1°    10' 

i°  20' 
i°  30' 
i°  40' 
i°  50' 

.3088 
.3668 
.4179 
.4637 
•5050 

58.0 
5I.I 

45-8 
4^-3 
•  17.8 

.  -9999 
•9999 
.  -9999 
'  .9998 
.9998 

.0 
.0 

.1 
.0 
.1 

.3089 
.3669 
.4181 
.4638 
•5053 

58.0 
'51.2 

45-7 
'  41-5 
37-8 

.6911 

.6331 

.5819 
•5362 

•4947 

88°  50* 
88°  40' 
38°  30' 
88°  20' 
88°  10' 

2°   0' 

8.5428 

•  -34..  8 

9-9997 

.0 

8.5431 

34.8 

1.4569 

88°  O' 

2°    10' 
2°   20' 
2°   30' 
2°   40' 
2°    50' 

.5776 
.6097 

•6397 

.6677 

.6940 

32.1 
30.0. 
28.0 
.  26.3 

24  8 

•9997 
.9996 
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30.0 
28.1 
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24.9 

.4221 
.3899 
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87°  50' 
87°  40' 
87°  307 
87o2c/ 
87°  10' 

3°  0' 

8.7188 

21  £ 

9-9994 

I 

8.7194 

2r  c 

1.2806 

87°  0' 

3°-io' 
3°.  20' 
3°  30'. 
.3°  40'. 
30.50' 

.7423 
.7645 
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.8059 

.8251  • 

•^JO 
22.2 
21.2 
'2O.2 
I9.2 

18  c 

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.1 
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.  -7429 
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.8261 

22.3 
21.3 

20.2 
194 
18.5 

.2571 
.2348 
•2135 
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86°  50' 
86°  40' 
86°  30' 
86°  20' 
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4°  10' 
4°  20' 
4°  30' 
4°  40' 
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5°'  id 

5°  2^. 
5°  30' 
5°  40' 
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8.8436 
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8.9403 

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9.0070 

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17.7 
17.0 
16.3 
15.8 
15.2 
14.7 
14.2 

13-7 
13-4 
12.9 

12.5 

9-9989 
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.9987 
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9-9983 
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8.8446 
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13-0 
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12.3 

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.0728 
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0-0437 
'  .0299 
.0164 
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0.9907 

86°  O' 

85050' 
85040' 
85°  30' 

85°  20' 

85°  10' 
85°  0' 

84°  50' 
84°  40' 
84°  30' 
84°  2d 
84°  id 

6°  0' 

9.0192 

II  Q 

9.9976 

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9.0216 

12.0 

0.9781 

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o     O    rrJ 

6°  10' 

6°    2d 

6°  30' 
6°  40' 
6°  50' 
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.0311 

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''  -0539 
.  .0648 

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10.7 
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10.8 
10.5 

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.  .9664 
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0.9109 

83°  5C/ 
83°  40' 
83°  30' 

83°  2d 

83°  10' 
83°  0' 

7°  10' 
7°  20' 
7°  30' 

.0961 
.1060 

•"57 

IO.2 

9-9 
9-7 

.9966 
.9964 
'  .9963 

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•0995 
.1096 

.1194 

10.1 

9.8 

.9005 
.8904 
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82°  50' 
82040' 
82°  30' 

D.I'. 

Sin. 

D.  1'. 

Cot. 

D.  1'. 

Tan. 

Angle. 

;;2  EXPERIMENTAL  ENGINEERING. 

LOGARITHMIC  FUNCTIONS  OF  ANGLES — Continued. 


Angle. 

Sin. 

D.I'. 

Cos. 

D.I'. 

Tan. 

D.I'. 

Cot. 

7°  30' 
7°  40' 
7°  50' 

9-II57 

.1252 

•1345 

9-5 

9-3 

9.9963 
.9961 
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.2 
I 

9.1194 
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.1385 

9-7 
9-4' 

Q.7. 

0.88o6 
.8709 
.8615 

82°  30' 
82°  20' 
82°  10' 

8°  0' 

9.1436 

•*• 

8a 

9-9958 

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9.1478 

Q.I 

0.8522 

82°  0' 

8a  io'. 

•I525 

.9956 

'..1569 

.8431 

81°  50^ 

8°  20' 
8°  30' 
8°  40' 
8°  50' 

.1612 
.1697 
.1781 
.1863 

8W  . 
•7 
8.5. 
8.4 
8.2  - 
•  80 

•9954 
'  .9952 

•995° 
-  .9948 

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.2 
.2 
.2 

.1658 

•1745 
.1831 

&7 

8.6 
8.4 

8.2 

.8342 
.8255 
.8169 
.8085 

8iQ>4o' 
81°  30' 
81°  20' 
81°  io' 

9°  0' 

9-I943 

9.9946 

2 

9.1997 

8  i 

0.8003 

81°  0' 

9°  io' 
9°  20' 
9°  30' 
9°  40' 
9°  50' 

,2022 
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.2176 
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.2324' 

7*9 

7-8 
.7.6 

7-5 
7-3 

7  1 

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.2 
.2. 
.2 
.2 

.2078 
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.2236 
•2313 
'  .2389 

8.0 
7.8 

g 

.7922 
.7842 
.7764 
.7687 
.7611 

80°  50' 
80°  40' 
80°  3c/ 

80°.  20' 

80°  io' 

10°  0' 

9-2397 

7.1 

9-9934 

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9-2463. 

7.3 

°-7537 

80°  0' 

10°  10' 

.2468 

•9931 

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79°  50' 

10°  20' 

.2538 

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79°  40' 

10°  30'. 

.2606 

'f.  Q  • 

.9927 

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.7320 

79°  3°' 

10°  40' 

.2674 

6  6 

.9924 

2  . 

•275° 

7.0 

6  Q 

.7250 

79°  20' 

10°  50' 

.2740 

6.6 

.9922 

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.2819 

.6.8 

.7181 

79°  io' 

11°  0' 

9.2806 

6.4 

9.9919 

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9.2887 

6.6 

0.7113 

79°  O' 

11°  io' 
n°  20' 

.2870 
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.9917 
.9914 

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•2953 
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6.7 

6  c 

•7047 
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78°  4o' 

n°  30' 

•2997 

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.9912 

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0.5 

O  A. 

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11°  40' 
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'  6.1 
60 

.9909 
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6.3. 

•6851 
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78°  20' 

78°  io' 

12°  0' 

9-3I79 

t  q 

9.9904 

9-3275 

6.1 

0.6725 

78°  0' 

12°  IO7 

12°  20' 

•3^38 
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5-8 

.9901 
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•3336 
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6.1 

6  T 

•  .6664 
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77°  40' 

12°  30' 

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•3353 
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8 

.9896 
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5-9 

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•  .3576 

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'3 

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5.6 

.6309 
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76°  40' 
76°  30' 

'3°  40' 

13°  5°' 

•3734 
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5-2 

•9875 
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3 

•3859 
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5-5 
5-5 

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9-3837 

CQ 

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9.9869 

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9.3968 

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0.6032 

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.3887 

.9866 

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5-3 

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75°  5°' 

14°  20' 

14°  30' 
14°  40' 
14°  50' 

•3937 
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4.9 

4-8 
4.7 

.9863 
.9859 
.9856 
.9853 

•3 

•4 
•3 
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.4074 
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.  .4178 
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5-3 
5-3 
5-1 
5-2 

C  T 

•5926 

.5873 
.5822 

•577° 

75o-4°'f 
75°  -or 
75°  io' 

15°  0' 

9.4130 

9.9849 

9.4281 

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0-5719 

75°  0' 

Cos. 

D.I'. 

Sin, 

D.I'. 

Cot, 

D.I'. 

Tan. 

Angle. 

LOGARITHMIC  FUNCTIONS  OF  ANGLES. 
LOGARITHMIC  FUNCTIONS  OF  ANGLES — Continued. 


773 


Angle. 

Sin. 

!>.!'. 

Cos. 

D.I'. 

Tan. 

D.  If.- 

Cot. 

15°  0' 

9.4130 

A  7 

9-9849' 

•7 

9.4281 

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0.5  7^9 

75°  0' 

15°  10' 
15°  20' 
15°  30' 
15°  40' 
15°  50' 

•41.77 
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M-./ 

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4.6 

4-5- 
4-5 

A     A    • 

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•4 
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4. 

.4331 
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•4430 
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.<_» 
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4-9 
4.9. 
4.8' 
48-" 

.5669 
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•5570 
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•5473 

74°  so' 

74°  40' 
74?  3C/ 
74°  2C' 
74°  10' 

16°  Q' 

9.4403 

A.  A. 

9.9828 

'•? 

94575 

TPT;  • 

47" 

0.5425 

74°  0' 

16°  10' 

I  6°    20' 

16°  30' 
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i  6°  50' 

17°  0' 

•4447 
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"94659 

4.4 

4-4.. 
4.2 

4-3. 
4-2 
4-1 
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.9825 
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9-4853! 

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4-7- 
4.6 
4.6 

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•5378 
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0.5147 

73°  50'' 
73°  40' 
73°  3o> 
73°  20' 
73°  10' 
73°  0' 

17°  10' 
1  7°  '20' 

17°  30' 
17°  4o' 
17°  50' 

.4700' 
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•  -5031 
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4*5 

44 
44" 

44 
v-j 

.5102 
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4925 

72°  50' 
72°  40' 
72°  30' 
72°  20' 
72°  ic/ 

18°  0' 

9.4900 

o-y 

9.9782 

A 

9.5118 

4.."? 

0.4882 

72°  0' 

i  8°  ior 
1  8°  20' 
18°  30' 

i  8°  40' 
1  8°  50' 

-4939 
•4977 
•5OI5 
•5°52 
.5090 

3-9 
3-8 
3-8 
3-7 
3-8 

•?.  6 

•97/8 
•9774 
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•4  , 
•4 
•5 
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.5161 
.5203 

•5245 
•5287 
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4.2 
4.2 
4.2 
4.2 
4.1 

4839 
4797 
4755 
47U 
.4671 

71°  5^ 
71°  40' 

71°  30' 

7l°  20' 

71°  10'. 

19°  O' 

9.  Si  26 

J-^ 

9-9757 

•  r 

9-5370 

4.1 

0.4630 

71°  0', 

19°  10' 
19°  20' 
19°  30' 
19°  40' 
19°  50' 

**$ 

•5  '99 
•5235 
•  -5270 
.5306 

3-1 

3-6 

3-6 
3-5 
3-6 
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•9752 
'  .9748 
•9743 
•9739 
'  -9734 

O 

4 
•5 

4  • 
•5 
4 

.5411 

•5451 
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•5531 
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f° 
4.0 

4.O.. 
4.0 
4.0 

4589 
4549 
45°9 
•4469. 
4429 

7°o  5°,' 

70°  40* 
70°  30' 

70°  20/ 

70°  ic/ 

20°  0'' 

9-5341 

9-9730 

.«; 

9.5611 

3-9 

0.4389 

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20°    10' 
20°    20* 
20°    30' 
20°.  40' 
20°    50' 

.  -5375 
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'  -5443 
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1 
3-4 
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3-4 
3-3 

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4  ' 
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.4 

-565° 
.5689 

•57J7 
.5766 
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3-9 

3-9 
3-8 
3-8 

435° 
43" 

4273 
4234 
.4196 

69°  50' 
69o  40' 
69°  .30' 

69°  207' 

69°  10' 

21°  O' 

9-5^43 

3-3. 

9.9702 

9.5842 

•7  7 

0.4158 

69°  0' 

21°    10' 
21°    20' 
21°    30' 
21°   40' 
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~~*576~ 
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.5641 
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3-3 
3-3 
3-2 
3-2 
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3-8 
3-7 
3-7 
3-7 
3-6 

.4121 

4083 
.4046 
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•3972 

6S°  50^ 
68°  407 
68°  30' 
68°  207 
68°  10' 

22°  0' 

0.1:716 

•2- 

9.9672 

9.6064 

16 

0.3936 

68°  0' 

22°    10' 
22°    20' 
22°    30' 

~T7~6~7 
.5793 
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3-1 
3-i 
3-o 

'.9667 
.9661 
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•5 
.6 
•5 

.6100 
'.6136 
.6172 

j>v 

3-6 
3-6 

.3900 

.3864 
.3828 

67°  50' 
67°  40' 
67°  3^ 

Cos. 

».!'. 

Sin. 

D.I' 

Cot, 

».  l'. 

Tan. 

Angle. 

7/4  EXPERIMENTAL  ENGINEERING. 

LOGARITHMIC  FUNCTIONS  OF  ANGLES — Continued. 


Angle, 

Sin. 

D.I'. 

Cos. 

D.I'. 

Tan. 

D.  1'. 

Cot. 

22°  .30' 
22°  40' 
22°  50' 

9.5828 

.5859 
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3-1 

3-o 

-j  o 

9.9656 
.9651 
.9646 

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9.6172 
.6208 
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3-6 

3* 

0.3828 
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67°  30' 
67°  20' 

67°  10' 

23°  O' 

9-59I9 

2  Q 

9.9640 

e 

9,6279 

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0.3721 

67°  O' 

23°  10' 

23°  20' 
23°  30' 
23°  40' 
23°  50' 

24°  0' 

24d  10' 

24°  20' 

24°  30' 
24°  40' 
24°  50' 

.5948 
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^o"^ 
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2.9 
2.9 
2.9 

2.8 
2.8 
2.8 
2.8 
2.8 

2.7 

2  7 

.9635 
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9-9607 
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.6 
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9.6486 
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3-5 
3-4 
3-5 
3-4 
3-4 
3-3 
3-4 
3-3 
3-4 

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.3686 
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•3617 
•3583 
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0.35*4 
•3480 
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•3346 

66°  5o< 
66°  40' 
66°  30' 
66°  20' 
66°  10' 
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65°  50' 
65°  40' 
65°  30' 

65°  20' 

65°  10' 

25°  0' 

9.6259 

2  7 

9-9573 

6 

9.6687 

•y  1 

o.33i3 

65°  0' 

25°  10' 

25°  20' 
25°  30' 
25°  40' 
250  50' 

.6286 

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2-7 

% 

2.6 

26 

•95^7 
.9561 

•9555 
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.6 
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.6720 
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.6850 

•3-2 
3-3 
3-2 
3-3 

•3.2 

•3280 
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•3215 
•3183 

•315° 

64°  50' 
64°  40'- 
64°  30' 

64°  20' 

64°  10' 

26°  0' 

26°  10' 
26°  20' 
26°  30' 
26°  40' 
26°  50' 
27°  0' 

9.6418 

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.6470 

•6495 
.6521 
.6546 
9.6570 

2.6 
2.6 

2.5 

•2.6 
2-5 

.2.4 

•  ">  C 

9-9537 
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9-9499 

-7 
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.6 

:l 

7  • 

9.6882 

•6914 
.6946 
.6977 
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^.7040 
97072 

3-2 
3-2 
3-i 
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3-i 
3-2 

3T 

0.3118 

"TjoScT 

•3054 
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.2991 
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0.2928 

64°  0' 

63°  50' 
63°  40' 
63°  30' 

63°  20' 

63°  10' 
63°  0' 

27°  lo7 

27°  20' 
27°  30' 
27°  40' 
27°  50' 

•6595 
.6620 
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—  J 

-•2.5 
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2.4 
2.4 

2  A 

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A 

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3-i 
3-i 
3-i 
3-o 
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•2835 
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62°  50' 

62°  40' 
62°  30' 

62°  20' 

62°  16' 

28°  0' 

28°  16' 

28°  20' 

28°  30' 
28°  40' 
28°  50' 

29°  O' 

9.6716 
"^6740" 
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.6787 
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9.6856 

2.4 

2-3 

2-4 

2.3 

2-3 

2.3 

2  2 

_9-9459. 

•9453 
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•9439 
•9432 
•9425 
9.9418 

.6 

•7 
•7 
•7 
•7 
•7 

7 

9-7257 
.7287 

•7317 
•7348 
.7378 
•7408 
9-7438 

3-o 
3-o 
3-i 
3-o 
3-o 
3-o 

0.2743 

•27U 

.2683 
.2652 
.2622 
•2592 
0.2562 

62°  0' 

61°  50' 
61°  40'- 

6!°  3C' 
6lc  20' 

61°  10' 
61  C0' 

29°  jo' 
29°  20' 
29°  30' 
29°  40' 
29°  50' 

.6878. 
.6901 
,6923 
.6946 
.6968 

2-3 
2.2 

2-3 

2.2 
2  2 

.9411 
.9404 

•9397 
•9390 
.9383 

•/ 

•7 
•7 
•7 

8 

.7467 

•7497 
.7526 

•7556 
•7585 

z.y 

3-o 

2.9 

3-o 
2.9 

2  O 

•2533 
•2503 
.2474 
;2444 
•2415 

60°  50' 
60°  40' 
60°  30'- 
60°  20' 
60°  io' 

30°  0' 

9.6990 

9-9375 

9.7614 

0.2386 

60°  0' 

Cos. 

D.I'. 

»SinC 

D.  1'. 

Cot. 

D.I. 

Tan. 

Angle. 

LOGARITHMIC  FUNCTIONS  OF  ANGLES. 
LOGARITHMIC  FUNCTIONS  OF  ANGLES — Continued. 


775 


Angle. 

Sin. 

D.I'. 

Cos. 

D.I'. 

Tan. 

D.I'. 

Cot. 

30°  O' 

9.6990 

2  2 

9-9375 

.7 

9.7614 

•}  o  • 

0.2386 

60°  (V 

30°  10' 

30°  20' 
30°  30' 
30°  40' 
30°  50' 

.7012 
•7033 
.7055 
7076 
.7097 

2.1 
2.2 
2.1 
2.1 
2.1 

.9368 
.9361 
•9353 
.9346 
.9338 

.7 

.7644 

•7673 
.7701 

•7730 
•7759 

o*w 

2.9 

2.8 

2.9 
2.9 

2.Q 

•2356 
.2327 
.2299 
".2270 
.2241 

9°  50f 
59°  40' 
59°  & 
59°  20' 
59°  10* 

31°  0' 

9.7118 

2.1 

9-9331 

.8 

9-7788. 

2.8 

0.2212 

59°  0' 

31°  10' 

3I°  20' 
31°  30' 
31°  40' 
31°  50' 

7'39 
.7160 
.7181 
.7201 
.7222 

2.1 
2.1 
2.0 
2.1 
2  O 

.9323 

•93*5 
.9308 
.9300 
.9292 

.8 

;I 

.8 
.8 

.7816 
.7845 

•7873 
.7902 

„  -7930 

2.9 

2.8 

2.9 

2.8 
2.8 

:2l84 

•2155 
.2127 
.2098 
.2070 

58°  50' 
58°  40' 
58°  307 

58°  20' 

58°  10' 

32°  O' 

9.7242 

2  O 

9.9284 

.8 

9-7958 

2.8 

0.2042 

58°  0' 

32°  10' 
32°.  20' 
32°  30' 
32°  40' 
32°  50' 

.7262 
.7282 
.7302 
.7322 
•7342 

2.0 
2.0 
2.O 
2.0 
In 

.9276 
.9268 
.9260 
.9252 
.9244 

.& 
.8 
.8 
.8 
.8 

.7986 
.8014 
.8042 
.8070 
.8097 

2.8 
2.8 
2.8 

2r7 
2.8 

.2014 
.1986 

.1958 
.1930 
.1903 

570  50' 
57°  40' 
57°  30' 
57°  20' 
57°  10' 

33°  O' 

9-736i 

9-9236 

8 

9.8125 

2.8* 

0.1875 

57°  0' 

33°  10' 

33°  20' 
33°  30' 
33°  40' 
33°  & 

.7380 
.7400 
.7419 
.7438 
<7457 

•y 
2.0 
1.9 
1:9 

1.9 

.9228 
.9219 
.9211 
..9203 
.9194- 

•9 
.8 
.8 

-9 
.8 

•8153 
.8180 
.8208 

•8235 
.8263 

2.7 

2.8 

ai 

2.7 

.1847 
.1820 
.1792 
•1765 
•1737 

56°  so' 
'56°  40' 
56°  30' 

56°  20' 

56°  10' 

34°  0' 

9.7476 

•y 

T  8 

9.9186 

Q 

9.8290 

2.7 

O.I7IO 

56°  0' 

34°  !</ 
34°  20' 

34°  30' 
34°  40' 
34°  50' 

•7494 
•75*3 
•7531 
•7550 
.7568 

1.9 

J.8 
1*9 

1.8 

T  & 

.9177 
.9169 
.9160 

-9151 
.9142 

.8 
•9 
•9 

•9 

g 

•8317 
.8344 
•837J 
.  .8398 
.8425 

2.7 
2.7 

2,7 

2-7 
2.7 

.1683 
,1656 
.1629 
.I$02 
•1575 

55°  50' 

55X 
55°  30 
55°  20^ 
55°  icy 

35°  0' 

9.7586 

T  S  ' 

9-9I34 

9.845* 

2.7 

0.1548 

55°  O' 

35°  10' 
35°  2C/ 
35°  30' 
35°  40' 
35°  So' 

.7604 
.7622 
.7640 
•7657 
•7675 

I.Q 

i.8 
1.8 

rl 

I  7 

.9125 
.9116 
.9107 
.9098 
^089 

•9 
•9 
•9 
•9 
.9 

.8479 
.8506 
•8533 
•8559 
.8586 

2.7 

2i 

2.6 
2-7 

2.7 

.1521 
.1494 
.1467 
.144! 

•H!± 

54°  50' 
54°  40 
54°  30 

54C  20 
54°  10' 

36°  O' 

9.7692 

J.*/ 

9.9080 

9.8613 

26 

0.1387 

54®  0' 

36°  10' 

36°  20' 
36°  30' 
36°  40' 
36°  5o/ 

.7710 
.7727 

•7744 
.7761 
.7778 

1.8 

i-7 
1-7 
i-7 

I;  7 

.9070 
.9061 
.9052 
.9042 
.9033 

•9 
•9 

I.O 

•9 

I  O 

.8639 

'.8692 
,,8718 
.8745 

3 

2.6 

2d. 

.1361 

.1334 
,1308 
.1282 
•1255 

,53°  50' 

53o4° 

53°  30 

53o  2C/, 
53°  10' 

37°  O' 

9.7795 

*-7 

T  A 

9.9023 

Q 

9.8771 

2.6 

.a  1  229 

53°  <K 

37°  10' 
37°  -20' 
37°  3o' 

.7811 

.7828 
.7844 

I.O 

1.6 

.9014 
19004 
.8995 

I.O 

•9 

•8797 
.8824 
.8850 

a 

.1203 
.1176 
,115° 

52o  5°! 
52°  40' 

52°  307 

Cos. 

D.I'. 

Sin. 

D.  1' 

Cot. 

D.I' 

Tan. 

Angle. 

776 


EXPERIMENTAL   ENGINEERING. 
LOGARITHMIC  FUNCTIONS  OF  ANGLES — Contimied. 


Angle. 

Sin. 

D.I'. 

Cos. 

D.I'. 

Tan. 

D.I'. 

Cot. 

37°  30/ 

9.7844 

9.8995 

9.8850 

?  6 

0.1150 

52°  30' 

37°  40' 
37°  50' 

.7861 
.7877 

1.6 
1.6 

.  -8985 
•8975 

I.O 
I  O 

.8876 
.8902 

2.6 
26 

.1124 

.1098 

52°  20' 
52°  io? 

38°  0' 

9-7893 

1.7 

9.8965 

I  O 

9.8928 

26 

0.1072 

52°  0' 

38°  10' 

38°  20' 
38°  30' 

38°  40' 

.7910 
.7926 
.7941 
•7957 

1.6 

li 

i  6 

•8955 
•8945 
.8935 
.8925 

-  i.o 

I.O 

I.O 

••8954 
.8980 
.9006 
*  .9032 

2.6 
2.6 
2.6 
~  f. 

.1046 

.1020 

.0994 
.0968 

51°  507 
5Io4°' 
51°  20' 

38°  50' 

•7973 

1.6 

.8915 

I.O 

•9058 

26 

.0942 

51°  10' 

39°  0' 

9.7989 

1.5 

9.8905 

I.O 

9.9084 

2.6 

0.0916 

51°  0' 

39°  10' 
39°  20' 
39°  30' 
39°  40' 

.8004 
.8020 
.8035 
.8050 

1.6 

.8895 
.8884 
r8874 
.8864 

I.I 

I.O 
I.O 

.9110 

•9J35 
.9161 
.9187 

3 

2.6 

.0890 
.0865 

.0839 

.0813 

50°  50' 
50°  40' 

50°  30f 
50°  20' 

39°  5°' 

.8066 

I.c 

.  .8853 

I  O 

..9212 

2  6 

.0788 

50°  10' 

40°  0' 

9.8081 

I.c 

9:8843 

I  I 

9.9238 

2  6 

0.0762 

50°  0' 

40°  10' 
40°  20' 
40°  30' 
40°  40' 
40°  50' 

.8096 
,8m 
.8125 
.8140 
•8i55 

'•5 

,1.4 

1.4 

.8832 
.8821 
.8810 
.8800 
.8789 

I.I 
I.I 

i.o 
I.I 

I  I 

.9264 
.9289 

•9315 
•9341 
.9366 

% 

2.6 

.0736 

.071-1 

.0685 
.0659 
•0634 

49°  50' 
49°  40' 
49°  30' 
49°  20' 
49°  10' 

41°  O' 

9.8169 

9,8778 

I  I 

9-9392 

0.0608 

49°  0' 

41°  10' 
41°  20' 
41°  30' 
41°  40' 
41°  50' 

.8184 
.8198 
•8213 
.8227 
.8241 

1.4 

'•5 

1.4 
1.4 

.1.4 

.8767 
.8756 
•8745 
•8733 

.8722 

I.I 
I.I 

1.2 

-  I.I 

J  J 

.9417 

•9443 
.9468 

•9494 
-OS19 

2.6 

2-5 
2.6 

2-5 

•0583 
•0557 
•0532 

.0506 

.0481 

48°  40' 
48°  30' 

48°  20' 

48°  10' 

42°  0' 

9-8255 

9.8711 

9-9544 

2-5 

0.04;  6 

48°  0' 

42°  ic/ 
42°  20' 
42°  30' 
42°  40' 
42°  50' 
43°  O' 

.8269 
.8283 
.8297 
.8311 
•8324 
9-8338 

1*4 

M 
1-4 

.8699 

.8688 
.8676 
.8665 
•8653 
9.8641 

I.I 

1.2 
I.I 
1.2 
1.2 

I  ^ 

"1)57°" 
•9595 
.9621 
.9646 

_19_6.7i 
9.9697 

2.6 

n 

2-5 
2-5 
2.6 

.0430 
.0405 
•0379 
•0354 
..0329 
0.0303 

.47°  50' 
47°  40' 
47°  30,' 
47°  20' 
47°  10' 
47°  0' 

43°  10' 
.13°  20' 
43°  30' 
43°  40' 
43°  50' 
44°  0' 
44°  10' 
44°  20' 
44°  30' 
44°  40' 
44°  50' 

•8351 
•8365 
.8378. 
•8391 
•8405 
9.8418 

•8431" 
.8444 

•8457 
.8469 
.8482 

1.4 

1.4 
•  •  '-3 
.1-3 

.1-3 

.1.2 
1-3 

.8629 
.8618 
.860-6 

•8594 
.8582 

9.8569 

•8557 
.8545 
•8532 
.8520- 
.8507. 

I.I 

i.2 
r.2 
J-3 

1.2 
1.2 

1.2 

1-3 
I  2 

.9722 
•9747 
•9772 
.9798 
.9823- 
9.9848 

^9877 
.9899 
.9924 
•9949 
•9975 

2-5 
2-5 
2-5 
2.6 

2-5 
2-5 
2.6 

2-5 
2-5 

2^6 

.0278 

.0253 

.0228 
.0202 

.0177 

0.0152 
.0126 

.OIOI 

.0076 
.0051 

.0025 

46°  50' 
46°  40' 
46°  30' 

46°  20' 

46°  10' 
46°  0' 

45°  50' 
45°  40' 
45°  3°' 
45°  20' 
45°  10' 

45°  '0' 

9.8495 

9.8495 

0.0000 

2-5 

o.oooo 

45°  0' 

Cos. 

D.I'. 

Sin.7 

D.  1'. 

Cot. 

D.  1'. 

Tan. 

Angle. 

NATURAL  FUNCTIONS  OF  ANGLES. 


777 


V. 

NATURAL   FUNCTIONS   OF  ANGLES. 


A. 

Sin. 

Cos. 

A. 

Sin* 

Cos. 

1' 

A. 

Sin. 

Cos. 

0° 

.000000 

I.OOOO 

90° 

3o; 

.1305 

.9914 

30' 

15C 

.2588 

•9659 

75° 

10' 
20' 

.002909. 

.005818 

1.  0000 
I.OOOO 

50' 
40' 

40 
50' 

•i  334* 
•1363 

.9911 
•9907 

20' 
10' 

10' 

xf 

.2616 
.2644 

.9652 
.1)644 

50' 
40' 

30;. 

.'008727 

I.OOOO 

30' 

8° 

.1392 

•9903 

82° 

30' 

.2672 

•9636 

30' 

40' 
50' 

.011635 
.014544 

.9999 

•9999 

20' 
10'' 

10' 
20' 

.1421 

.1449 

•9899 
.9894 

50' 

40' 

40' 
50' 

.2700 
.2728 

.9628 
.9621 

20' 
10' 

ld 

.017452 

.9998 

89° 

30; 

•1478 

.9890 

30; 

16° 

.2756 

.9613 

74c 

10' 

20' 

.02036 

.02327 

.9998 
•9997 

.50' 
40' 

40' 

50' 

-1507 
.1536 

.9886 
.9881 

20' 

I0< 

.10' 

20' 

.2784 
.281? 

•9605 
.9596 

50' 

40 

3°' 

.02618 

•9997 

30; 

9° 

.1564 

•9877 

81° 

30' 

.2840 

.9588 

30' 

4o' 
50' 

.02908 

.03199 

.9996 
•9995 

20' 

10' 

10' 

20' 

•1593 
.1622 

.9872 
.9868 

50; 
40' 

40' 
50' 

.2868 
.2896 

.9580 
•9572 

20' 
10' 

2° 

.03490 

•9994 

88° 

^30' 

.1650 

•9863 

30' 

17° 

.2924 

•9563 

73° 

10' 

20' 

.03781 

.04071 

•9993 
.9992 

50; 
40' 

40' 
50' 

.1679 
.1708 

..9858 
.9853 

20' 
'10' 

10' 

20' 

.2952 
.2979 

•9555 
•9546 

50/, 
40' 

30' 

.04362 

.9990 

30' 

10° 

•1736 

.9848 

80f 

30; 

.3007 

•9537 

30' 

40 

50' 

.04653 
•04943 

.9989 
.9988 

20' 
10' 

10' 

20' 

.1765 
.1794 

.9843 
.9838 

.5°: 
40' 

40' 
50' 

•3°35 
.3062 

.9528 
.9520 

20' 
10' 

3C 

.05234 

.9986 

87° 

30' 

.1822 

•9833 

30' 

.18° 

.3090 

•95  1! 

72° 

10' 

20' 

•05524 

.05814 

•9985 
•9983 

50' 
40' 

40 
50' 

.1851 

.1880 

.9827 
.9822 

20' 

10' 

10' 

20f 

.3118 
•3*45 

.9502 
.9492 

50; 
40'- 

30' 

.06105 

.9981 

30; 

11° 

.1908 

.9816 

79C 

30' 

•3173 

•9483 

30; 

40' 

50' 

.06395 
.06685 

.9980 
.9978 

20' 
10' 

10' 

20' 

•1937 
1965 

.9811 
.9805 

50' 

40' 

40' 

50' 

.3201 

.3228 

•9474 
•9465 

20' 

10' 

4° 

.06976 

.9976 

86° 

30; 

1994 

•9799 

30' 

19C 

3256 

•9455 

71° 

•10' 

20' 

.07266 

•07556 

•9974 
.9971 

s°; 

4o' 

40 
50' 

2O2  2 
2O5I 

•9793 
•9787 

20' 
10' 

10' 
20' 

3283 
33ii 

.9446 
•9436 

5c/ 
4o' 

.30; 

.07846 

.9969 

30; 

12° 

2079 

.9781 

78^ 

30' 

3338 

.9426 

30; 

40' 
50' 

'.08136 

.08426 

-.9967- 
•9964 

20' 
10' 

10' 

20' 

2108 

2136 

•9775 
.9769 

50; 
40' 

40' 
50' 

33^5 
3393 

.9417 
.9407 

20' 
10' 

5° 

.08716 

.9962 

85° 

30' 

2164 

.9763 

30; 

20° 

3420 

•9397 

70^ 

10' 
20' 

.09005 

.09295 

•9959 
•9957 

5oJ 

-1° 

40' 
50' 

2193 

2221 

•9757 
•975° 

20'- 
10' 

10' 

20' 

3448 
3475 

.9387 
•9377 

s°; 
4o' 

30' 
40' 
50' 

•09585 
.09874 

.10164 

•9954 
.995^ 
.9948 

30; 

20' 
10' 

13° 

10' 

20' 

2250 

~2iy$ 
2306 

•9744 
•9737 
•973° 

77C 
50; 
40' 

30j 
40' 
50' 

3502 
3529 
3557 

•9367 
•9356 
•9346 

^ 

20' 

10' 

6° 

.10453 

•9945 

84° 

30; 

2334 

•9724 

30; 

21° 

3584 

.9336 

«9U 

10' 

20' 
30; 
40 

50' 

.10742 
.11031 

.11320 

.11609 

.11898 

•9942 
•9939 
.9936 
•9932 
.9929 

50; 
40' 

3°r 
20' 

10' 

40 

50' 

14C 

10' 

20' 

2363 

23_9-I 
•'2419' 

•2447 
.2476 

•97  i  7 
_i9-Ir^. 
_J9/03_ 
.9696 
.9689 

20' 
10' 
76C 

50' 
4°' 

10' 
20' 
30; 
40' 
50' 

3611 
3638 
3665 
3692 
37'9 

.9325 
.9315 
.9304 
.9293 
•9283 

5°; 
4o' 

30' 

20' 
10' 

7° 

.12187 

.9925 

83C 

30; 

.2504 

.9681 

30 

22° 

3746 

•92/2 

«8L 

10' 

?o' 

.12476 

.12764 

.9922 
.QQ  I  S 

50; 
4° 

40 
50' 

•2532 
.2560 

.9674 
.9667 

20' 
10' 

10' 

20' 

3773 
3800 

.9261 
•9250 

50' 
40 

30' 

•13053 

.9914 

30' 

15° 

.2588 

.9659 

75° 

30' 

3827 

.9239 

30' 

Cos. 

Sin. 

A. 

Cos. 

Sin. 

A. 

Cos. 

Sin. 

A. 

EXPERIMENTAL   ENGINEERING. 
NATURAL  FUNCTIONS  OF  ANGLES—  Continued. 


A. 

Sin. 

Cos. 

A. 

Sin. 

Cos. 

A. 

Sin. 

Cos. 

30j 

.3827 

.9239 

30' 

30° 

.5000 

.8660 

60° 

30; 

.6088 

•7934 

30' 

40 
50' 

.3854 
,3881 

.9228 
.9216 

20' 
10' 

10' 
20' 

•5025 
.5050 

.8646 
.8631 

SO' 
40' 

40 
50' 

.6lll 
.6134 

.79ib 
.7898 

20' 
10' 

23° 

•3907 

.9205 

67° 

30' 

•5°75 

.8616 

30' 

38° 

.6157 

.7880 

52° 

10' 

20' 

•3934 
.3961 

.9194 
.9182 

50' 
40' 

40' 

50' 

.5100 
•5125 

.8601 
,8587 

20' 
I0/ 

10' 

20> 

.6r8o 
.6202 

.7862 
.7844 

50'' 
40' 

30; 

.3987 

.9171 

30' 

31° 

•5150 

.8572 

59° 

30' 

.6225 

.7826 

30' 

40 
50' 

.4014 
.4641- 

•9159 
.9147 

20' 

10' 

10' 
20' 

•5'75 
.5200 

•8557 
.8542 

50; 
40' 

40 
50' 

.6248 
.6271 

.7808 
^7790 

20' 
10' 

24° 

.4067 

.9135 

66° 

30; 

•5225 

.8526 

30' 

39° 

.629; 

.7771 

51° 

10' 

20' 

.4094 
.4120 

.9124 
.9112 

So,' 
40' 

40' 
50' 

•525o 
•5275 

.8511 
.8496 

20' 
10' 

10' 

20' 

.6316 
.6^8 

•7753 
•7735 

5oJ 
40' 

30' 

.4147 

.9100 

30' 

32° 

•5299 

.8480 

58° 

30' 

.6361 

.7716 

30' 

4«y 

5°' 

.4173 
.4200 

.9088 
.9075 

20' 

10' 

10' 
20' 

.5324 
•5348 

.8465 
•8450 

50; 
40' 

4°! 
50' 

.6383 
.6406 

.7b98 
.7679 

20' 
10' 

25° 

.4226 

.9063 

65° 

30' 

•5373 

•8434 

30' 

40° 

.6428 

.7660 

50° 

10' 
20' 

•4253 
.4279 

.9051 
.9038 

50; 
40' 

40' 

5c/ 

•5398 
•5422 

.8418 
.8403 

20' 

10'. 

10' 

20' 

.6450 
.6472 

.7642 
.7623 

5<y 
40' 

£ 

•4305 

.9026 

30' 

33° 

5446 

.8387 

57° 

3°; 

.6494 

.7604 

3o'. 

4u 
50' 

•433  i 
.4358 

.9013 
.9001 

20' 

10' 

10' 
20' 

547i 
5495 

.8371 
.8355 

50' 
40' 

4<y 
50' 

.toSi7 

•6.S39 

•7585 
.7566 

20' 

10' 

26^ 

•4384 

.8988 

64° 

3C/ 

55^9 

.8339 

V 

41° 

.6s6i 

•7547 

49° 

10' 

20' 

.4410 
•4436 

.8975 
.8962 

5oJ 
40' 

4o' 
5o' 

5544 
5568 

.8323 
.8307 

20' 
10' 

10' 

20' 

.6583 
.6604 

.7528 
•75°9 

50' 
40' 

30' 

.4462 

.8949 

3o; 

34° 

5592 

..8290 

56° 

30' 

.6626 

.7490 

30' 

4U 
50' 

.4488 

45  *  4 

.8936 
.8923 

20' 

I07 

10' 

20' 

5616 
5640 

.8274 
.8258 

50; 
40' 

40. 
50' 

6648 
6670 

-.7470 
•745i 

20' 
10' 

27° 

•4540 

.8910 

63° 

50; 

5664 

.8241 

30' 

42° 

6691 

•7431 

48° 

10' 

20' 

.4566 
4592 

.8897 
.8884 

5oJ 

40' 

40' 

SO' 

5688 
5712 

.8225 
.8268 

20' 
10' 

10' 
20' 

6713 
6734 

.7442 
•7392 

So; 
40; 

30' 

.4617 

.8870 

3o; 

35° 

5736 

.8192 

55° 

30' 

6756 

•7373 

30' 

4O 
50' 

4643 
.4669 

.8857 
.  -8843 

20' 

10' 

10' 
20' 

5760 
5783 

.8175 
.8158 

50' 

40' 

40' 

So' 

6777 
6799 

'•7353 
•7333 

20' 
10' 

28U 

•4^95 

.8829 

62° 

30' 

5807 

.8141 

30' 

43° 

6820 

•7314 

47° 

IC/ 
20' 

.4720 
.4746 

.8816 
.8802 

so; 
4o' 

4°! 
50' 

5831 
5854 

.8124 
.8107 

20' 
10' 

10' 
20' 

6841 

6862 

•7294 
.7274 

So; 
407 

30' 
/in' 

.4772 

.8788 

30; 

36° 

5878 

.8090 

54° 

30' 

6884 

•7254 

30' 

4° 
50' 

•4797 
.4823 

.8774 
.8760 

20' 

10' 

10' 

2C/ 

590i 
5925 

.8073 
.8056 

50'. 
40' 

40' 

So' 

6905 
6926 

•7234 
.7214 

26' 

!</ 

29° 

.4848. 

.8746 

61° 

30' 

5948 

.8039 

30' 

44° 

6947 

•7J93 

46° 

10' 

20' 

.4874 
.4899  - 

.8732 
.8718 

5oJ 
40'- 

40' 
50' 

597^ 
5995 

.8021 
.8004 

20' 
10' 

10' 

2d 

6967 

6qS8 

•7173 
.7153 

5°; 

4° 

JO 
AO' 

.4924 

.8704 

30' 

37° 

6018 

,7986 

53° 

30; 

7009 

•7133 

30' 

40 
50' 

•495° 
.  -4975- 

.0009 
.8675 

20' 
10' 

10' 

«Q' 

6041 
6o6s 

.7969 
•7951 

50; 
40' 

40' 
50' 

7030 
7050 

.7112 
.7092 

20' 

ia' 

30° 

.5000 

.8660 

60° 

30 

6088 

•7934 

30' 

45° 

7071 

.7071 

45° 

Cos. 

Sin. 

A. 

Cos.  | 

Sin. 

A. 

2os. 

Sin. 

A. 

NATURAL   FUNCTIONS   OF  ANGLES. 
NATURAL  FUNCTIONS  OF  ANGLES— Continued. 


779 


A. 

Cot. 

A. 

Tan 

.     Cot. 

A. 

Tan 

Cot. 

0° 

.000000 

op 

90° 

.30; 

.131; 

*  7-595* 

30 

15° 

.267 

3-7321 

75° 

10' 

20' 

.002909 

.005818 

343-7737 
171.8854 

So' 
40' 

40' 
50' 

•i34t 
•'37* 

)  7.428; 
>  7.268; 

20 
,IO' 

10' 

?r/ 

.271 
.274 

3.6891 

1  6J.7C 

50' 

30' 

.008727 

114.5887 

30' 

8° 

''405 

7-"54 

82 

30' 

.277 

3.6050 

30' 

4U 
50' 

.01  1636 

.014545 

85-9398 
68.7501 

20' 
10' 

10' 
20' 

•'435 
.146^ 

6.9682 
6.8269 

50' 
40' 

40' 
So' 

.280 
.28} 

3-565^ 

3.5261 

20' 
10' 

1° 

•017455 

57.2900 

89° 

30' 

•1495 

6.6912 

30' 

16Q 

.286 

3-4874 

74C 

10' 
20' 

.02036 
.02328 

49.1039 
42.9641 

50' 
40' 

40' 
50' 

.1524 
•1554 

6.5606 
6.4348 

20' 

I0/ 

10' 

20' 

.289 
.293 

3-4495 
3.4124 

50' 

4O' 

30| 

.02619 

38.1885 

30' 

9y 

.1584 

6.3138 

81C 

30' 

.296 

3-3755 

-,o' 

40 
50' 

.02910 
.03201 

34.3678 
31.2416 

2p' 
10' 

10' 

20' 

.1614 
.1644 

6.1970 
6.0844 

50' 
40' 

40' 
SO' 

•2994 
.302 

3-3402 
3-3052 

20' 
10' 

2° 

.03492 

28.6363 

88C 

30' 

-1673 

5-9758 

30' 

17° 

-30  s 

3.2709 

73°. 

ro' 

20' 

30; 

•03733 
.04075 

.04366 

26.4316 
24.5418 
22.9038 

50' 
40' 
.30' 

40 
5of 
10° 

1703 
•1733 
•1763 

5.8708 
5-7694 
5-6713 

20' 
10' 

80° 

10' 

20' 
30; 

.3089 
.312 
.315; 

3-2371 
3.2041 
3.1716 

50': 
40'.: 
30' 

40' 
50' 

.04658 
.04949 

.21.4704 
20.2056 

•20' 

10' 

10' 

20' 

•1793 
.182^ 

5-5764 
5.4845; 

50; 

40' 

40' 

SO' 

•3'8_ 
•1217 

3-1397 
3.1084 

20' 
10' 

3° 

.05241 

19.0811 

87C 

30' 

•'853 

5-3955 

30' 

18° 

•3249 

3-0777 

72C 

10' 

20' 
30' 

•05533 
.05824 

.06  1  1  6 

18.0750 
17.1693 
16.3499 

50' 

40' 
30; 

^ 

50' 
11° 

1883 
:_r_9!i 

1944 

5-3093 
_5f2_57 
5.1446 

20' 

10' 

79C 

10' 
20' 

30' 

•3281 
•33  1  4 
-3346 

3.0475 
3.0178 
2.9887 

50' 
40' 
30' 

40' 
50 

.06408 
.06700 

15.6048 
14.9244 

20' 

10' 

10' 

20' 

1974 

2004 

5.0658 
4.9894 

5oJ 
40' 

40' 
50' 

•3378 
34U 

2.9600 
2.9319 

20' 
10' 

4^ 

.06993 

14.3007 

86C 

30' 

2035 

4.9152 

30' 

19° 

•3443 

2.9042 

71C 

10' 

20' 

.07285 
•07578 

13.7267 
13.1969 

50; 

40' 

40' 
50' 

2065 
2095 

4.8430 
4.7729 

20' 
10' 

10' 
20' 

•3476 
3508 

2.8770 
2.8502 

50' 
4° 

30' 

.07870 

12.7062 

30' 

12° 

2126 

4.7046 

78? 

30' 

354J 

2.8239 

30' 

40' 
50' 

.08163 
.08456 

12.2505 
11.8262 

20' 
10' 

10' 

20' 

2I56 
.2186 

4.6382 
4-5736 

50; 
40' 

40' 

50' 

3574 
3607 

,2.7980 
2-7725 

20' 
10' 

5° 

.08749 

11.4301 

85° 

30' 

.2217 

4-5I07 

30' 

20° 

-3640 

2-7475 

70C 

10' 

20' 
JO) 

.09042 

•09335 
.09629 

11.0594 
10.71  19 
10.3854 

50; 
g 

^ 

S^ 
13° 

.2247 
.2278 
.2309 

4.4494 
4-3897 
4o3i5 

20' 
10' 

77° 

10' 
20' 
30' 

.3673 
•37°6 
•3739 

2.7228 
2.6985 
2,6746 

50' 
40' 

30' 

40' 

50' 

.09923 
.10216 

10.0780 
9.7882 

20' 
10' 

10', 

20' 

-2339 
.2370 

4-2747 
4.2193 

50' 
40' 

40' 
50' 

•3772 
3805 

2.6511 
2.6279 

20' 
10' 

GJ 

.10510 

9-5r44 

84C 

30' 

2401 

4-1653 

30' 

21° 

3839 

2.6051 

69° 

10' 

20' 

.10805 
.11099 

9-2553 
9.0098 

£ 

40 
50' 

.2432 
2462 

4.1126 
4.0611 

20' 
10' 

10' 

2d 

3872 
}906 

2.5826 
2-5605 

5°: 
4o' 

30; 
40' 

50' 

•"304 
.11688 
.11983 

8.7769 
8-5555 
8-345° 

£ 

10' 

14° 

10' 

207 

±1?J 
2524 
2555 

4.0108 

T9~6i7 
3-9*36 

76L 

50; 

40' 

30' 
40' 
50' 

3939 
3973 
4006 

2.5386 
2.5172 
2.4960 

3-0; 
20 

10' 

70 

.12278 

8.1443 

83C 

30; 

2586 

3.8667 

30; 

22° 

4040 

2-4751 

68C 

10' 
20' 

•12574 
.12869 

7-9530 
7.7704 

5°; 
40' 

40' 
50' 

26I7 
2648 

3.8208 
3-7760 

20' 

JO7 

lo' 

20' 

4074 
4108 

2-4545 
2.4342 

5°' 
40' 

30' 

.13165 

7-5958 

30' 

15° 

2679 

3-7321 

75° 

30' 

4142 

2.4142 

30' 

Cot. 

Tan. 

A. 

Cot, 

Tan. 

A. 

Cot. 

Tan. 

A. 

EXPERIMENTAL   ENGINEERING. 
NATURAL  FUNCTIONS  OF  ANGLES — Continued. 


A. 

Tan. 

Cot. 

A. 

Tan 

Cot. 

A. 

Tan 

Cot. 

30' 

.4142 

2.4142 

30' 

30° 

•5774 

1.732 

60° 

30; 

•767 

1.303 

30' 

40 
50' 

.4176 
.4210 

2-3945 
2-375° 

20' 
10' 

10' 

20' 

.5812 

•S8si 

1.7205 
1.7090 

So; 
40' 

40' 
50' 

.7720 
•776 

1.295 
1.287 

20' 

lo' 

23° 

.4245 

2-3559 

67° 

3oJ 

.5890 

1.6977 

3oJ 

38° 

.781 

1.279 

52C 

10' 
20' 

.4279 
•43H 

2.3369 
2.3183 

50' 
40' 

40' 
50' 

•5930 
•5969 

1.6864 
I-6753 

20' 

10' 

10' 
20> 

.7860 
79° 

1.272 
1.264 

50' 
40' 

30' 

4348 

2.2998 

30' 

31° 

.6009 

1.6643 

59° 

30' 

•7954 

1-257 

30' 

40 

50' 

•4383 
.4417 

2.2817 
2.2637 

•20' 
10' 

10' 

20' 

.6048 
.6088 

1.6534 
1.6426 

50; 
40' 

49 

50' 

.8050 

1.249 
1.242 

20' 
10' 

24° 

•445  2 

2.2460 

66° 

30' 

.6128 

1.6319 

30' 

39° 

.8098 

1,234 

51° 

10' 
20' 

.4487 
.4522 

2.2286 
2.2113 

50' 
40' 

40 
50' 

.6168 
.6208 

I.62I2 
1.6107 

20' 

10' 

10' 

20' 

.8146 
.8iq 

1.227 
1.220 

50' 
40' 

30' 

•4557 

2-1943 

30; 

32° 

.6249 

1.6003 

58° 

30' 

.8243 

I.2I3 

30' 

40- 

50' 

•4592 
.4628 

2-1775 
2.1609 

20' 

10' 

10' 

20' 

.6289 
.6^0 

1.5900 
J-5798 

5°l 

40' 

40' 
50' 

.8292 
-8342 

1.2050 
I.I988 

20' 
10' 

25° 

.4663 

2.1445 

65° 

30' 

.637. 

1-5697 

30' 

40° 

.8391 

I.I9I8 

50? 

10' 
20' 

.4699 
•4734 

2.12^3 
2.II23 

5°; 
40' 

40 
507 

.0412 
•6453 

1-5597 
1-5497 

20' 

10' 

10' 

20' 

•8441 
.8491 

1.1847 
1.1778 

s°; 
40' 

30; 

4?72 

2.0965 

3°; 

33° 

.6494 

1-5399 

57° 

30; 

.8541 

I.I7O8 

30' 

40 
50' 

.4806 
.4841 

2.0809 
2-0655 

20' 

10' 

10' 

20' 

6536 
6577 

i-530i 

1.5204 

50' 

40' 

40' 
50' 

.8591 
.8642 

1.1640 

I-I57i 

20' 
10' 

26^ 

.4877 

2.0503 

64° 

30' 

6619 

1.5108 

3o; 

41° 

.8693 

1.1504 

49° 

10' 

20' 

•4913 
•495° 

2-0353 
2.0204 

50' 
40' 

40' 
50' 

6661 
6703 

1.501; 
1.4919 

20' 

10' 

10' 

20' 

•8744 
8796 

1.1436 
1.1369 

50' 
4° 

30' 

.4986 

2.0057 

3oJ 

34° 

6745 

1.4826 

56° 

30' 

88i7 

1-1303 

30' 

40' 
50' 

.5022 
•5°59 

1-99.12 

1.9768 

207 
10' 

jo' 

20' 

6787 
6830 

J-4733 
1.4641 

50' 
40' 

40; 
50' 

8899 
8952 

1.1237 
1.1171 

20' 
10' 

27U 

•5095 

1,9626 

63° 

30' 

6873 

1.4550 

30' 

42° 

9004 

1.1106 

48° 

10' 

20' 

•5132 
.5169 

.1.9486 
1-9347 

5C/, 
40' 

^ 
S& 

6916 
6959 

1.4460 
1-4370 

2Q> 
10' 

10' 
20' 

•9057 
.9110 

1.1041 
1.0977 

50; 
4of 

30| 

.5206 

1.9210 

30' 

35° 

.7002 

1.4281 

55° 

30' 

.9163 

1.0913 

30' 

40 
50' 

•5243 
.5280 

1.9074 
1.8940 

20' 
10' 

10' 
20' 

.7046 
.7089 

I.4I93 
1.4106 

50' 
40' 

40' 
50' 

.9217 
.9271 

1.0850 
1.0786 

20' 
10' 

28° 

•5317 

1.8807 

62° 

30' 

•7133 

1.4019 

30' 

43° 

•932  s 

1.0724 

47° 

id 

20' 

•5354 
•5392 

1.8676 
1.8546 

5o; 
40' 

4Cy 
50' 

.7177 
.7221 

1-3934 
1,3848 

20' 

10' 

10' 

20' 

•9380 
.9471: 

i.  0661 
1.0599 

50' 
40? 

30' 

•5430 

1.8418 

30' 

30° 

.7265 

1-3764 

54° 

30' 

9490 

1.0538 

30' 

40' 
50' 

•5467 
•5505 

1.8291 
1.8165 

20' 

10' 

10' 
20' 

73io 

•7355 

1.3680 
J-3597 

50' 
40' 

40' 
50' 

9545 
9601 

1.0477 
1.0416 

20' 
10' 

29° 

•5543 

1.8040 

61° 

3C/ 

.7400 

1-35M 

30' 

440 

96^7 

'•°355 

46° 

10' 

20' 

•558i 
.5619 

1.7917 
1.7796 

50' 
40' 

40' 
50' 

7445 
7490 

I.3432 
i-335i 

20' 

lo' 

10' 
2C/ 

9713 
9770 

1-0295 
i  .0235 

50' 

W 

3°; 

'S?r 

r-7675 

3o; 

37U 

7536 

1.3270 

53° 

30; 

9827 

1.0176 

30* 

4° 
50' 

.5696 

•5735 

'•7556 
1-7437 

20' 
10' 

10' 

20' 

7581 
7627 

1.3190 
1.3111 

50; 
40' 

40' 
50' 

9884 
9942 

1.0117 

1.0058 

20' 
10' 

80U 

•5774 

1.7321 

60° 

30' 

•7673 

1.3032 

30' 

45° 

[.0000 

I.OOOO 

45° 

Cot. 

Tan. 

A. 

Cot. 

Tan. 

A. 

Cot. 

Tan. 

A. 

COEFFICIENTS,  STRENGTH    OF  MATERIALS.  78 1 

VI. 
TABLE  OF  COEFFICIENTS,  STRENGTH   OF  MATERIALS. 


Ultimate  Strength. 
Tons  per  Square  Inch. 

Moduli. 
Tons  per  Sq.  Inch. 

Tension. 
T 

Com- 
pression. 

c 

Shearing. 
S 

Elasticity. 
£ 

Rig. 
Et 

5i-io| 
7 
14 
15-20 

27-29 
24 

22 

19 
27-29 

25 
19-24 
25-50 

26-32 

30-45 
40-65 
80 
72 
70 
150 

10-14 

I5-I6 

28 

8-13 

22 
11-23 
15-26 

2-3 
7-10 

2 
0.9 

3-7 
H-3i 
4 
4-7 
4-6 
4-7 

25-65 
42 
36-58 
60-75 

20 

35 
5 

3 

Si 

2-4 
4 
3i 

2f-S 

14-2* 

ii-3 
i-6 

9-13 
II 

1 
-  18-22 

J 

]        * 

8, 

3 
1     a. 

J  ? 

10-14 

i 
i 

5«oo 

f       to 

6000 

12,000 

to 

13,000 

) 
12,000 

r   to 

13,000 

13,000 
7000 

8000 
5500 

6400 

4500-6000 

6000 

5500 

1000 

800 

600 
950 

750 
650 

1300 
to 

2500 
50OO 

5000 
to 
5200 

2800 
1500 

22OO 
1700 
24OO 

Average        .            •    •        • 

American  ordnance  

Repeatedly  melted         . 

Wrought-iron  — 
Finest  Low-  j  with    grain., 
moor  plates:  (  across    "     .. 

r.  .  j                  (  with        " 
Bndge-.ron:  j  ^^    ,.    || 

Bars  finest         

Bars   soft  Swedish  

Wire    

Steel— 
Mild-^teel  plates   

Crucible  tool-    "    

Chrome               "      

Tungsten            "    

Piano-wire     ..       

Copper  — 
Cast  

Rolled               

Brass 

Wire            

Phosphor  bronze              ...    .  . 

Tin              

Lead  

Timber  — 
Oak  

Ash  .    

Beech      

Mahogany              

Stone  — 

Brick  

From  Vol.  XXII.,  Encyc.  Britannica. 


EXPERIMENTAL   ENGINEERING. 

VII. 
STRENGTH    OF   METALS   AT    DIFFERENT   TEMPERATURES. 

[EXPERIMENTS  OF  A.  LE  CHATELIER,  PARIS,  1891.] 

CAST-BRASS. 
Strength  remains  about  constant  until  500°  C. 


Temperature 
Centigrade. 
Deg. 

Breaking-load 
per  Square  Inch. 
Lbs. 

Elongation. 
Per  Cent. 

15 

19.457 

0.24 

155 

17,864 

0.71 

230 

17,508 

0.35 

480 

17,693 

0.89 

540 

11,677 

0.54 

690 

5,66o 

0.71 

TIN-BRONZE. 


Temperature 
Centigrade. 
Deg. 

Breaking-load 
per  Square  Inch. 
Lbs. 

Elongation. 
Per  Cent. 

Duration  of  Test. 

M.    S. 

15 

22,614 

5-7 

8     30 

140 

23,582 

7.08 

5     30 

230 

20.524 

3-9 

6     30 

250 

18,717 

4.28 

21      0 

300 

17,124 

-      2.0 

17    o 

350 

15,574 

1.4 

16    o 

415 

9,03l 

2      30 

ALUMINIUM-BRASS. 


Temperature 
Centigrade. 
Deg. 

Breaking-load 
per  Square  Inch. 
Lbs. 

Elongation  in  5.502 
Inches. 
Per  Cent. 

15 
140 
230 
320 

49»l83 

46,168 
42,IOO 
30,380 

30.7 

37-0 

33.2 
15.6 

IMPORTANT  PROPERTIES  OF  FAMILIAR   SUBSTANCES.  783 


VIII. 
IMPORTANT    PROPERTIES   OF   FAMILIAR   SUBSTANCES. 


Specific 
Gravity. 
Water,  i. 

Specific 
Heat. 
Water,  i. 

Absorbing 
and  Radiat- 
ng  Power  of 
Bodies  in 
Jnits  of  Heat 
per  Square 
Foot  for  Dif- 
ference of  i°. 

Conducting 
Power  in 
Units  of  Heat 
per  Square 
Foot  of  Sur- 
face with 
Difference 
of  i°. 

Weight 
Pounds 

Melting 
Points. 
Degrees 
Fahr. 

Meta\s  from  32°  to  212°— 

6  1  102.65 
6.712 
9.823 
8.1 
8.788 
7-5 
7-744 
19-258 
11.352 
13.598 
8.800 
16.000 
10.474 
7-834 
7.291 
7.191 

2.784 
3-I56 
2.240 
2.686 
2.650 

.86 
•55 

•  44 
J-43 

1.  00 

2.89 
2.03 

•9 
,88 
.0006 
.87 
i  .000 

.922 

.00122 
.00127 

.000089 
.OOlgS 

.212 

.0508 
.0308 
•0939 
.092 
.1298 
.1138 
.0324 
.0314 
•0333 
.1086 
.0324 
.056 
.1165 
.0562 
•°953 

.2149 
.2174 

.2694 
.2158 

•57 
-65 

.2415 
.2411 
.203 

.1977 
.2026 

.6588 

'% 

.416 

I.OOO 

.504 

.238 

.2412 

3.2936 

.2210 



Per 
cu.  in. 

O.I  100 

0.2428 

0.3533 
0.2930 
0.3179 
0.2707 
0.2801 
0.6965 

0.410^ 

0.4918 
0.3183 

°-57ll 

0.3788 

0.2916 
0.2637 
0.26 
Per 
cu.  ft. 
174.0 
197.0 
140.0 
168.0 
165.0 

III 

a? 

62.5 
180.7 

127.0 

57-5 
55-0 
.050 

54-37 
62.35 

57-5 

.0807 
.0892 
•00559 
•  «34 

too 

476 
1692 
1996 
2250 
2900 
2590 
608 

r$ 

3700 

2OOO 
4000 
446 
680 

Bismuth   .  ..  

.049 

.0327 
.648 
.566 

.1329 
.0265 

Copper   

5*5-0 
233.0 
233.0 

113.0 

Iron  cast        

Gold  
Lead 

Mercury  at  32°  
Nickel            



Silvfer  

Steel 



Tin 

•  0439 
.049 

.6786 
•735 
•735 
•735 
•735 

•73 
•73 

Zinc             

225.0 

Stones  — 
Chalk 

Limestone  



Marble,  gray  

28.0 
22.4 

,  '  ':k 

Marble,  white  
Woods- 
Oak                  

Mineral  substances  — 
Charcoal,  pine  
Coal,  anthracite.  .  .  . 
Coke  
Glass,  white  



.5948 

i:48o' 
i.o853 

6.6 

Sulphur         

Liquids- 
Alcohol,  mean  
Oil,  petroleum  
Steam  at  212°  
Turpentine  
Water  at  62°  

Solid— 
Ice  at  32°             .  .  . 

Gases— 

Oxygen  

Carbonic  acid  

See  also  pages  338  and  383. 


784 


EXPERIMENTAL   ENGINEERING. 


IX. — COEFFICIENTS    OF   FRICTION.      (MORIN.)    (Page  196.) 


No. 

Surfaces. 

Angle  of 
Repose. 

Coefficient  of 
Friction. 

<*> 

/  =  tan  <t> 

«  +S 

I 
2 

3 
4 

6 

8 
9 

10 

ii 

12 

13 
M 

15 

16 

i? 

18 
19 

Deg. 
14    to  26^ 
Il|  to     2 
26£  to  31 
I3i  to  I4i 

Hi 
n|  to  14 
28 
18* 
15    to  igi 
29i 

20 
13 

8* 
8|  to  n| 
i6| 

4      to    4| 
3 

if  to     2 

3? 

0.25  to  .  5 

.2      tO   .04 

.5    to  .6 
.  24  to  .  26 

.2 
.2     tO   .25 

•53 
•33 
.27  to  .38 
.56 
•36 
•23 
•15 

.15  tO  .2 

•3 
.07  to  .08 

•05 
.03  to  .036 

.05? 

4  to  2 

5  t"  25 

2  tO   I    67 
4.17  103.85 

5 
5  to  4 
1.89 

3 
3.7    to  2.  86 

1.79 

2.78 

4-35 
6.67 
6.67  to  5 
3-33 

14.3   to  12.5 

20 
33.3    to  27.0 
2O? 

«'       "      "       soaked  

"        "     "      wet  

Leather  on  oak     .              ...        . 

Leather  on  metals,  dry      

«         «        «       wet 

"        "        "       creasy 

"         "         "        oilv     . 

•I         «<         «       wet 

Smooth     surfaces,     occasionally 

Smooth      surfaces,      continually 
greased    

Smooth  surfaces,  best  results  
Bronze  on  lignum  vitae,  wet.    .  .  . 

NOTE.— The  above  table  is  defective  since  the  pressure  per  square  inch  is  not  given.  The 
coefficient  of  friction  diminishes  with  increase  of  pressure,  so  that  in  some  kcases  the  total  friction 
remains  constant- 

X. — HYPERBOLIC    OR   NAPERIAN    LOGARITHMS. 


N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

N. 

Log. 

1.  00 

o.oooo 

•30 

.8329 

3-60 

.2809 

4.90 

.5892 

6.40 

8563 

1-05 

0.0488 

•35 

•8544 

3-65 

.2947 

4-95 

•5994 

6.50 

.8718 

.10 

0.0953 

.40 

.8755 

3-7° 

-3083 

5.00 

.6094 

6.60 

.8871 

•15 

0.1398 

•45 

.8961 

3-75 

.3218 

5-05 

.6194 

6.70 

.9021 

.20 

0.1823 

•50 

.9163 

3-8o 

•3350 

5.10 

.6292 

6.80 

.9169 

•25 

0.2231 

•55 

.9361 

3-85 

•  3481 

5-*5 

.6390 

6.90 

•93JS 

•30 

0.2624 

.60 

•9555 

3-90 

.3610 

5-20 

.6487 

7.00 

•9459 

•35 

0.3001 

•65 

.9746 

3-95 

•3737 

5-25 

-6582 

7.20 

•9741 

•40 

0.3365 

.70 

•9933 

.00 

•3863 

5-30 

.6677 

7.40 

•  0015 

•45 

0.3716 

•75 

.0116 

.05 

•3987 

5-35 

.6771 

7.60 

.0281 

•50 

0.4055 

.80 

.0296 

.10 

.4110 

5-40 

.6864 

7.80 

•0541 

:S 

0.4383 

0.4700 

•85 
.90 

•«473 
.0647 

.20 

.4231 

•4351 

5-45 
5-50 

.6956 
.7047 

8.00 
8.25 

.0794 

.1102 

•  65 

0.5008 

•95 

.0818 

•25 

•4469 

5-55 

•7«38 

8.50 

.1401 

.70 

0.5306 

3-00 

.0986 

•30 

.4586 

5-6o 

.7228 

8-75 

.169! 

•75 

0.5596 

3-05 

•"54 

•35 

.4701 

5-65 

•  73T7 

9.00 

.1972 

.80 

0.5878 

3.10 

•  1314 

.40 

.4816 

5-70 

•7405 

9.25 

.2246 

.85 
.90 

0.6152 
0.6419 

3-»5 

3-20 

.1474 
•  1632 

•45 
•50 

.4929 
.5041 

5-75 
5-8o 

•  7492 

•7579 

9-50 
9-75 

•2513 

•2773 

•95 

0.6678 

3-25 

.1787 

-55 

5-85 

.7664 

10.00 

.3026 

.00 

0.6931 

3-30 

•1939 

.60 

•  5261 

5-90 

•775° 

II.  OO 

•3979 

•05 

0.7178 

3-35 

.2090 

-65 

•5369 

5  95 

.7834 

12.00 

4849 

.10 

•15 

0.7419 

3-40 
3-45 

•2238 
.2384 

.70 

•7s 

•5476 

6.00 
6.10 

.7918 
.8083 

13.00 
14.00 

•5649 
.6391 

.20 

0.7885 

3  50 

•  2528 

/So 

.'5686 

6.20 

.8245 

15.00 

.7081 

•25 

0.8109 

3-55 

.2669 

-85 

.5790 

6.30 

.8405 

16.00 

.7726 

MOISTURE  ABSORBED  BY   THE  AIR— HUMIDITY.     785 


XL 

MOISTURE   ABSORBED   BY   AIR.* 

THE  QUANTITY  OF  WATER  WHICH  AIR  is  CAPABLE  OF  ABSORBING  TO 
POINT  OF  MAXIMUM  SATURATION,  IN  GRAINS  PER  CUBIC  FOOT 
FOR  VARIOUS  TEMPERATURES. 


Degrees 

Fahr. 

Grains  in  a 
Cubic  Foot. 

Degrees 
Fahr. 

Grains  in  a 
Cubic  Foot. 

—  20 

0.2IQ 

55 

4.849 

—  10 

0.356 

57 

5.IQI 

-    5 

0.450 

60 

5.744 

0 

0.564 

62 

6.142 

5 

0.705 

65 

6.782 

10 

0.873 

67 

7.241 

15 

1-075 

70 

7.980 

20 

I.32I 

72 

8.508 

25 

1.611 

75 

9.356 

30 

1.958 

77 

9.961 

32 

2.113 

80 

10.933 

35 

2.366 

85 

12.736 

40 

2.849 

90 

14.791 

45 

3-414 

95 

17.124 

50 

4.076 

IOO 

19.766 

52 

4-372 

105 

22.751 

XII. 

RELATIVE   HUMIDITY  OF  THE  AIR.* 


Difference  of 
Temperature, 
Wet  and  Dry 
Bulb. 

Temperature  of  the  Air. 

S..F. 

7o«  F. 

90*  F. 

0.5 

I 

95 
90 

98 

95 

98 
96 

2 

79 

90 

92 

3 
4 

69 
59 

86 
81 

88 
85 

5 

50 

77 

81 

6 

40 

72 

78 

68 

75 

I 

21 

64 

12 

60 

68 

9 
10 

3 

55 

65 

12 

48 

59 

40 

53 

33 

47 

18 

26 
19 

41 
36 

13 

32 

24 

7 

26 

»From  Weather  Bulletin  No.    127,  U.   S.  Dept.  of  Agriculture,  1897. 

barometer  q2.4 


EXPERIMENTAL   ENGINEERING. 


VTTT 

(Page  202.) 

TABLE   OF    BEAUME'S    HYDROMETER   SCALE   WITH    CORRE- 
SPONDING  SPECIFIC   GRAVITIES. 
FOR  LIQUIDS  LIGHTER  THAN  WATER.     TEMP.  60°  FAHR. 


Beaume". 

Specific 
Gravity. 

Beaum<*  . 

Specific 
Gravity. 

Beaume*. 

Specific 
Gravity. 

Beaume". 

Specific 
Gravity. 

10 

I.OOOO 

31 

0.8695 

52 

0.7692 

73 

0.6896 

II 

0.9929. 

32 

0.8641 

53 

0.7650 

74 

0.6863 

12 

0.9859 

33 

0.8588 

54 

0.7608 

75 

0.6829 

13 

0.9790 

34 

0.8536 

55 

0.7567 

76 

0.6796 

14 

0.9722 

35 

0.8484 

56 

0.7526 

77 

0.6763 

15 

0.9655 

36 

0.8433 

57 

0.7486 

78 

0.6730 

16 

0.9589 

37 

0.8383 

58 

0.7446 

79 

0.6698 

*7 

0.9523 

38 

0.8333 

59 

0.7407 

80 

0.6666 

18 

0.9459 

39 

0.8284 

60 

0.7368 

81 

0.6635 

19 

0-9395 

40 

0.8235 

61 

0.7329 

82 

0.6604 

20 

0-9333 

41 

0.8l87 

62 

0.7290 

83 

0.6573 

21 

0.9271 

42 

0.8139 

63 

0.7253 

84 

0.6542 

22 

0.9210 

43 

0.8092 

64 

0.7216 

85 

0.6511 

23 

0.9150 

44 

0.8045 

65 

0.7179 

86 

0.6481 

24 

0.9090 

45 

0.8000 

66 

0.7142 

87 

0.6451 

25 

0.9032 

46 

0-7954 

67 

0.7106 

88 

0.6422 

*6 

0.8974 

47 

0.7909 

68 

o.  7070 

89 

0.6392 

17 

0.8917 

48 

o.  7865 

69 

0.7035 

90 

0.6363 

?8 

0.8860 

49 

0.7821 

70 

O.7OOO 

29 

o.  8805 

50 

0.7777 

7i 

0.6965 

50 

0.8750 

51 

0.7734 

72 

0.6930 

FOR  LIQUIDS  HEAVIER  THAN  WATER.     TEMP.  60°  FAHR. 


Bea^«ne\ 

Specific 
Gravity. 

Beaume. 

Specific 
Gravity. 

Beauine*. 

Specific 
Gravity. 

Beaume". 

Specific 
Gravity. 

I 

1.0069 

*9 

•1507 

37 

.3425 

55 

.6111 

2 

1.0139 

20 

.1600 

38 

•3551 

56 

.6292 

3 

.0211 

2T 

.1693 

39 

.3679 

57 

.6477 

4 

.0283 

22 

.1788 

40 

.3809 

58 

.1666 

5 

•0357 

23 

.1885 

4i 

•3942 

59 

.6860 

6 

.0431 

24 

.1983 

42 

.4077 

60 

.7056 

7 

.0507 

25 

.2083 

43 

.4215 

6  1 

.7261 

8 

•0583 

26 

.2184 

44 

•4356 

62 

.7469 

9 

.0661 

27 

.2288 

45 

-4500 

63 

.7682 

10 

.0740 

28 

•2393 

46 

.4646 

64 

.7901 

ii 

.0820 

29 

.2500 

47 

•4795 

65 

.8125 

12 

.0902 

30 

.2608 

48 

.4949 

66 

.8354 

13 

.0984 

31 

.2719 

49 

.5104 

67 

.8589 

14 

.1068 

32 

.2831 

50 

•5263 

68 

.8831 

15 

."53 

33 

.2946 

5i 

•5425 

69 

.9079 

16 

.1240 

34 

.3063 

52 

•5591 

70 

•  9333 

17 

.1328 

35 

•3;8i 

53 

.5760 

18 

.1417 

36 

1.3302 

54 

•5934 

COMPOSITION  OF   VARIOUS  FUELS   OF   U.    S.  787 

XIV. 

COMPOSITION    OF  VARIOUS   FUELS  OF  THE    UNITED    STATES. 


Mine  or  Name. 

Locality. 

Coal  as  Received. 

B.T.U. 
perlb 
Comb. 

Fixed 
C. 

Vol. 
Matter. 

Ash. 

Water 

B.T.U. 

Mount  Pleasant  
Exeter  (Rice)  .   . 

Scranton,  Pa.  ....... 
Pittston,  Pa  

Scranton,  Pa.,  Slate 
out....    ...   
Scranton  Pa  

80.54 
79.41 
74  73 

87.96 
83.98 
75  29 
81.68 
84.46 
85.70 
86.68 
91-45 
83-13 
79-23 

7'54 
8.16 

5-71 

2.30 
4-99 
5-47 
5.78 
5  37 
5-95 
5-89 
5.03 
5-98 
3  73 

10.65 
12.18 
18.90 

6-77 
9  91 

18.43 
10.84 
9.20 

L?I 

2.  17 

9  62 
"3  7' 

i  27 

:3 

2.97 

I.  12 

.81 
1.70 

97 
1.04 

1.28 

»  35 
1.27 

3-33 

12.307 
12,400 
11.360 

13-324 
12.903 
",430 
12,036 
12,294 
12.934 
13.051 
I3-254 
12.943 
12,149 

13-973 
14  160 
14.122 

14.760 
i4-503 
14.152 
13.760 
13.684 
14.120 
14.095 
'3,756 
T4,525 
14.642 

j 

< 

ll 

J.  G 

1 
1 

Exeter 

Coxe's  No.  i  

No.  ii  Forty-foot  
York  Farm  (Bkwt)... 
Jermyn  .               

Schuyikill  Co.,  Pa... 
Pottsviile,  Pa  

Cayuga.         ...      . 

Manville  Shait     .  .. 

Avondale  
Oxford       

Continental  
Woodward-  

Cumberland  
Eureka  
Antrim  

Maryland  .... 

75  5° 
70  47 
69  30 
67.32 
72.90 
68.88 
67.45 

17.00 

23.86 

18.57 
25.01 
20.42 

21  .8l 
20.4I 

6  oo 
4.87 
10.90 

II  .  12 

«;.oo 
6.75 
"  33 

i  5° 
.80 
1-23 
1-55 
1.18 
2.56 
.81 

14.700 
14-195 
13-528 
12,965 
15.200 
14.580 
12.789 

15,900 
15-046 
I5»397 
14.845 
16.200 
16.070 
14-555 

Pennsylvania  

Towanda.  Pa  
West  Virginia  

Wales 

Long-  Valley  
New  River  

Cardiff.                .... 

Union  

Jerome  Park,  Colo.  . 
New  Castle,  Colo..  .  . 
Illinois  

52-86 
50.80 
44.10 
53.80 
44  30 
49  55 

36.70 
35.80 

33  10 
30.70 
36  35 
39-94 
32  30 
32  .  80 
30.60 
42.23 
34.10 
36.23 
30.73 
•36  .  30 
34.60 

33  5° 
38.03 
27  82 
34.22 
32.25 
28  27 
3°'77 
34.60 
33.00 
31.29 
28.71 
42  84 
30.42 

8.44 
10  90 
14.70 
8.00 
1-40 
1  74 

?:2 

I.  00 

11.48 
7.30 
71.63 

10  90 
8  30 
4-30 
15.50 
6  91 
ii  .09 
4.22 
12.50 
983 
9.16 
0.70 

13    40 
783 

6  10 
15.36 
4  03 

2.00 
2.50 

8.10 

7-5° 
7-95 
3-7* 

17.  OO 

15.50 
9.70 

5  89 
4.00 
«;  49 
2  88 
6.50 
4.80 
*-45 
5  23 

21 
2.  II 

1.25 

3-oo 
i  03 
2.40 
3  oo 
2.27 
1.93 
.48 
i  .  ii 

13,650 
11,900 
10.600 
12.400 
ii.  600 
10.506 
10,900 

IO.2OO 

11,300 
11.546 
12.800 

12.  060 
II.SOO 
12.  CIS 
12.900 
I2.4OO 
II966 
12.935 
14.150 
12,900 

"•539 
14.  142 
12,400 
12.750 
13.126 
15.005 
12.224 
15,266 

15*240 
13.750 
13-730 
14.675 
14,380 
12.425 
14-583 
14.030 
14.250 
13-97? 
I4-43° 
14.550 
13,685 
14,100 
14.200 
14,930 
13.619 
M.583 
15.107 
M.958 
14.386 
15.746 
14.107 
15.250 
14.600 
16.313 
U.523 
16,091 

New  Castle  (Lump).  . 
Mt.  Olive  (Lump)  
Big  Muddy  

Streator  (Lump)  
Gillespie   

Streator,  111  
Illinois  

Ladd  (Lump)   
Wilmington  (Lump).. 
Indiana  Block  
New  Pittsburgh  
Vanderpoo!  (Lump).. 
Wills  Creek 

Wilmington.  Ill  
Brazil,  Ind  
Indiana  Block.  
Kentucky...   
Ohio        ....,,  

39-9° 
53  7« 
40.40 
54.60 
46  €5 
5S-5O 
48  90 
56  30 
49-5^ 
49  83 
60.88 
59-45 
54  °° 
58  90 
59  °4 
53  3° 
so  60 
58.61 
63.96 
41  32 
6<  44 

Jackson  Hii!  
Hocking  Valley  
Brier  Hill        .... 

i 

« 

Weilsville 

( 

Goshsn 

i    * 

Hastings  

Nebraska  
Monongahela  R.,  Pa. 
Pennsylvania  
ConneHsvi)le,Pa  
Pennsylvania.  

Turtle  Creek  

Youghiogheny  
Trotter 

Reynoldsville  
Pittsburgh                  .  . 

Summer  Hill  (Slack).. 
Monongahela  

it 

Monongahela  R..  Pa. 
Connellsville.  Pa  
Peyton.  W.  Va.  
Nova  Scotia  

Canne'l  
Cooperstown  

ANALYSES   OF  ASH. 


Specific 
Grav. 

Color 

of  Ash. 

Silica. 

Alum- 
ina. 

Oxide 

Iron. 

Lime. 

Mag- 
nesia. 

Loss. 

Acids 
S.&P. 

Pennsylvania  Anthracite  
Bituminous  
W*^sh  Anthracite               .... 

1-559 

*-372 

i.  32 

Reddish 
Buff. 
Gray. 

45-6 
76.0 
40.0 

42.75 

21.  OO 

44.8 

9-43 
2.60 

1.41 

12.0 

0-33 
trace 

0.48 
0.40 

2.97 

Scotch  Bituminous  
Lignite  

1.26 
1.27 

.::. 

37-6 
19-3 

52.0 
ii.  6 

5-8' 

3-7 
23-7 

1.  1 

2.6 

:.'." 

5.02 
33-8 

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EXPERIMENTAL  ENGINEERING. 


XVI. 
ENTROPY     OF    WATER     AND     STEAM. 


Absolute 
Pressure, 
Pounds  per 
Square  Inch. 

Entropy  per  Pound.    B.T.U. 

Absolute 
Pressure, 
Pounds  per 
Square  Inch 

Entropy  per  Pound.     B.T.U. 

Water. 

Steam. 

Water. 

Steam. 

I 

0.134 

.987 

**5 

0.490 

1.586 

2 

0-175 

.924 

I2O 

0.494 

1-583 

3 

O.20I 

.887 

125 

0.498 

•580 

4 

0.220 

.861 

130 

0.501 

•577 

5 

0.235 

.841 

J35 

0-5°5 

•574 

6 

0.247 

.825 

140 

0.508 

•571 

7 

0.257 

.814 

145 

0.512 

•569 

8 

0.268 

.800 

150 

o-SJS 

.566 

9 

0.277 

.790 

155 

0.518 

•563 

10 

0.285 

.781 

1  60 

0.521 

.561 

IS 

o.3J5 

•747 

165 

0-524 

•559 

20 

o-338 

.722 

170 

0.527 

•557 

25 

°-356 

.704 

175 

0-530 

-555 

3° 

0.370 

.689 

1  80 

o-533 

•552 

35 

0.384 

.677 

185 

0-536 

•55° 

40 

0-395 

.666 

190 

o-539 

.54» 

45 

0.405 

-657 

195 

0.542 

.546 

5° 

0-415 

.649 

2OO 

0-544 

•545 

55 

0.423 

.641 

205 

0-547 

•543 

60 

0-431 

•634 

2IO 

0-549 

•541 

65 

0.438 

.628 

215 

0-551 

•540 

70 

0.444 

.623 

22O 

0-554 

•538 

75 

0.450 

.617 

230 

0-559 

•535 

80 

0-455 

.612 

240 

°-563 

•532 

85 

0.461 

.608 

250 

0.567 

•529 

9° 

0.466 

.  604 

260 

o-57i 

.526 

95 

0.476 

•596 

270 

o-575 

•523 

100 

0.480 

•593 

280 

0-579 

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105 

0.482 

•593 

290 

0-583 

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no 

0.485 

•59° 

300 

0.587 

•5i5 

DISCHARGE    OF  STEAM. 


795 


XVIL  (Page  30,) 

DISCHARGE   OF   STEAM    IN    POUNDS    PER    HOUR   CALCULATED 
BY    NAPIER'S   FORMULA. 


Absolute 
Pressure. 
Pounds. 

Pounds  of  Steam. 

Diameter  of 
Orifice  ^z  inch. 

Diameter  of 
Orifice  ^g  inch. 

Diameter  of 
Orifice  J-  inch. 

I 

0.039 

0.158 

0.631 

2 

0.079 

0.3:6 

1.262 

3 

O.IlS 

0.473 

1.893 

4 

0.158 

0.631 

2.524 

5 

0.197 

0.789 

3-155 

6 

0.237 

0.947 

3.786 

7 

0.276 

1.104 

4.417 

8 

0.315 

1.262 

5-048 

9 

0-354 

1.420 

5.680 

10 

0.395 

1.578 

6.311 

20 

0.789 

3.155 

12.622 

30 

1.183 

4-733 

18.937 

40 

1.578 

6.311 

25.244 

50 

1.972 

7.880 

3L556 

60 

2.367 

9.467 

37.867 

70 

2.761 

11.045 

44.178 

80 

3.156 

12.623 

50.488 

go 

3-550 

14.  200 

56.800 

100 

3-947 

15.778 

63.H5 

XVIII.  Page420, 

PER    CENT    OF    WATER    AND    STEAM  EXHAUSTING    INTO 

ATMOSPHERE.— BY   THROTTLING  CALORIMETER. 

(Per  cent  of  moisture.) 


Tempt,  in 
Calorimeter. 


Gauge-pressure  on  Main  Steam-pipe. 


Degrees  Fahr. 

40 

45 

5° 

55 

60 

65 

70 

75 

80 

515  

.0233 

.0253 

.0271 

.0290 

•0307 

.0322 

.0338 

.0354 

.0368 

.0227 

.0245 

.0263 

.0280 

.0296 

.0311 

.0327 

.0340 

0181 

.0218 

.0237 

.0253 

.0269 

.0284 

.0300 

.0313 

30  

.0154 
.0128 

•0173 
.0147 

.0192 
.0165 

.0210 
.0184 

.0227 

.0200 

.O242 
.0215 

.0257 

.0230 

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.0246 

.0287 

.0200 

40  

.0102 
.0076 

.0122 

.0005 

.0139 
.0112 

•0157 
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•  0173 
.0147 

.0189 
.Ol62 

.0204 
.0177 

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.0192 

•0333 
.0206 

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.0104 

.0120 

•OI35 

.0150 

.0165 

.0179 

.0059 

.0077 

.0093 

.0108 

.0123 

.0138 

.0152 

p::::::::::::: 

65 

.  OOO5  — 

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si  . 

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.0011  — 

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.0015 

8s 

.0100  — 

0082- 

.0067  — 

.0053— 

.0038- 

.0024  — 

.ooia— 

)iff.  i°  Fahr  .  .  . 

.00052 

.00052 

.00053 

.00053 

.00053 

.00054 

.00054 

00054 

.00054 

The  minus  sign  indicates  superheat. 

This  amount  divided  by  0.48  and  multiplied  by  the  value  of  the  latent  heat  will  Rive  the 
egree  of  superheat. 


OF  EVAPORATION. 


797 


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EXPERIMENTAL   ENGINEERING. 


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799 


DENSITY  AND    WEIGHT  OF   WATER. 
XXI. 

FOR    VARIOUS    TEM- 


WEIGHT    OK    WATER 


WEIGHT  OF  WATER  PER  Ctmc   FOOT,  PROM   31°  TO'  „,.   F.,  AND 
UNITS  PER  POUND.  RECKONED  ABOVE  37°  F. 


H£AT 


of 

. 

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3 

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05 

tfl 

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h-H  j3 

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6 

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i 

if! 

Iff 

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3 

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1 

14 

€ 

3 

f 

£0. 

a 

—- 

£* 

& 

|2Q 

£ 

1 

|20 

g* 

1 

32 

33 
34 

i 

39 

<to 

41 
42 
43 
44 
45 
46 

49 
50 
51 
52 
53 
54 
55 
56 

62.4 
62.4 

62.42 
62.4? 
62.42 
62.42 
62.42 
62.42 

62.42 

62.42 
62.42 

62.42 

62.42 
62.42 

62.42 
62.42 
62.41 
62.41 
62.41 
62.41 

62.40 

62.40 
62.40 

62.39 
62.39 
62.39 

\ 

£ 

12. 

16. 
'7- 
18. 
'9. 

20. 
21.01       1 
22.  OI       1 
23.01       1 
24.01       1 
25.01       1 

_£ 

78 

79 
80 
81 
82 

1 

86 

89 
90 
9i 
92 
93 
94 
95 
<?6 
97 
98 
99 
ioo 

102 

103 

62.25 
62.24 
62.23 
62    22 
62.21 
62.20 
62.19 
62.18 
62.17 
62.16 
62.15 
62.14 
62.13 
62.12 
62.11 
62.10 
62.09 
62.08 

62.06 
62    05 
62.03 
62.02 
)2.0I 

6  .00 
6  -99 

46.03 
47-03 
48.04 
49.04 
50.04 
51.04 
52.04 
53-05 
54-05 
55-05 
56.05 
57-05 
58.06 
59-06 
60.06 
61.06 
62.06 
63.07 
04.07 
65-07 
66.07 
67.08 
68.08- 
69-08 
70.09 
71.09 

123 
124 
125 
126 
127 

128 
129 
130 

132 
J33 
r34 

136 
'37 

139 
140 
141 
142 
143 
144 

146 
148 

6l.68 
61.67 
61-65 
61.63 

61.61 
6t.6o 
61.58 
61.56 

61.54 
61.52 
61.51 
61.49 
61.47 

61-45 
61.43 
61.41 
61.39 
61.37 
61.36 
61.34 
61.32 
61.30 
61.28 
61.26 
61.34 
61.22 

91.  i 
92.1 
93-1 

94.1 
95-' 
96  i 
97.1 
98.1 
99.2 

IOO.  2 
IOI.2 
IO2.2 
103.2 
104.2 
105-2 

106.2 

107.24 
Io8.2< 

109  25 
110.26 
111.26 
112.27 

I  '3  -2* 

'5.29 
16.29 

168 
169 
170 
171 
172 
173 
'74 

176 
'77 
178 
179 
180 
181 
182 
'83 
184 
'85 
186 
187 
188 
189 
190 
191 
192 
'93 

60.8 
60.7 

|-7 
60.7 
60.7 
60  6 
60.6 
60.6 
60.6 
60.59 
60  57 
60.55 
60.53 
60.50 
60.48 
60.46 
60.44 

6o-4' 
60.39 
60.37 
60.34 
60.32 
60.29 
60.27 
60.25 

136.44 
'37-45 
138.45 
'39-46 
140.47 
141.48 
142.49 
'43-50 
H4-51 
'45-52 
146.52 
'47-53 
'48  54 
'49-55 
'50-56 
'5'  57 
152.58 
'53-59 
154-60 
'55  -61 
156.62 
'57-63 
158-64 
159-65 
160.67 
161.68 

5** 

02  .38 

26.OI              I 

104 

6  -97 

72.09 

149 

61.20 

17.30 

60.22 

162.69 

59 

62.38 

27.01       I 

IO5 

.96 

73-  'o 

150 

61.18 

18.31 

'95 

b.2O 

63.70 

JO 

61 
62 

62.37 

62.37 
62.36 

28.01       1 
29.01       1 
30.01       1 

106 
107 
108 

•95 
•93 
92 

74.10 
75-10 
76.10 

151 
J52 

61.16 
61.14 

6l.I2 

'9-31 
20.32 

121.  -53 

i 

60.17 
60.15 
60.12 

j  ' 
64.71 

63 

62.36 

31.01       1 

109 

77.K 

'54 

61.  10 

122.33 

199 

60.  10 

67-74 

64 

62.35 

[2.OI       1 

no 

.89 

78.11 

155 

61.08 

'23.34 

200 

60.07 

68.75 

g 

67 

62.34 
62.34 
62.33 

33-oi     1 

34-02     1 
35-02     1 

in 

112 

"3 

'.86 
85 

79.11 
80.12 

81.12 

156 
158 

61.04 
61.06 
61.02 

'24.35 
'25.35 

126.36 

201 
202 
203 

60.05 
60.02 
60.00 

,           '9 

69-77 
70.78 
71.79 

68 
69 

62.33 
62.32 

6.02       I 
7-02      I 

114 

83 
i  82 

82.13 
83-13 

'59 
160 

61.00 
60.98 

'27.37 
128.37 

204 

205 

59-97 
59-95 

72.80 
73-8i 

70 

62.31 

8.02      1 

116 

i  80 

84-13 

161 

60.96 

129.38 

206 

59-92 

7' 

62.31 

9-02       I 

117 

1.78 

85-  '4 

162 

60.94 

130.39 

2O7 

59-89 

75-84 

73 

62.30 

O.O2      1 

118 

1.77 

86.14 

163 

60.92 

131.40 

208 

59-87 

76.85 

73 

62.29 

1.  02     1 

119 

'•75 

87-  '5 

164 

60.90 

'32-  41 

209 

59-84 

77.86 

74 

62.28 

2.03  1 

120 

'•74 

88.15 

165 

60.87 

'33-4' 

210 

59.82 

78.87 

75 
76 

62.28 
62.27 

3.03    1 
4-03  1 

121 
122 

1.72 
1.70 

89.'5 
90.16 

1  66 

167 

60.85 
60.83 

I34-42 
'35-43 

211 
212 

59  79 
59.76 

79.89 
80.90 

77 

62.26 

5.03  1 

WEIGHT  OF  WATER  AT  TEMPERATURES  ABOVE  212°  F. 

Porter  (Richards'  "  Steam-engine  Indicator,"  p.  52)  says  that  nothing  is  known  about  the 
expansion  of  water  above  212°  F.  Applying  formulae  derived  from  experiments  made  at  tern- 
peratures  below  212°  F.,  however,  the  weight  and  volume  above  212°  F.  may  be  calculated, 
but  in  the  absence  of  experimental  data  we  are  not  certain  that  the  formulae  hold  good  at 
higher  temperatures. 

*  Kent's  "  Pocket-book  for  Mechanical  Engineers." 


Soo 


EXPERIMENTAL   ENGINEERING, 


XXII. 

HORSE-POWER   PER   POUND  MEAN   PRESSURE. 


SPEED  OF  PISTON  IN  FEET  PER  MINUTE. 


6  "^ 

5 

100 

240 

300 

350 

400 

450 

500 

550 

600 

650 

750 

4 

.038 

.091 

.114 

•  133 

•  152 

.171 

.19 

.209 

.228 

.247 

«8S 

4* 

.048 

•"5 

.144 

.168 

.192 

.216 

.24 

.264 

.288 

.312 

'360 

tj 

.06 

•144 

.18 

.21 

.24 

.27 

•3° 

-33 

•36 

•39 

•450 

tx 
1 

.072 

.216 

.252 

.288 

•  324 

.36 

.396 

-432 

.468 

•540 

.086 

.205 

.256 

•299 

•  342 

.385 

.428 

.471 

•555 

.641 

.102 

.245 

•  307 

•391 

.409 

.464 

.512 

•563 

&4 

.698 

.800 

7 

.116 

.279 

-348- 

.466 

•524 

•583 

.641 

.699 

.756 

•874 

7* 

.134 

.321 

.401 

!468 

•534 

.602 

.669 

•735 

.802 

.869 

.002 

8 

•  152 

-365 

-456 

•  532 

.608 

-685 

.761 

.837 

.912 

•989 

.121 

8* 

.172 

•413 

-516 

.602 

.638 

•774 

.86 

.946 

.032 

1.118 

.290 

9 

.192 

.215 

.462 
•  515 

•577 
.644 

-674 
•751 

•  770 

-859 

.866 
.966 

•963 
.074 

•059 

•  i54 
.288 

1.251 
1-395 

•444 
.610 

»o 

.238 

•571 

.714 

-83? 

•952 

.071 

.190 

-309 

.428 

1-547 

-785 

.262 

•787 

.919 

.050 

.181 

•3X3 

•  444 

•575 

1.706 

.969- 

ii 

.288 

'.691 

.864 

1.008 

•152 

.296 

•44 

.584 

.728 

i  -872 

.i£ 

XlJ 

•  754 

•943 

i  .  i 

•  257 

.414 

•572 

.729 

.886 

2.043 

•357 

12 

•342 

.820 

i  .025 

1.  195 

.366 

•540 

.708 

.880 

.050 

2.222 

•564 

13 

.402 

.964 

1.206 

1.407 

.608 

.809 

2.OI 

.211 

.412 

2.613 

3-015 

.466 

1.119 

T  .398 

1.631 

.864 

•097 

2.331 

•564 

•797 

3-029 

3-495 

15 

•535 

1-285 

1  .606 

1-873 

•  I3I 

.409 

2.677 

•945 

.212 

3-479 

4.004 

16 

.609 

1.461 

1.827 

2.131 

.436 

•741 

3-°45 

3-349 

-654 

3-958 

4-567 

17 

.685 

1.643 

2.054 

2.396 

•739 

.081 

3.424 

3.766 

.108 

4-450 

5-135 

18 

.771 

1.849 

2.312 

2.697 

3-083 

.468 

3-854 

4-239 

.624 

5.009 

5-780 

19 

•859 

2.061 

2-577 

3  006 

3.436 

.865 

4-295 

4.724 

5-!54 

5.583 

6.442 

20 

•952 

2.292 

2.855 

3-331 

3.807 

.285 

4-759 

5-234 

5-731 

6.186 

7-138 

21 

1.049 

2.518 

3.148 

3.672 

4-197 

.722 

5-247 

5-771 

6.296 

6.820 

7.869 

22 

1.152 

2.764 

3-455 

4.031 

4.607 

5.183 

5-759 

6-334 

6-911 

7.486 

8-638 

23 

1-259 

3.021 

3-776 

4-405 

5-035 

5.664 

6.294 

6.923 

7-552 

8.181 

9-44 

24 

1.370 

3-289 

4.111 

4-797 

5.482 

6.167 

6.853 

7-538 

8.223 

8.908 

10.279 

25 

1.487 

3-569 

4.461 

5-105 

5.948 

6.692 

7-436 

8.179 

8  923 

9-566 

26 

1.609 

3.861 

4.S26 

5.630 

6-435 

7.239 

8.044 

8.848 

9.652 

10.456 

I  2  .  O§S 

37 

1-733 

4.159 

5-I9Q 

6.066 

6.932 

7-799 

8.666 

9-532 

10  399 

11.265 

I  2  .  998 

28 

1.865 

4-477 

5-596 

6.529 

7.462 

8-395 

9-328 

10.261 

11.193 

12.125 

1  3  .  991 

39 

2.002 

4-805 

6.006 

7.007 

8  008 

9.009 

10.01 

II.  Oil 

12.012 

13.013 

15.015 

3° 

2.142 

6.426 

7-497 

8.568 

9-639 

10.71 

11.781 

12.852 

i3-923 

16.065 

31 

2.288 

5^86 

6.865 

8.001 

9.144 

10.287 

"•43 

12-573 

13.716 

14.866 

'7-145 

33 

2.436 

5.846 

7-308 

8.526 

9-744 

10.962 

12.  18 

13-398 

14.616 

15-834 

18.270 

33 

2.590 

6.216 

7.770 

9-065 

10.360 

"•655 

12.959 

I4-245 

15-54 

16.835 

19-425 

34 

2.746 

6.59 

8.238 

9.611 

10.984 

12-357 

13-73 

15.103 

16.476 

17.849 

20.595 

35 

2.914 

6-993 

8.742 

10.199 

i  i  .  656 

T3-"3 

14-57 

16.027 

17.484 

18.941 

21.855 

36 

3.084 

7.401 

9-252 

10.794 

12.336 

13-878 

15.42 

16.962 

18.504 

20.046 

23-130 

37 

3.253 

7.819 

9-774 

11.403 

13.032 

14.861 

16.29 

17.919 

19.548 

21.177 

24  433 

38 

3.436 

8.246 

10.308 

12.026 

r3-744 

15-462 

17.18 

18.898 

20.6l6 

22.334 

25-770 

39 

3.620 

8.648 

10.86 

12.67 

14.48 

16.29 

18.1 

19.91 

21.62 

23-53 

27-150 

40 
41 

3.808 

4.002 

9.139 
9.604 

11.424 
12.006 

13  328 
14-007 

15.232 
16.008 

17.136 
18.009 

19.04 

20.00 

20.944 

22.  Oil 

22.848 
24.012 

24-752 
26.013 

28.560 
30.015 

42 

4.198 

10.065 

12.594 

14-693 

16.792 

18.901 

20.99 

23-089 

25.188 

27.287 

31-485 

43 

4.40 

10.56 

13.20 

15-4 

17.6 

19.8 

22.00 

24  2 

26.4 

28.6 

33.00 

44 

4.606 

1  1  .  046 

13.818 

16.  121 

18.424 

20.727 

23-03 

25-333 

27-636 

29-939 

34-545 

45 

4.818 

"•563 

14-454 

16.863 

19.272 

21.681 

24.09 

26.399 

28.908 

3!-3i7 

36  135 

46 

5.043 

12.086 

15.128 

17.626 

20.144 

22.662 

25.18 

27.698 

30.216 

32  754 

37  770 

47 

5.256 

12.614 

15-768 

18.396 

21.024 

23-652 

26.28 

28.908 

V  •  S36 

34.164 

39.420 

48 

5.482 

£2.846 

16.446 

19.187 

21.928 

24.669 

27-41 

30-I51 

y.  152 

35-633 

41  "5 

49 

5.714 

12.913 

17.142 

19.999 

22.856 

25-7I3 

28.57 

3I-427 

34.284 

37-M1 

42.855 

5° 

14.28 

17-85 

20.825 

23.8 

26.775 

29.75 

32-725 

35-7 

38-675 

44.623 

5* 

6.  180 

14-832 

18.54 

21.665 

24.76 

27-855 

30.95 

34-045 

37.08 

40.205 

46.425 

S2 

6.432 

J5-437 

19.296 

22.512 

25-728 

28.944 

32.  16 

35.376 

38.592 

41.808 

48  240 

53 

6.684 

16.041 

20.052 

23.394 

26.736 

30.078 

33-42 

36.762 

40.104 

43-446 

50.130 

54 

6.940 

16.656 

20.82 

24.29 

27.76 

31-23 

34-7 

38-17 

41.64 

45-1! 

5**°5 

55 

7.198 

17-275 

21.594 

25-193 

28.792 

32.391 

35-99 

39-589 

43-188 

46.787 

53.985 

56 

7.462 

17.909 

22.386 

26.117 

29*48 

33-579 

37-31 

41.041 

44-772 

48-503 

57 

7-732 

i8.557 

23.196 

27.062 

30.928 

34  794 

38.66 

42-526 

46.392 

50.258 

57-99 

58 

8.006 

19  214 

24.018 

28,021 

32.024 

36.027 

40.03 

44-033 

48.036 

52.039 

60.045 

8.284 

19.902 

24-852 

28.964 

33.I36 

37-278 

41.42 

48.704 

53-846 

62.13 

60 

8.566 

20.558 

25-698 

29.981 

34  264 

38.547 

42-83 

47-113 

51-396 

55-679 

64-245 

WATER-COMPUTATIOK   TABLE. 


80.1 


moo  N.  mONO   O  N  O 
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in  in  mo  O  O  t^  t~»  r^oo  co  oo  ON  O  O  O  O 


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^oSin&Hi^SSSm^^n^^^^^S-^SmR^^ 
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H.  rtoo  -  moo  M  inco  M  u->co  M  moo  HI  moo  M  inoo  M  5JK3  5? IN 
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q  co  q  •* 

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t^>  co  co  ^  *^   O  O  O  oo  me 

incoco  M  cocoo  t^N  t^O  HI  O   Or>>T}-Hi 


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inoo  HI  coo  co  O  co  m  r^.  O 
'     O  -f  r^  o  coo 

O  O  O  O  O  O 


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OIDOO  or-^r-~oOHiO  w  Ococo^-  mo  Ooo^  i—oo^ 
^-  r**  Tt~oo  O  oo  co  r^  o  OO  co  O  ^*  f^oo  t^*o  m  N  oo  ^* 


co   rj-  Q  ID  M  in  O 
NO  O  cor->-O   •^• 

HI    >->    CM    N.    N    COCO 


NO  O  co  r-^  O  coo  ON  in  r->.  o  co 


co  m  r~»  O  N  *i-o 

r^  o  coo  Q  coo 

»  o  o  o  o  o  o 


r^r^^t-MO  O  HI  o  mt^ooo  eocoiDf^oo  TJ-<*OO  w  IDCO-H 

^SxS^^^mco^lD-^  9^f  ««9i  -  ^^ t"«  *~ 

ct^ico^sfor:.^^^  i^i'isi  isiMiitiii 

HIM  HI  NN  cococo^^'^'iDiDiDOOO  i^r^r^oooooo  OOO 


5  Sslf 


fl 


cio  ocorO  -rt^       SPJC'S  ^  ^"S  ^ 
O  coo  O  co  r-.  O  co  r-  O   coo   O  coo   O 
'5'T^'>^'lf>ir)OOO  r-r^r^oooc 


HI  co  m  r>-  O 


85 


t-00   00   M  c,   co^mo  ^oo   00   «  N   cojt.00  rjCO    00  M 


<'802 


EXPERIMENTAL  ENGINEERING, 


C*  T}-\O  eo  co  en  co  co  en  to  coco  O  t  e»  O  co  o 
»n  i^»  r>«  in  inco  M  t  t-*>  O  co  m  t  mco  co  oco 

M  Ooo  in  t  N  O  O  MO   O  rn  M  O   O  tO  co 


O 
N 


r>^  co  o  m  M  tx 


M  M  i-i  N 


co  O  M  N  co  to  O  r»co   o  >-<  c»  co  t 
coo  O  N  vo   O  N  vnco  M  t  r>.  O  co  r>«  O  coo 
cocottttvnin  vno  O  <O  t~*  i^»  r^-co  co  co  &>  &•  & 


rt^-'stTl-'^-TtOO    NCO   rf 

too  wvo  O   OOO   rfOt^ 

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«CO  -^O  COmr^Ot-i  CO 
N  t^iomM  a  r^o  O  r^ 
Oco  i^ir>r>-O^O  «  CJ  M 


tOO  M  ir>iDir>«ntnintoO  tONO  O  too  MO  O  tcoo  t  N  Oco 
ir)ONcor^c^r^pjr^c4r^cocou-)OOir>"-)i^-wooi^r>.cooooor>. 
t^  r>«  in  a  O  OO  coco  coo  M  co  coco  M  t  o  r^co  x^o  t  uioo  o  o  M  O 


MwMCiN 


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Ocoo  tttttt  to  co  O  N 
<->  to  co  too  N  co  to  r»MO 
incoOcor^mMr^MinOOCMO 


O  w  co  to  i^  O  O 


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&  O     M     N     CO  4-  10 


^  53 


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COEFFICIENT  OF  DISCHARGE. 


803 


The  following  tables  give  coefficient  of  discharge  as  collated 
from  Hamilton  Smith's  experiments  by  Professor  Merriman. 

XXIV. 
WEIRS   WITH    PERFECT   END  CONTRACTION. 


LENGTH  OF  WEIR  IN  FEET. 

Effective 

HpaH 

rlcHQ 
in  Feet. 

0.66 

1 

» 

3 

5 

1O 

19 

O.I 

0.15 

O.2 

0.632 
.6:9 
.611 

0.639 
.625 
.618 

0.646 
.634 
.626 

0.652 
•  638 
.630 

0.653 
.640 
.631 

0.655 
.641 
•633 

0.656 
.642 
.634 

0.25 

.605 

.612 

.621 

.624 

.626 

.628 

"j* 
.629 

0-3 

.601 

.608 

.616 

.619 

.621 

.624 

.625 

0.4 

•595 

.601 

.609 

.613 

.615 

.618 

•  O2O 

°-5 
0.6 

•59° 
.587 

.596 
•593 

•60S 
.601 

.608 
.605 

.611 
.608 

.615 
.613 

.617 
•615 

0.7 

•590 

.598 

.603 

.606 

.612 

.614 

0.8 

•595 

.600 

.604 

.611 

.613 

0.9 

•592 

.598 

.603 

.609 

.612 

I.O 

•59» 

•595 

.601 

.608 

.611 

1.2 

•585 

•  591 

•597 

.605 

.610 

1.4 

.580 

•587 

•594 

.602 

.609 

1.6 

.582 

•591 

.600 

.607 

*  See  p.  274. 

XXV. 
WEIRS  WITHOUT  END   CONTRACTION. 


Effective 


LENGTH  OF  WEIR  IN  FEET. 


Head 
in  Feet. 

3 

3 

4 

5 

7 

1O 

19 

O.I 

0.659 

0.658 

0.658 

0.657 

0.15 

O.2 
0.25 
03 
0.4 
0.5 

0.6 
°-7 
0.8 
0.9 

I.O 
1.2 

••4 

1.6 

0.652 
•645 
.641 
•639 
.636 

'$1 

.638 

.640 

'ell 
[648 

0.649 
.642 
•  638 
.636 
•  633 
•  633 
.634 
•  635 
.637 
•  639 
.641 
.646 

0.647 
.641 
.636 
•  633 
.630 
.630 
.630 
.631 
.633 
.635 
.637 
.641 
.644 
.647 

•645 
.638 
.634 
.631 
.628 
.627 
.627 
.628 
.629 
.631 

•<3I 
.636 

.640 
.642 

.645 
.637 
.633 
.629 
.625 
.624 
.623 
624 
.625 
.627 
.628 
.638 
.634 
.637 

.644 

.637 
.632 
.628 
.623 
.621 
.620 
.620 
.621 
.622 
.624 
.626 
.6.9 
.631 

.643 
•  635 
.630  • 
.626 
.621 
.619 
.618 
.618    • 
.618 
.619 
.619 
.620 
.622 
•623 

804 


EXPERIMENTAL   ENGINEERING. 


XXVI. 

HORSE-POWER  LINE-SHAFTING  WILL  TRANSMIT  WITH  SAFETY 
BEARINGS,  8  TO  10  FT.  CENTRES. 


Diameter  of 
Shaft 

Horse-power 
in  one 

Diameter  of 
Shaft 

Horse-power 
in  one 

Diameter  of 
Shaft 

Horse-powei 
in  one 

in  Inches. 

Revolution. 

in  Inches. 

Revolution. 

in  Inches. 

Revolution. 

if 

.008 

2Tf 

.216 

5*1 

.728 

.0156 

.272 

617g- 

2.195 

*A 

.027 

•343 

°T!" 

2.744 

1  11 

.043 

.424 

7rV 

3.368 

1  16 

.064 

.512 

7rf 

4.096 

1 

.091 
.125 
.166 

$ 

.728 

1.  00 

1.328 

1 

9-iV 

4.912 

5.824 
6.848 

For  jack-shafts,  or  main  section  of  line-shafts,  allow  only  three-fourths  of 
the  horse-power  given  above,  and  also  provide  extra  bearings  wherever  heavy 
strains  occur,  as  in  main  belts  or  gears. 

XXVII. 

HORSE-POWER   BELTING  WILL  TRANSMIT  WITH   SAFETY. 


Width  of 

Horse-power  per  100  Feet. 
Velocity  of  Belt. 

Width  of 

Horse-power  per  100  Feet. 
Velocity  of  Belt. 

Belt 

Belt 

in  Inches. 

ir\  Inches. 

Single  Belt. 

Double  Belt. 

Single  Belt. 

Double  Belt. 

I 

.09 

.18 

12 

1.09 

2.l8 

2 

.18 

.36 

14 

1.27 

2-55 

3 

.27 

•55 

16 

1-45 

2.9I 

4 

.36 

-73 

18 

1.64 

3.27 

5 

•45 

.91 

20 

1.82 

3.64 

6 

•55 

.09 

22 

2.00 

4.00 

7 

.64 

.27 

24 

2.18 

4.36 

8 

•73 

.46 

28 

2-55 

5-09 

9 

.82 

.64 

32 

2.91 

5-82 

10 

.91 

.82 

36 

3-27 

6.55 

ii 

i  .00 

2.OO 

40 

3.64 

7.27 

In  the  calculations  for  horse-power  in  the  above  table,  the  belt  is  assumed 
to  run  about  horizontally;  the  semi-circumference  of  smaller  pulley  has  been 
considered  as  the  ordinary  arc-contact  of  belt.  Any  reduction  of  this  contact 
will  make  approximate  proportional  reduction  of  horse-power. 


EXPERIMENTAL  ENGINEFRINQ,  BIBUEV  COLLEGE,  CORNELL  UNIVERSITY, 


INDEX. 


PAGE 

Abrasion  Test !g5, 

"  Paving-brick jgo 

Absolute  Pressure ^36 

"       Zero 338 

Absorber  in  Refrigeration 747 

Absorption  Dynamometer 235 

"        Test  of  Bricks 179 

Accelerated  Cement  Test 190 

Accidental  Errors 18 

Accuracy  of  Numerical  Calculations 19 

Acidity  Tests  for  Oil 215 

Adiabatic  Compression,  Loss  of  Work  by 729 

' '        Curve  fer  Gases 712 

"  "for  Steam,  Formula  for 556 

' '        Curves  for  Ammonia 745 

' '        Definition 342 

' '        Expansion  of  Gases 711 

f<  "    .      "  Steam,  Formula 554 

Admiralty  Tests 172 

Admission -line  Diagrams.  . .  - 5^4 

Air,  Coefficients  of  Discharge 29& 

"     Formulae  for  Adiabatic  and  Isothemal  expansion 711 

"          "          "    Flow  of  in  Pipes 7ir 

c  c    Measurement  of  Velocity.. 3°^ 

"    Velocity  of  Flow 

"          "      of,  Measured  by  Heating 7^6 

"    Volume  Discharged *& 

11    Weight 


808  INDEX. 

PV  >  E 

Air-compressor,  Clearance  Space 723 

' '  .                   Data  and  Results,  Tests  of 730 

"                      Formulae  for  Compression 711 

' <                     Types  of 720 

Air-pyrometer 381 

Air  Refrigerating-machine 741 

Air-thermometer 371 

' '                      Construction 376 

' '                      Corrections 377 

' '                      Directions  for 378 

1 '                      Form  of 379 

« «                      Formula  for 374 

"                     Uses  of 377 

Alcohol  Thermometer 371 

Alden  Brake 241 

Allen's  Draft-gauge.  .. 351 

Ammonia  Absorption  System.  .  . ; 748 

"'       illustrated.. . .....' 750 

' '        Adiabatic  Curves  for. 745 

' '        Anhydrous  Properties  of. 740 

' '        Compression  Cylinder. 744 

'  *                               Relation  of  Pressure  and  Volume 711,  744 

"        Gauge.  ..... 358 

' '        Refrigerating-machine 742 

1 '        Refrigeration  Data  and  Result  Sheets 749 

Amsler's  Planimeter. " 30 

Analysis  of  Flue-gas.  . 474 

' '      Proximate,  Coal  and  Coke 470 

Analyzer  in  Refrigeration 747 

Anemometer  Calibration.  . 307 

1 '          Described. 306 

' '           for  Measuring  Air 725 

Angles,  Functions  of,  Table 771 

' '       Table  of  Natural  Functions 777 

Anhydrous  Ammonia,  Properties  of 738 

Approximate  Calculation,  Formulas 16 

Artificial  Building  Stone,  Test  of 178 

Ash  Analysis,  Table 787 

Ash,  Determination  of 470 

Ashcroft's  Oil-testing  Machine 227 

Asphalt,  Tests  of / . . , 180 

Aspirator  for  Flue-gas 478 


INDEX.  809 

PAGE 

Atmospheric  Line r,Q 

~  54o 

Pressure ,  336 

Atomic  Weight  Definition 

Autographic  Apparatus,  Olsen IXI 

1 '          Diagrams 2I 

Extensometer. x  „ 

Torsion  Machine . 


B 

Bachelder  Dynamometer 255 

' '        Indicator ^2^ 

Back -pressure  Line 549 

Barnett  Gas-engine yO2 

Barrel  Calorimeter 402 

"  "  Directions 405 

Barrus  Continuous  Calorimeter 4IO 

' '      Superheating  Calorimeter 398,  416 

Bauschinger's  Extensometer 125 

Beau  de  Rochas  Cycle 702 

Beaume's  Hydrometer  Scale,  Table  of 786 

Belt  Test,  Directions 266 

' '•      "     Forms 268 

"    Testing  Machine 264 

1 '    Dynamometer 263 

1 '    Friction 199 

' '    Testing  Methods 263 

Belting,  Table  of  H.P 304 

Bending  Moment 76 

Test : 166 

Bernoulli's  Formula 276 

Berthelot's  Fuel-calorimeter 457 

Berthier's  Fuel-calorimeter 45^ 

Blowers,  Types  of -723 

Boiler  Efficiency 493 

' '      Horse-power 494 

' '      Leakage  Locomotive  Test 648 

' '      Test,  Abbreviated  Directions 5Z4 

"         "  "  Form 5i3 

li     Analysis  of  Coal 5°4 

"         "     Analysis  of  Flue-gas 5°4 

"         "     Calculations  of  Efficiency 5°5 


8 10  INDEX. 


PAGE 

Boiler  Test,  Calibration  of  Apparatus 497 

"         * '     Correction  for  Leakage 498 

"         ' '     Definitions 493 

"         "     Duration 499 

' '         ' '     for  Locomotives 639 

"     Forms  for  Data  and  Results 507 

"     Fuel ." 496 

"       "    Value 472 

' '     Graphical  Log 495 

11     Heat  Balance 506 

' '         "     Measurements 496 

"        ' '     Object 492 

"         ' '     Pumping-engines 618- 

1 '     Quality  of  Steam 501 

' '     Records 501 

"         "     Sampling  of  Coal 502 

' '         "     Smoke  Observations 506 

"         "     Standard  Method 495 

'  *         ' '     Starting  and  Stopping 499 

' '         "     Uniformity  of  Operations 500 

Boiling-point,  Table 423 

"  Test  for 380 

Test  for  Cement 190 

Bomb  Fuel-calorimeter 457 

Boston  Extensometer 132 

Boult's  Oil-testing  Machine 227 

' '        Directions 230 

Bourdon  Gauge 357 

Boyer  Speed-recorder 650 

Brake,  Alden 241 

' '       Constants 244 

' '       Designing • 236 

1 '       Different  Forms 239 

' '       Directions  for  Use '. 243 

* '       Fan  Form 245 

' '       Horse-power 239 

' '       Hydraulic 242 


235 

Pump  Form 245 

Self-regulating 241 

Strap  Stresses 235 

Transfer  of  Heat ' 2 


INDEX.  8ll 

Breast  Water-wheels  .................................... 

Brick,  Abrasion  Test  .........................  iSo 

11      Testof  ..............................  '.''.''.''.'.'.''.'.'.'.'.'.'.'.''.'.  I78 

Bridge  Material,  Specifications  ..................  j6 

''''' 


" 


" 


i68 

Brine,  Specific  Heat  of y-2 

Briquettes,  Form  of 14! 

Brown  Speed-indicator (.-- 

Brumbo  Pulley '....  531 

Burning-point  Test  for  Oils 2I2 

Buzby  Extensometer I2y 

C 

Calibration  of  Anemometer 307 

' '  Apparatus  for  Engine  Test 578 

"  "  Differential  Dynamometer 256 

' '  "  Drum  Spring 542 

Forms  for  Gauges 368 

of  Gauges 363 

Gauges  with  Mercury  Column 366 

Indicator  Spring 535 

Morin  Dynamometer 249 

"  "  Planimeter 52 

"  "  Tachometer 291 

' '  Testing-machina 97 

' '  * '  Venturi  Tube .287 

"  Weir.  .: 285 

Caliper,  Micrometer 59 

' '       Sweet 60 

' '       Vernier 57 

Calorie 339 

Calorific  Power  of  Fuels 444 

Calorimeter,  Barrel.  . 4°2 

' '  Barrus  Continuous. 4JO 

"       Superheating -416 

Chemical 44Q 

"  Collecting-nipples -399 

' '  Comparative  Value • •  44i 

' '  Condensing 395 

"  Continuous-jet  Condensing 4°5 

' '  Diagram  for  Results  from  Temperatures 428 


812  INDEX. 

PAGE 

Calorimeter,  Diagram  for  Throttling • 425 

"  Effect  of  Errors 396 

' '  Forms 414 

* '  Fuel,  Bomb 457 

"  "     Heat  Equivalent 452 

"     Mahler's -. 461 

"  "    Thompson 455 

1 '  Hoadley 407 

' '  Injector 406 

' '  Limits  of  Throttling 427 

"  for  Locomotive  Tests 653 

Measure  of  Water  Equivalent 401 

Method  of  Sampling  Steam 399 

Principles  of  Fuel 451 

Separating >. 430 

"  "  Formula  for  Use 436 

Superheating 398 

Table  of  Errors 397 

"  Throttling 418 

Diagram  for  using 796 

11          Formula 398 

' '  " .  .      Table  for  using 795 

Use  of,  on  Pumping-engine 621 

Calorimetric  Method  of  Engine  Testing 590 

' '  Pyrometer 1 381 

Capacity  of  Pumps,  Definition.  . 329 

How  Computed 628 

Carbon,  Determination  of 470 

' '       Dioxide  Absorbents 475 

' '        Monoxide  Absorbents 476 

Carbonic  Acid  Absorbents 475 

Carburetter , 709 

Car-wheel  Tests 167 

Carnot  Cycle  for  Gas-engines 714 

Carpenter  Calorimeter  for  Steam 422 

Draft-gauge 351 

Fuel-calorimeter 463 

Separating-calorimeter 435 

Cast-iron  Tensile-test  Piece 139 

Cathetometer 62 

Cement,  Definitions .'.. 181 

"     '  Fineness  Test .    i84 


INDEX.  813 

PAGE 

Cement  Moulds I4I 

' '        Natural,  Definition ^ 

1 1        Normal  Consistency  Test jStj 

1 1        Portland,  Definition ^ 

"  •      Sieves 184 

11       Specific  Gravity  Test 183 

1 '        Specifications 190 

' '        Tensile  Strength  Required: 192 . 

11        Test,  Mixing 187 

•"          "     Piece 140 

* '        Tests,  Forms  for 194 

"        Testing 182 

"  "       Tensile 189 

"  "       Machine 119 

"  "  ' '        Fairbanks 120 

"  "  "        Olsen 121 

Riehle 122 

Centrifugal  Blower,  Data  and  Results 732 

"  "        Theory  of 729 

"         Fans,  Types  of 724 

11         Pumps,  Test  of 331 

Chain-test  Piece 139 

Chemical  Calorimeter 44o 

'  *         Equivalents,  Table 444 

Chill-point  Test  of  Oil i 214 

Chloride  of  Calcium,  Specific  Heat 752 

Chromous  Chloride 475 

Chronograph 573 

' '  Record 57^ 

Chronometer  for  Locomotive  Testing 650 

Cistern  Manometer 347 

Classification  of  Calorimeters : 39* 

Clay-ball  Pyrometer 

Clearance,  how  measured 5 

1 '          from  Indicator  Diagram 5 

"          in  Compressor,  Effect  of 72S 

Line 

Coal  and  Coke,  Proximate  Analysis 

"     Calorific  Tests 

"     Method  of  Determining  Moisture 

"     Sampling 

11    Test,  Form  of  Report  for  Locomotives 


8,4 


Coal  Test  on  Locomotives  ........ 

Coefficient  of  Discharge  .................. 

<«         "  Friction  ...................... 

Coffin  Planimeter.  .  .  .....................  ' 

Cold  Tests  for  Oil  ....................  ' 

Column  Testing,  Directions.  •.•'••••.  ......  '     ** 

Combined  Diagram,  Method  of  Drawing  .................... 

Inertia  and  Indicator  Diagrams..  . 
Combustible,  Definition  ................................ 

Combustion,  Definition  ............................. 

Heat  of,  Table  .............. 

Method  of  Determining  when  Perfect  .............. 

Products,  Object  of  Analysis  .... 

Temperature,  How  Determined  ........................   448 

Composition  of  Fuels,  Table  ..................................... 

Compound  Engine  Diagrams  ................................... 

«  '  '      Hirn's  Analysis  .................................   6°4 

Pumping-engine  Test  Examples  ..........................   63Z 

Compressible  Fluids,  Flow  of  ......................................   295 

Compression,  Effect  of  Clearance  ..................................   728 

Formula  ............................................     74 

of  Gases,  Formula  for  ................................   711 

Test,  Directions  .....................................   J54 

"  "     Pieces  ......................  ....................   J42 

"  "     Results  .............  '•  ..........................   i55 

Compressor,  Ammonia  ............................................   742 

"          for  Air,  Test  of  ........................................   73° 

Types  of  .............................................   720 

Computation  Machine  ............................................     64 

Condensation  in  Cylinder  .........................................   561 

Condenser  for  Steam,  Surface  ......................................   576 

Test  ................................................  ..   578 

Condensing  Calorimeters  ..........................................  395 

Consistency,  Normal,  Test  of  ......................................    185 

Constancy  of  Volume,  Definition  .........................  .  .........   189 

Test  ........................................   192 

Constant  Head  Viscosometer  .......................................   207 

Contraction,  Coefficient  for  ........................................   271 

Cornell  University  Experimental  Engine,  ............................  657 

Corradi  Roller  Planimeter  .........................................     45 

Counter  of  Speed  .................................................   572 

Crosby  Gauge-testing  Apparatus  ...................................  363 


INDEX.  815 

PAGB 

Crosby  Indicator _2I 

Cross-section  Paper 

Curtis  Steam-turbine 600 

Curve,  Adiabatic,  Formula  for  Steam ^-5 

' '      Isothermal,  Formula  for ^^~ 

' '      of  Expansion  Steam 5^5 

' '       ' '  Saturation,  Formula  for ^ 

Cycle,  Four-stroke ^O2 

' '      Two-stroke y02 

' '     of  Gas-engine ^3 

* '      "  Refrigerating  Machine 734 

Cylinder  Condensation ^ 

1 '  Loss  by  Diagram 563 

D 

Definitions,  Friction  Tests 196 

Steam-engine  Terms 569 

Deflectometer 135 

Degree  of  Superheat 390 

"      "         "         Formula  for 393 

DeLaval  Steam-turbine,  Description  of 687 

Density  of  Steam 342 

"      Test,  Oil 202 

Diagram,  Autographic 21 

' '         of  Experiments 20 

' '         from  Indicator,  Combined 567 

"            "    Indicators 563 

"         Inertia 664 

"         Locomotive  Tests .652 

"         Reduction  of 22 

11         Represents  Work. 21 

"         of  Shaft  Motion 567 

Strain 69,  144 

* '         for  Throttling-calorimeter 425 

"         Thurston's  Torsion  Machine 115 

Diameters  and  Squares,  Table  of 

Diaphragm,  Discharge  through 

Gauge 359 

' '  Loss  of  Head  through 

Diesel  Oil-engine 7 

Differential  Dynamometer 

«                   "            Calibration 256 


8l6  INDEX. 


Dilution  Coefficient  ...............................................  488 

Dimensions,  Experimental  Engine,  Institute  of  Technology  ............  605 

"  "  "        Sibley  College  ....................  657 

"          of  Pipe,  Table  of  .....................................   798 

Directions  for  Belt  Test  ...........................................   266 

11        Tension  Tests  ..........................................   145 

Discharge,  Coefficient  for  ..........................................   271 

Draft  Gauges.  .  .  .'  ................................................  351 

Draw-bar  Pull  of  Locomotives  .....................................  649 

Drop  Test,  Directions  ............................................   164 

'  '     Testing  Machine  ............................................   119 

Drum  Motion  of  Indicator  ........................................  540 

'  '     Spring  Calibration  .......................................  _____  542 

"         "      Testing  Device  ......................................  541 

Ductility  of  Specimens  ............................................   143 

DuLong's  Formula  ...............................................  445 

Durability  Test  Lubricants  ........................................   226 

Duty,  Definition  .................................................  328 

"     How  Computed  .............................  *.  ..............  628 

"     Test,  Pressure-gauge  ........................................  620 

"     Trial,  Pumping-engines  .....................................  618 

Dynamometer,  Absorption  .........................................   235 

Alden  .............................................   24I 

Belt  ................................................   263 

Classes  of  ..................................  ........   2$$ 

Differential  ................  .  ......  .................   255 

Emerson's  .........................................   259 

Horse-power  .......................................  ^ 

Lewis  .............................................   2t-2 

Locomotive  Tests  ..............................  651 

Pillow  Block  ............................  .  .....  .  .  .  .  .   252 

Records,  Locomotive  Tests  .............  640 

Steelyard  .................................  .'.'.'.'.'.'.'.'.'   250 

Traction  ...........................................   246 

Transmission  ...........................  247 

Van  Winkle  ............  6' 

Webber  .......................  ".".".'.'.*!.'.".".'.*".".'!.!;  255 


E 

Efficiency,  Boiler  .......... 


(( 


of  Ideal  Refrigerating  Machine '.['. 

Mechanical,  Definition.  . 

5°9 


INDEX.  817 

Efficiency  of  Perfect  Engine 

"  «  Plant 

run*-  •  •  • ; 570 

' '  Refrigerating  Machine M-^ 

Test  of  Pumps .........*.  330 

' '  ll     Steam-engines .  ego 

«  u 

Thermodynamic,  Definition tjyo 

Elastic  Curve x  CJQ 

Elasticity 68 

' '       Modulus 73 

' '       and  Rigidity  Modulus,  Relation  of 83 

Elbows,  Loss  of  Head 277 

Electric  Ignition 704 

' '      Pyrometer 385 

Elliott's  Flue-gas  Apparatus 479 

Elongation,  in  Test  Piece 68 

' '          Measure  of 134 

Emerson's  Power  Scale • 259 

Emery  Scale  Beam 106 

' '      Testing  Machine 94,  96 

* '      Vertical  Machine 102 

'  *      Weighing  System 106 

Empirical  Formula,  How  Deduced 10 

Engine  Fitting  for  Testing 582 

"       Hot-air 694 

"      Inertia  of  Parts 660 

' '       Locomotive  Test 652 

' '       Method  of  Measuring 583 

"       Methods  of  Testing 5«i 

"       Water  Pressure 3°9 

1 '      Test,  Calibration  of  Apparatus 578 

"          "     Directions 585 

1 '         "     Form  for  Results 584 

1 '         "     Indicator  Practice 584 

11         "     for  Leaks 

'«          "     Measurement  of  Speed 571 

11     Object 

1 '         "     Quality  of  Steam 5Sl 

tt         «c     Weighing  Steam 5Sl 

Entropy,  Definition 343 

Table  of 

Ericsson  Hot-air  Engine °94 


8l8  INDEX. 

PAGE 

Ericsson  Hot-air  Engine,  Method  of  Operating 700 

Errors,  Classification  of 5 

1  *      Combination  of 9 

"      Probability  of 6 

"      When  to  Neglect 18 

Euler's  Formula 75 

Evaporation,  Table  of  Factors 797 

Expansion  Curve,  Method  of  Drawing 554 

1 '         Fuel  Calorimeter 463 

' '         of  Gases,  Formula  for 7n 

' '         Ratio  of 550 

Experiment  vs.  Theory. 2 

Experimental  Engine  Dimensions,  Institute  of  Technology 605 

' *      Sibley  College,  Dimensions  of 657 

"  "      Use  of 656 

Experiments,  Classification ^ 

Objects  of ! 

Extensometer,  Autographic ™ 

Bauschinger's z  2^ 

Boston j  «2 

Buzby ...;,;   I27 

Henning I29 

How  to  Apply I4g 

Johnson's I2g 

Marshall 

"  Paine. . 


Roller  and  Mirror I2- 

Strohmeyer's I26 

Thurston... ' 

"           Unwin's '   HI 

"  Wedge 

Eye-bars,  Specifications  of * 

F 

Factor  of  Safety 

"      "  Evaporation,  Definition. . 

Factors  of        "  Table. 

Fairbanks  Cement  Machine 

Testing  Machine. . 

Fan  Brake [['  92 

Fan,  Data  and  Results  245 


INDEX.  819 


PAGE 


Fan,  Theory  of 

Fans,  Types  of 724 

Fatigue  of  Metals X55 

Favre  &  Silbermann  Fuel  Calorimeter 453 

Feed-water  Measurement 616 

Temperature,  Determinations  of 615 

Fineness  of  Cement 102 

"       Test 184 

Flash  Test  of  Oils 210 

Floats 282 

"      Use  of 289 

Flow  of  Air 296 

"     "     "  in  Pipes 299 

* '     ' '  Compressible  Fluids 295 

"     "  Gas 302 

' c     "  Steam  through  Orifice 300 

"'     "  Water  in  Pipes 288 

1 '     "        ' '     Measurement  of 281 

Flue-gas  Analysis,  Computations  from 486 

' '              * '         Forms  and  Computations 490 

"              "        Methods 474 

"             "        Object  of 473 

"             ' '        Process  of 476 

Reagents 475 

*  *       Aspirator 478 

'  *        Sampling  of 477 

Flue-gases,  Analysis  of 5°4 

Flue  Losses  from  Flue-gas  Analysis •  4^8 

Fluid  Friction 

Porging  Test 

Form  for  Data  and  Results  Steam  Injector. 

*  *  Record,  Locomotive  Tests 64^ 

y      "  Report  of  Test,  Steam-turbine 

M      "   Report,  Pumping  Test 

M   Results  of  Engine  Test 

"      "   Tension  Test.   

"  Test  of  Pulsometer 

Forms  for  Air  Thermometer 

><       'l   Beit  Test 

ri   Calibration  of  Gauges 

' '       •  •  Calorimeter 

"   Cement  Test I94 


820 


INDEX. 


Forms  for  Hirn's  Analysis 598 

««       "Oil  Test 233 

"      "  Pump  Tests 332 

"       "  Separating  Calorimeters 439 

"       "  Test,  Hot-air  Engine • 698 

«       "  Testing  Hydraulic  Motors 326 

1  •       "  Throttling-calorimeter 43° 

Formula,  Air  Thermometer 374 

Bernouilii 1 276 

11        for  Approximate  Calculation 15 

"         "  Compression 74 

"        Empirical,  Deduction  of IO 

"         "  Friction T98 

"         "  Pressure,  Volume  and  Temperature,  Relations  of  Gases.  . .   711 

Formulae  for  Hirn's  Analysis 591 

Freezing  Machine,  Cycle 734 

"        Point  of  oil,  Test  for 38° 

Friction,  Classification 19? 

* '       Coefficient  of J96 

"       Formula *97 

' '       Lubricated  Surfaces 201 

"       of  Belts 199 

"  Fluids 200 

"       "Gears 199 

"       "  Journals 198 

"       "  Pivots 198 

"       Table  of  Coefficients 784 

' '       Test  of  Engine 589 

"       Tests,  Definitions 196 

Frost  Test  for  Stones 176 

Fuel  Calorimeter,  Bomb 457 

1 '    Calorimeters,  Principle  of 451 

1 '    Consumption,  Definition 569 

"    Measurements,  Locomotive  Testing. 641 

1 '    Method  of  Sampling 452 

"    Test,  Locomotive 635 

' '    Value  by  Boiler  Trial 472 

' '    Weight  of,  Engine-testing 582 

Fuels,  Composition  of 451 

Table  of  Composition 787 

Fulcrums  for  Emery  Machine 95 

Fuller's  Slide  Rule 28 


INDEX.  821 


PAGE 


Furnace  Efficiency  from  Flue-gas  Analysis  ...........................  4go 

Maximum  Temperature  from  Flue-gas  Analysis  ..............  488 

G 

Gas  Analysis  Apparatus  ..........................................  47Q 

'  '    Composition  of,  Table  .  ......................................  -o^ 

*  '  Measurement  of  Flow  ........................................  ~02 

Gas-engine,  Classification  ..........................................  OQ 


Compression  Type 


Cycles  ...........................................  ....  ?I3 

Diagram  .............................................  7I6 

Four-cycle  ............................................  706 

Ignition  .......................  „.  ......................  703 

Indicator  .............................................  524 

Optical  Indicator  ......................................  525 

Report  of  Test  ........................................  716 

Theory  ...............................................  711 

Two-cycle  .................  ...........................  707 

Gas  Measurement,  Dry  Meter  .....................................  305 

"             '  '              Wet  Meter  .....................................  303 

'  '    Meter,  Testing  Device  ........................................  303 

Gasoline  Engines  .................................................  708 

Gas-  or  Oil-engine  Testing  ........................................  714 

Gauge,  Apparatus  for  Testing  .....................................  363 

'  '       Calibration  by  Mercury  Column  .......  .  ......................  366 

*  '       Correction  of  .............................................  367 

11       Makers,  list  of  ............................................  361 

'  '      Marking  Device  ...........................................  113 

"       Tension  Test  .............................................  147 

Gauges,  Recording  ...............................................  613 

'  '       for  Steam-pressures  .......................................  357 

Gear-teeth  Friction  ...............................................  199 

Gibbs's  Viscosometer.  .  ...........................................  205 

Giffard  Injector  ....................  ................                          •  670 

Graphical  Log  of  Boiler  Test  .....................................  495 

Multiplication  .......................................  64 

'  '        Representation  of  Data  ................  ........... 

Gumming  or  Drying  Test  .........................................  2I° 

H 

Hammer  Test  ................................................  l66 

Hancock  Inspirator  ...............................................  "72 


822 


INDEX. 


PAGE 

Hardening  Test  ..................................................   \ 

Head,  Lost  by  Contraction  .......................... 

«       «'     at  Elbows  ............................................  279 

«       «      «  Entrance  of  Pipe  ....................................   278 

«       "      in  Perforated  Diaphragm  ...............................   279 

"       "      "  Pipes,  Measurement  of  ...............................   289 

"       "    by  Valves  .............................................   279 

"     Producing  Velocity  .........................................  27J 

"     Relation  to  Pressure  ........................................  324 

"     of  Water,  Measurement  of  ...................................  2Sl 

Heat  Application  to  Isothermal  Expansion  ..........................   7*3 

"     Balance  ...................................................  494 

"          "       in  Boiler-testing  ..........................  •  ..........  5°6 

"     of  Combustion  ..............................................  444 

"     Consumption,  Ideal  Engine  ..................................  569 

"     Equivalent  of  Fuel  Calorimeter  ...............................  452 

"     Interchanges  from  Saturation  Curve  ...........................  612 

"     Losses  in  Refrigerating  Machine  ..............................   738 

"     Mechanical  Equivalent  of  ...........  .........................  339 

"     Specific,  definition  .....................  .....................  338 

"         "      of  Brine  ..............  ..............................   752 

"     and  Temperature  .......................  ,  ...................  337 

"     Transfers  of  Refrigerating  Machine  ...........................   735 

"     Units,  definition  ............................................  339 

'  '        '  '     per  Horse-power  .......................................  569 

Heating  Value  Measured  by  Oxygen  ................................  446 

Heisler  Calorimeter  ...............  ...........  .....................  421 

Hempel's  Flue-gas  Apparatus  ......................................  483 

"       Fuel  Calorimeter.  ,  ......................................  456 

Henning  Extensometer  ............................................   129 

Hennings's  Mirror  Extensometer  ...................................   130 

Higgins's  Draft-gauge  .............................................  3$$ 

Hirn's  Analysis  ..................................................  590 

1  '       for  Compound  Engine.  ..............................   603 

4  '       Directions  for  ..............................  ........  ^gtj 

"         "        Forms  for  .........................................  59g 

Institute  of  Technology  Engine  .......................  605 

for  Non  -condensing  Engine  ..........................  603 

by  Saturation  Curve  ................................  611 

for  Triple-expansion  Engine  ..........................  604 

Hoadley  Air-thermometer  ...................  ^72 

"       Calorimeter  ..............................  ...".'.'."!!.'.'!;.'."!  407 


" 
" 


INDEX.  823 


PAGE 


Hoadley's  Calorimetric  Pyrometer 

Draft  Gauge 35 - 

Hook  Gauge 2g2 

Hornsby-Akroyd  Oil-engine ^  z 

Horse-power,  Boiler 494 

Brake 239 


Formula  for 


Si? 

Method  of  Computing 552 

"  per  Pound  M.E.P.,  Table 800 

Hot-air  Engines 694 

' '       Engine  Forms 698 

"       Theory 697 

Hot  Test  for  Cement 192 

' '    Tube  Ignition 704 

Humidity  of  the  Air,  Table 785 

Hydraulic  Engines 309 

' '         Machinery,  Classification 308 

* '         Motor,  Forms  for  Testing 326 

' '         Power  System,  Parts  of 309 

"         Ram 321 

"  "     Directions  for  Testing 325 

* '         Testing  Machine 92 

Hydraulics,  Flow  of  Water 270 

Hydrometric  Pendulum 295 

Hyperbola,  Method  of  Drawing 554 

Hyperbolic  Logarithms,  Table  of 784 

I 

Ice-making  Plant,  Illustrated • 746 

Ignition,  Methods  of,  in  Gas-engines 7°3 

Impact  Test,  Directions 

' '       Testing  Machine 

Impulse  Steam-turbine,  Description  of 

11        Water-wheel 

Indicated  and  Dynamometric  Power 

"         Horse-power 

1 1  «  Method  of  Computing 

Indicator,  Applied  to  Locomotive. . . 

"       Attachment  to  Cylinder 

Attachments,  Engine -testing 

Care  of 545 


824 


INDEX. 


Indicator  Cock  ..................................................  543 

Cord  ......................................  '  ...........  529 

«  *  *  '    Attachment  of  .....................................  532 

I  «  "    Tension  on  ........................................  541 

"        Diagram  ...............................................  5l6 

«  «  "        Clearance,  How  to  Find  .........................  56r 

«  ««        Combined  .....................................   567 

«  "        Definitions  .....................................  547 

"  "        General  Discussion  .............................   562 

«  "        Form  for  Ideal  Case  ............................   553 

"  "        Hot-air  Engine  .................................  699 

"  «  '        with  Loop  .....................................   552 

«  <  "        Weight  of  Steam  from  ...........................   557 

"        Diagrams,  Measurements  of  ..............................   551 

Method  of  Taking  .............................   544 

'  '        Dimensions,  Table  of  ....................................   528 

I  '         Drum  Motion  ..........................................   54° 

II  Early  Forms  ...........................................   5J7 

External  Spring  .........................................   523 

4  '         for  Gas-engines  .........................................   524 

1  '         Gas-engine,  Use  of  ......................................   7*5 

'  '         Gear  for  Locomotives  ...................................   638 

"         for  Inertia  .......................................  ......   66  1 

Optical  ................................................   525 

"         Paper  Drum  ...........................................   529 

"        Parts  ..................................................   526 

'  '        Pencil  Mechanism  ......................................   526 

"  "    Movement  Test  ...................................   539 

Practice,  Engine  Test  ....................................   584 

Reducing  Motions  ......................................  529 

Spring  ................................................   527 

'  *      Calibration  ................    .................  535,    579 

Standardization  .........................................   534 

of  Steam-engine,  Use  of  .........................  .  ........  515 

Tests  of  Locomotive,  Form  for  ....................  .  ........  653 

Inertia  Diagram  .................................................  664 

'  '      Indicator  ......................  .........................   661 

"      and  Indicator  Diagram  Combined  ............................   668 

'  '      Moment,  Experiment  for  ...................................     go 

II  Moments,  Table  ...........................................     7g 

'  '      of  Parts  of  Steam-engine  ...............  .............  660 

Injector,  Directions  for  Testing  ....................................  679 


INDEX. 


825 


Injector,  General  Directions  for  Use 


Limits  of  .................................... 

Mechanical  Theory  .......................................  6' 

Thermodynamical  Theory  .................................  672 

Institute  of  Technology  Engine  Dimensions  ..........................  605 

Intercooler  ..............  ....................................          ^2I 

Investigation,  Method  of  ..................................  2 

Involution  by  Diagram  ..................................  20 

Isothermal,  Definition  ...........................................   -42 

Expansion  of  Gases  ....................................  7II 

J 
Johnson's  Extensometer  ...........  .  ...............................   I2p 

Jolly  Air-thermometer  .............................................   ?*? 

Journal  Friction  ..................................................   Zgg 

Jump-spark  Ignition  ..............................................  705 

K 

Kellogg  Testing  Machine  ..........................................  03 

Kent  Calorimeter  ...............................................  .  409 

Kent's  Draft  Gauge  ..............................................  355 

Knife-edge  of  Testing  Machine  ....................................  95 

L 

Latent  Heat  of  Steam  .............................................  341 

"    Table  of  .............................................  788 

Lazy  Tongs  .....................................................  532 

Leakage  of  Boilers,  Locomotive  Tests  ...............................  648 

"        Test  of  Pumps  ...........................................  622 

Leaks,  Test  for,  in  Engine  .........................................  582 

Least  Squares  ...............  .....................  ...............      5 

Le  Chatelier  Specific  Gravity  Apparatus  .............................  183 

Lenoir  Gas-engine  ................................................   701 

Lewis  Dynamometer  ..............................................  252 

Lime,  definition  of  ...............................................  181 

Limits  of  Throttling-calorimeter  ....................................  429 

Linde  Ice-machine  Test  ..........................................   748 

Lloyd's  Tests  for  Steel  ............................................  173 

Load  Variation  Diagram  ..........................................  564 

Locomotive  Boiler  Test  .........................................  639 

"          Coal  Tests  ...........................................  642 


826  INDEX. 

PAGE 

Locomotive  Test,  Object ^34 

"     Standard  Method °34 

«  <  <     Water  Measurement 645 

' '          Tests,  Form  for ^53 

«  "      General  Results 654 

«  "      Speed  Recorder 650 

11     Staff  for 652 

Logarithm  Table,  Use  of 64 

Logarithms,  Common  Table  of 769 

Hyperbolic,  "      " 7»4 

Logarithmic  Paper 23 

Lubricants,  Durability  Test 226 

Lubricant  Testing 201 

Lubricated  Surfaces,  Friction  of 201 


M 

McNaught's  Steam-engine  Indicator 517 

Machinery,  Hydraulic,  Classification 308 

Machines  for  Computation 64 

Mack  Non-lifting  Injector 670 

Mahler's  Fuel  Calorimeter 461 

Maillard  Testing  Machine 94 

Manographie 525 

Manometer 345 

* '  Cistern  Form 347 

U-shaped 345 

Marshall  Extensometer 131 

Materials,  Strength  of,  Table 781 

Material  Tests 67 

Mean  Effective  Pressure 550 

M.E.P.,  Table  for  Equivalent  H.P 800 

Mean  Error 7 

'  *     Ordinate,  Length  of 22 

Measurement  of  Feed-water 616 

Mechanical  Efficiency 569 

"        How  Computed. 628 

Equivalent  of  Heat 339 

Mercurial  Thermometer 369 

Weight  Thermometer 370 

Mercury  Column,  Calibration  of  Gauges 366 

"^ 351 


Use  of. 


INDEX.  827 

Mercury  Columns 

"      Table  of  Depression 350 

Metal,  Strength  of,  at  Different  Temperatures 782 

Metals,  Table  of  Specific  Gravity 782 

"       Table  of  Specific  Heat 783 

Metallic  Pyrometer ^81 

Meter,  Gas ^03 

"      Prover 3o4 

Meters  for  Water 283 

Method  of  Taking  Indicator  Diagrams 544 

Metric  Measures,  Table  of 754 

Micrometer 5o 

"           Caliper 59 

Mirror  Extensometer I25 

Mistakes,  Rejection  of 71 

Modulus  of  Elasticity 73 

"      "Rigidity 83 

Moisture  Absorbed  by  Air,  Table 785 

Moment  of  Flexure 76 

Moments,  External,  Table 79 

1 1      of  Inertia 80 

"      "       "     Table 78 

Morin  Dynamometer 247 

' c                             Calibration 249 

Morse  Thermal  Heat  Gauge 386 

Mortar 182 

Moscrop  Speed-recorder 577 

Moulds  for  Cement 141 

Multiplying  Draft  Gauges 355 

N 

Naperian  Logarithms,  Table  of 7^4 

Napier's  Formula,  Table  of  Discharge  of  Steam 795 

Necking  of  Test  Specimen M3 

Needle,  Vicat 186 

Noel's  Optical  Pyrometer -3s6 

Normal  Consistency  Test 185 

Nozzle  Calibration 

' '       Discharge,  DeLaval  Turbine 

Nozzles,  Discharge  Through .' 

Numerical  Calculations,  Accuracy  of -. 

"        Constants,  Table  of • 756 


828  INDEX. 


Oil  Adulteration 202 

"   Density 202 

"   Engines 7°9 

"   Test  for  Acids - < 2I5 

"      ' '      ' '  Burning-point 2I2 

"      "     "   Durability 226 

"      "     "  Evaporation 212 

"      "     Flash 210 

"      "     Forms 233 

"      "     for  Freezing 213 

"       "      "Gumming 210 

11      "    with  Limited  Feed 231 

"      "     of  Viscosity 204 

1 '    Testing 201 

Machine,  Ashcroft's 227 

"        Boult's 227 

'  *        Directions 222 

R.R 218 

"        Richie's 224 

' '         Theory 220 

'  *        Thurston's •  •   217 

Machines 215 

Oleography 214 

Olsen  Autographic  Apparatus in 

' '     Cement  Machine 121 

"      Testing  Machine 92,110 

"     Torsion  Machine i88a 

Optical  Indicator 525 

' '       Pyrometers 386 

Ordinate,  Mean 22 

Orsat's  Flue-gas  Apparatus 482 

Otto  Cycle ; 702 

Otto  &  Langen  Gas-engine 701 

Overshot  Water-wheels 311 

Oxygen  Absorbents 475 

Method  of  Measuring  Heating  Value 446 


INDEX.  829 


PAGE 

Paine  Extensometer I2- 

Pantograph _     t--x . 

Paper  Drum  for  Indicators 529 

' '      Logarithmic 2, 

Parsons'  Steam-turbine 68^ 

Paving  Materials,  Test  of ^g 

Peabody  Calorimeter ; . . . .  4IQ 

Peclet's  Draft-gauge 353 

Pelton  Motor,  Test  of 324 

* '      Water-wheel 315 

Pencil  Mechanism  of  Indicator 526 

' '      Movement  on  Indicator,  Test  of 539 

Pendulum  Reducing  Motion 530 

' '  Viscosometer 209 

Pennsylvania  R.R.  Viscosometer 204 

Perfect  Engine  Efficiency 570 

Perkins  Viscosometer 205 

Phcenix  Testing-machine 93 

Phosphorus * 475 

' '        Determination  of '. 470 

Pillow-block  Dynamometer .  252 

Pipe-fitting  Calorimeter  for  Steam .422 

Pipes,  Flow  Through .277 

Pipe,  Table  of  Standard  Dimensions 79& 

Piston  Air-compressor 72° 

' '      Displacement,  how  measured 583 

Pitot  Tube -292 

"      for  High  Pressures 294 

"        "     Use  of,  for  Measuring  Air .726 

Pivot  Friction •   ^ 

Planimeter  Adjustment 

"          Calibration .' 52,  780 

' '          Directions 51 

11          Errors 

"          Measurement  of  Diagrams •  55* 

Roller 

' '          Suspended 

Plant  Efficiency 

Platinum  Ball  Pyrometer 

Polar  Planimeter 

"  ' '          Theory 


830  INDEX. 

PAGE 

Portland  Cement,  Definition 191 

"             ' '        Specifications 192 

Testing 182 

Potassium  Pyrogallate , 475 

Power-pumps,  Tests  of 331 

' '      Systems  Testing  Machines 89 

Pressure  of  Atmosphere 336 

1 '        by  Gauge 336 

1 '        Measured  by  Manometer 347 

Units,  Table  of 336 

"        and  Volume,  Formulae  for  Compression  of  Gas 711 

Relations  of,  in  Refrigeration 744 

Preston  Air-thermometer 372 

Priestman  Oil-engine 710 

Probable  Error 7 

Probability  of  Errors 6 

Products  of  Combustion,  Object  of  Analysis 473 

Prony  Brake 235 

"      Designing 236 

' '      Directions 244 

"           "      for  Engine -testing 582 

"      Brakes,  Various  Forms 239 

Properties  of  Steam 340 

Pulsometer,  Description  of 683 

'  *            Form  for  Tests 684 

1 '            Theory  of : 684 

Pump  Brake 245 

"     Test,  Computation  and  Results 628 

' '      Forms  for 332- 

' '      Form  of  Report 624 

Pumps,  Centrifugal,  Test  of 331 

' '       Classification  of 327 

' '       Duty  and  Capacity  of 328 

"       Efficiency  Test 33o 

' l       Measurement  of  Work 329 

' '       Rotary 328 

* '       Slip  of 330 

Pumping-engine,  Leakage  Test 622 

Observations 620 

Pumping-engines,  Duty  Trial 618 

Punching  Test !66 

Puzzuolana ./. . 


Pyrometer  Calibration 

'  '         for  Locomotive  -testing 
Pyrometers 

Comparison  of 


INDEX.  831 


Q 

Quality  of  Steam,  Definition  ..............................  .  ........  ,90 

11       "     "       Duty  Test  .....................................  '*  62I 

"       "     "        Formula  for  .....................................  393 

"       "     "        Methods  of  Determining  ..........................  394 

"       "     '  '       from  Saturation  Curve  ............................  610 

R 

Ram,  Hydraulic  ..................................................  321 

Rankine's  Formula  ...............................................     74 

'  '          Oil-testing  Machine  .....................................  215 

Reaction  Steam-turbine  ...........................................  689 

<  '          Turbine  ................................................  316 

'  '          Water-wheel  ............................................  319 

Recording  Gauges  .....  ...........................................  361 

Records  of  Boiler-test  ....................  ........................  501 

Rectangular  Weir  ................................................  272 

Reducing  Motion  for  Indicators  ....................................  529 

"  *  '       "  Locomotives  ..................................  637 

"      Test  of  ..................  •  579 

11        Wheels  .................................................  532 

"        Wheel  for  Indicator  .................................  524 

Re  -evaporation  ..................................................  S^1 

Refrigerating  Machine  of  Air  ......................................   74i 

"  '  *       Ammonia  ...................................  74* 

««  "       Defined  ............................  •  734 

"  «  '       Efficiency  ...................................   736 

««  "       Heat  Exchanges  ..................  -735 

"  "       Ideal  Efficiency  .....  •   735 

«  "       Negative  Heat  Losses  ......................   738 

«  "       Test  .....  '.  .................................   748 

«  '  Plant,  Illustrated  .....................................   74^ 

Refrigeration,  Absorption  System  ................................ 

"  Data  and  Result  Sheets  ........................ 

Regenerator  Hot-air  Engine  .................................. 

Relation  of  Pressure  and  Temperature  of  Gases  ......................  7" 


832  INDEX. 

PAGE 

Report,  Form  of 3 

of  Test,  Steam-turbine , 693 

Residual 7 

Resilience , 68 

"        Torsional 83 

Revolution-counter 572 

Richards's  Indicator 518 

Rider  Hot-air  Engine 695 

"     Method  of  Operating 700 

Riehle  Cement  Machine 122 

' '      Extensometer 128 

.    ' '      Hydraulic  Machine 107 

1 '      Oil-testing  Machine 224 

'  *      Power  Machine 108 

1 1      Testing  Machine 91 

"      Torsion  Machine 118 

Rigidity 68 

"      Modulus  of  Wire 83 

Roller  Planimeter 45 

Rope  Test-piece 140 

Rotary  Pumps 328 

Rubber,  Effects  of  Strain 86 

S 

Sample  of  Steam  for  Calorimeter 399 

Sampling  of  Flue-gas 477 

"  Fuel 452 

Sand,  Standard 187 

Saturation  Curve,  Formula  for 555 

' '              "      Heat  Analysis  from 609 

"              "      Heat  Interchanges  from 6n 

Screws,  Micrometer ^o 

Seaman's  Pyrometer 385 

Sellers's  Injector 671 

Separating  Calorimeter • • 430 

: 439 

Formula 436 

Table  of  Accuracy 431 

Various  forms 432 

Setting  of  Cement IO2 

"      "  Valves  of  Steam  Engine.  y 586 


Forms. 


1C 


INDEX.  833 

01         ft.    T^'  PAGB 

Shaft  Diagram ^ 

Shafting,  Table  of  H.P ..........  "..  SOA 

Shear,  Parallel 

Shearing  Strain,  Theory.  . gx 

' '        and  Normal  Stress g4 

Sibley  College  Experimental  Engine,  Dimensions 657 

Sieves  for  Cement jg4 

Signs  and  Tangents,  Table  of 777 

Simple-lever  Machines oo 

Slide-rule,  description 24 

' '        Directions 25 

"        Fuller's 28 

' '        Thatcher's 27 

Slip  of  Pumps 330 

Smoke  Observations  in  Boiler-testing 505 

Specifications  Bridge  Material 169 

' '            for  Cement 190 

* '            of  Eye-bars 171 

' '            Iron  Plate 172 

"            for  Steel,  Lloyd's 173 

"            Steel  Plate 172 

' '            Water-pipe 174 

Specific  Gravity  of  Cement  required 191 

"  Metals,  Table  of •  v  783 

11            "       Table  corresponding  to  Beaume's  Scale 786 

"  "       Test  of  Cement -183 

Specific  Heat,  definition 338 

"      of  Brine 752 

"      Chloride  of  Calcium 752 

"          ' '      Determination 3^2 

"      of  xAiel-gases,  Table 45° 

11         "      of  Metals,  Table  of 

"          "      and  Melting-point,  Tables  of •  383 

Speed-counter 

Speed-indicator 

"  Calibration 

Speed  Measurement  with  Chronograph 

«  <  <  ' '    Tachometer 

Speed-recorder,  Locomotive  Tests 

Square-inch  Gauge-testing  Apparatus 

Squares  and  Diameter,  Table  of 

Standard  Form  Test-pieces J36 


834  INDEX. 

PAGE 

Standard  Method  of  Testing  Boilers 495 

"      Cement 182 

"  "       "  Locomotive  Testing 634 

' '        Test  of  Pum ping-engines '. . . .  614 

Steam-boiler  Test  Definitions 493 

Steam-boilers,  Object  of  Test 492 

Steam  Calorimeter  for  Locomotive  Tests 655 

Steam  Calorimeters,  Classification 391 

Steam-chest  Diagram 567 

Steam  Accounted  for  by  Indicator,  References  to  Tables 560 

"      Density  and  Specific  Volume  Formula 342 

' '      Dfy  and  Saturated 340 

"      Flow  of,  Through  Orifice 300 

"      Formula  for  Heat,  Contents 393 

M        "  Quality...  ., = 393 

"      Fuel-  and  Heat- consumption,  of  Engine  Definitions 569 

"      per  I.H.P.  from  Indicator-diagram 558 

' '      Measurement  of  Heat,  Contents 394 

' '      Methods  of  Determining  Quality 394 

* '      Properties  of 340 

' '      Quality  of,  Definition 390 

"       Relations  of  Pressure  and  Temperature " 339 

' '       Sample  for  Calorimeter 391 

' '       Superheated  Properties 340 

'  *       Table  of  Entropy 301,  794 

"       Table  of  Properties 788 

' '       Weight  Discharged  Through  Orifice 302 

Steam-engine  Clearance,  how  measured 583 

"  Compound,  Test  of 631 

"  Efficiency  Test 589 

Indicator 515 

"         Careof 545 

Early  Forms 517 

for  Locomotives 638 

Parts 526 

"  Inertia  of  Parts 660 

Methods  of  Testing 581 

Optical  Indicator 525 

References 325 

"  Terms  Defined 569 

"  Test  for  Friction 589 

"  Test,  Hirn's  Analysis 590 


INDEX.  835 


PAGE 


Steam-engine  Valve-setting g^ 

Steam-engines,  Water-consumption  Tables 

Steam  Gauges ^ 

Steam-gauge  Calibration _ 

Steam-injector,  Description 67O 

Directions  for  Handling  and  Applying 670 

"  Testing , ;;;;;  679 

' c  Form  for  Data  and  Results 681 

Limit  of  Suction-head 678 

Limits  of  Capacity 676 

"  "of  Temperature 677 

"  Mechanical  Theory 674 

"  Theory  of 672 

Steam  Pumping-engines,  Standard  Test  of 614 

Steam-separator,  Use  of 615 

Steam  Tables 340 

"          "       Compared 344 

"       Use  of 392 

Steam-turbine,  Description  of 686 

' '  Testing 691 

Steelyard  Dynamometer 250 

Stillman's  Viscosometer 206 

Stones,  Frost  Test 176 

11       Testsof .175 

Straight  Line  Indicator 525 

"        Lyne       "        525 

Strain,  Definition  of 68 

' '     Diagram  Torsion  Machine .116 

' '      Diagrams 69,  144 

"  "          Autographic -145 

( (     Relation  to  Temperature 86 

Strap-brakes •   24° 

Strength  at  High  Temperature -167 

' '        of  Materials,  Notation 

«        <  <         "          Table  of  Coefficients •   78i 

Strengths  after  Repeated  Applications  of  Load •   167 

Stress,  Definition 

' '    Twisting  with  Bending 

"  "         lt    Longitudinal ^4 

Stresses,  Brake-strap 

11        Combination  of 

Strohmyer's  Extensometer 


" 


836  INDEX. 

PAGE 

Sulphur,  Determination  of,  in  Coal 470 

Superheating  Calorimeters 398 

Surface  Condenser 576 

Suspended  Planimeter 41 

Sweet  Measuring -machine 60 

Swelling  Test  of  Cement 192 

T 

Table,  Air,  Moisture  Absorbed  by 785 

"      Angles,  Natural  Functions  of 777 

c  *      Analysis  of  Ash 787 

1 '      Anhydrous  Ammonia,  Properties  of 740 

' '      Beaume  Hydrometer  Scale 786 

'  *      of  Boiling-points 423 

"      "  Chemical  Equivalents 444 

"      "  Coefficients  of  Friction 784 

«      "         "  "  Strength 781 

"      "  Composition  of  Fuels 451 

"      "  "  Fuels  of  U.  S 787 

"      "  "  Gases 703 

"      "  Depression,  Mercury  Column 350 

Dimensions  of  Wrought-iron  Pipe 798 

Discharge  of  Steam  by  Napier's  Formula 795 

'  *      Entropy  of  Steam 301 

' '      Errors  in  Calorimeters. 397 

' '       External  Moments 79 

' '       Factors  of  Evaporation 797 

1 '       Heat  of  Combustion 446 

* '       Horse-power  of  Belting 804 

"per  Pound  M.E.P 800 

of  Shafting 804 

' '       Humidity  of  the  Air 785 

'  *       Hyperbolic  Logarithms 784 

Indicator  Dimensions 528 

Logarithmic  Functions  of  Angles 771 


" 
" 
'  '  Logarithms 

*  ' 


Materials,  Important  Properties  of  ...........................  783 

Maximum  Temperature  of  Combustion  .......................  450 

of  Feed-water  for  Injector  .............  678 

"       Moisture  Absorbed  by  Air  ..................................  785 

"       Moments  of  Inertia  .......  /.  ................................ 


INDEX.  837 

PAGE 

Table  of  Numerical  Constants ^g 

'  *      Pressure,  Units  of -,36 

' '      Specific  Heat  of  Gases 4^0 

' '      Specific  Heat  and  Melting-points 383 

"     Specific  Heat  of  Water 338 

' '     Steam-injector,  Limits  of 677 

* '     Steam,  Properties  of 788 

' '     Strength  of  Metal  at  Different  Temperatures 782 

* '     Suction-head,  Limit  of,  in  Injector 678 

' '     Thermometric  Scales 337 

* '     Throttling-calorimeter,  Limits  of 429 

' '     Throttling-calorimeter,  Application 795 

' '     Transverse  Loads 78 

"     U.  S.  Standard  and  Metric  Weights 754 

* '     Water,  Density  and  Weight  of 799 

' '     Water  Consumption  for  Steam-engines 802 

11     Weir  Discharge 803 

Tabor  Indicator 520 

11  "        External  Spring .524 

Tachometer  for  Measuring  Speed 572 

"  "  Water  Measurements 290 

Tagliabue  Viscosometer 205 

Temperature 342 

'  *  Produced  by  Combustion ...  448 

"  Effect  on  Strength -167 

' '  Maximum,  Table  of 45° 

"  Measured  by  Hot  Body •  3Sl 

' '  Measurement  of  Steam -400 

11  Relation  to  Heat ••••337 

"  "         "  Strain 86 

' '  Rise  in  Adiabatic  Compression •   729 

Temperatures  of  Feed-water,  How  found -615 

Tension,  Specimen  Gauge 

Tensile  Strength,  Cement 

11  "        Formula 

Tension  Test,  Blank 

"          "      Directions I45>  * 

11     Forms 

'<         "     Necking 

«          "      Piece 

"      Report 

Test  by  Abrasion J 


838  INDEX. 

PAGE 

Test,  Admiralty,  for  Iron  Plate 172 

11            "          Steel  Plate 172 

11     of  Asphalt 180 

*  *     by  Bending 166 

"     of  Bricks 178 

"     "  Bridge  Materials 168 

"     "  Car  Wheels 167 

"     "  Cement 182 

' '     li  Compound  Pumping-engine 631 

"     "  Condenser 578 

"     ' '  Density 203 

"     by  Drop  Method 164 

"     of  Efficiency 3 

by  Forging 166 

"     of  Belts 263 

"     "  Gas-  or  Oil-engines 714 

"     "  Gauges 363 

1 1    by  Hammer 166 

"     "  Hardening 166 

' '    of  Hot-air  Engine 697 

'  *     by  Impact,  Directions 163 

*  *     of  Injector .* 679 

1 '     "  Lubricants It 201 

"     "  Materials % 67 

"     "  Paving  Materials 171 

* '     "  Power-pumps 339 

'  *      ' '  Pulsometer 684 

1  i     "  Refrigerating-machine 748 

' '     by  Repeated  Loading 166 

' '    of  Specific  Gravity  of  Cement 183 

* '     * '  Steam-turbines 691 

'  *     "  Stones 1 75 

' '     "  Torsion,  Long  Specimens 1 186 

'*      il  Viscosity 204 

' '  Water-pipe 1 74 

Test-pieces,  Cast-iron ^ 139 

Cement I4o 

"            Chain I39 

Compression I42 

Form  of I36 

Rope I4o 

"  Tension.  .  .128 


INDEX.  839 

PAGE 

Test-pieces,  Torsion I42 

Transverse I42 

"      of  Wire-rope I40 

"       "  Wood I3g 

Testing  of  Water-motors 322 

"       by  Welding Z65 

Testing-machine,  Calibration 97 

Cement 119 

Classification 90 

Compound  Lever 91 

Differential  Lever 91 

Emery 102 

Extensometer 124 

Frame 97 

"  Fulcrum 95 

"  Hydraulic 92 

"  ' '        and  Lever 93 

Impact  and  Drop 119 

"  Olsen no 

Power  System •• 89,  98 

Requirements  of 88 

"  Riehle,  Hydraulic 107 

"  "      Power 108 

"  Shackle's 89,98 

"  Simple-lever 90 

"  Torsion,  Thurston 114 

"  Varieties  and  Forms 88 

"  Watertown  Arsenal IO° 

Wedges •   I0° 

"  Weighing  Devices 

"  Weighing  System 9^ 

Thatcher's  Slide-rule 

Theory,  Hot-air  Engine 

Thermodynamic  Efficiency 

Thermometers,  Air • 

Thermometer,  Alcohol 

Calibration 3&>,  5 

Cups 

«  Mercurial 

"  Rules  for  Handling 

Thermometric  Scales,  Table  of 

Thompson's  Fuel  Calorimeter 


840  INDEX. 


Thompson  Indicator 519 

Three-way  Cock 544 

Throttling-calorimeter.  .  .  .  t 398,  418 

"                   Diagram 425 

« '                          "for  use 796 

' '                   Forms 430 

"                  Limit  of 427 

' '                  Table  for  use 795 

Thurston  Extensometer 129 

Thurston's  Oil-testing  Machine,  Directions 222 

<  <                  ' '               * '         Standard, 217 

"                  < «               ' '         Theory 220 

' '          R.R.  Oil-testing  Machine 219 

Torsion-machine 114 

* (                        "             Diagram 115 

11                       "             Directions 161 

Torsion-machine  Thurston 114 

"               Olsen n8a 

Riehle 117,  118 

Torsion  Strain,  Theory 82 

Torsion-test,  Directions 160 

Forms  for  Report 162 

Torsion  Testing-machine.  . 114 

Torsion-tests,  Long  Specimens 1 186 

Torsion  Test-pieces 142 

Torsional  Resilience 83 

Traction  Dynamometer 246 

Transmission  Dynamometer 247 

Transverse  Deflectometer 135 

' '         Formula 76 

"         Loads,  Table 78 

' '         Test,  Directions 156 

"           "     Elastic  Curve 159 

"            "     Forms 157 

1 '     Specimens 142 

Trapezoidal  Weir 272 

Triangular  Weir 272 

Triple-engine,  Hirn's  Analysis 604 

Triple-expansion,  Diagrams 565 

Tuning-fork  Chronograph 574 

Turbine,  Steam-,  Description  of 686 

"         Water-wheel ^ 315 


INDEX.  841 


PAGE 


Turbine,  Water-wheel,  Forms  of  Test ,jg 

•   "         Theory '.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.'.  .3,6 

Twisting  and  Bending  Stress g- 

' '        "    Longitudinal  Stress g4 

Two-cycle  Gas-engine o 


U 
Undershot  Water-wheels.  . 


313 

Unwin's  Extensometer I2^ 

U-shaped  Manometer ~,- 

V 

Vacuum  Gauge 360 

11          "      Calibration 367 

Vacuum  Line ^g 

Valve-setting 586 

Valves,  Loss  of  Head 279 

Van  Winkle  Power-meter 261 

Variation  of  Load,  Diagram 564 

Velocity  of  Approach 283 

"        ' '  Discharge,  Coefficient  for 271 

"  Flow  of  Air...' :..   297 

11      .Head... 271 

' '        of  Nozzle  Discharge,  DeLaval  Turbine 688 

Venturi  Tube  Calibration 287 

11     Flow  Through .   275 

Vernier 29 

"       Caliper 57 

Vicat  Needle 186 

Viscosity  of  Materials 70 

11  Metals 167 

"        "  Oil 203 

'  *        Test,  Directions 208 

Viscosbmeter,  Carpenter's •   207 

Gibbs's -   205 

"  Pendulum -209 

"  Pennsylvania  R.R 204 

Perkins 205 

"  Stillman -206 

"  Tagliabue -205 


" 


842  INDEX. 

;  PAGE 

Volume  of  Air  Discharged  .........................................  296 

"       "    "   Measured  by  Heat  absorbed    ......  .  ____  .....  %  ........  727 

W 

Water,  Computation  Table  for  Steam-engine  .........................  802 

'  '      Energy  of  Falling  ..........................................  309 

"      Equivalent  of  Calorimeter  ...................................  401 

'  '      Flow  in  Circular  Pipes  .....................................  277 

"          "     through  Nozzles  ......................................  275 

under  Pressure  ............  .  ..........................  276 

in  Streams,  Measurement  of  ............................  289 

"         "     through  Venturi  Tubes  ................................  275 

11         "     over  Weirs  ......................................    272,  281 

'  '      Measurement  of  Flow  .....................................  281 

"  "  ll       "     in  Pipes  .............................  288 

"     with  Pitot's  Tube  .....................  292 

'  '     Measurement  of  Head  .........  ..............................  281 

'  '     Measurement  with  Hydrometric  Pendulum  ....................  295 

'  '     Measurements,  Locomotive  Tests  ............................  645 

'  '     Meters  ....................................................  283 

'  '     Meter  Calibration  ..........................................  579 

'  '      Errors  ..............................................  284 

'  *      Locomotive  Test  ..................................   64,  645 

'  '     Motors,  Measurement  of  Head  ......................  .........  323 

Testing  of  .........................................  322 

"     Table  of,  Density  and  Weight  ...............................  799 

'  '     Theory  of  Flow  .................  ...........................  270 

Water-pipe  Specifications  ..........................................  174 

Water-pressure  Engines  ...........................................  309 

"        Test  of  ..........  ...........................  325 

Water-power  System,  Parts  of  ......................................  309 

Water  Ram.  ....................................................  321 

Water-  vapor  for  Refrigeration  ......................................  739 

Water-wheels,  Breast  ...................................  .  .........  313 

"  Classified  ...........................................  310 

Impulse  ............  ................................  314 

Overshot  ...........................................  311 

Poncelet  ...........................................  314 

Reaction  Type  ......................................  319 

Water-wheels,  Test  of  .............................................  325 

Turbines  ...........................................  315 

Undershot  ........................  „  .............  ...  313 


INDEX. 


843 


Watertown  Testing-machine 

Watt  Steam-engine  Indicator. 

Wearing-test  Paving-brick J^Q 

Weathering  Quality  of  Stone I7g 

Webber  Dynamometer 2__ 

Wedge  Extensometer I2 

Wedgewood's  Pyrometer. ~gj 

Weighing  Device,  Testing-machines gg 

Scales  Calibration $jg 

System  Testing-machine.  < 0 

Weight  of  Steam  from  Indicator  Diagram; ^ 

Weir  Calibration 285 

Weirs,  Coefficients  for 274 

' '       Different  Forms 272 

' '       Discharge  over,  Table  of 803 

' '       Formula  for 273 

Measurement  of  Water,  Errors  in 282 

Measurement  of  Head 281 

' '       Requirements  for  Accuracy 282 

Welding  Test 165 

Welter's  Method  of  Measuring  Heating  Value 446 

Werder  Testing-machine 93 

Westinghouse  Gas-engine 706 

Williams's  Inertia  Indicator 661 

Willis's  Planimeter 45 

Wilson's  Flue -gas  Apparatus •  481 

Wind  Resistance,  Locomotive  Tests.  .  .  .  , ...  651 

Wipe  Spark-ignition 7°4 

Wire-drawing 55° 

Wire -rope  Test-piece •  140 

Wooden  Tension  Test-pieces. . .                                                                 •  13& 

Work-diagram 2I 

Work  Lost  due  to  Heating  in  Compression •  729 

"      Mechanical,  Isothermal  Expansion -712 

Y 
Yield  Point ^ 

Z 

Zero  Absolute 338 

"    Circle,  Theory 

Zeuner's  Valve-diagram 587 


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'Snow's  Principal  Species  of  Wood 8vo,  3  50 

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' 

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Molecule i2mo,  2  50 

*  Bruff 's  Text-book  Ordnance  and  Gunnery 8vo,  6  oo 

Chase's  Screw  Propellers  and  Marine  Propulsion 8vo,  3  oo 

Cloke's  Gunner's  Examiner 8vo,  i  50 

Craig's  Azimuth 4to,  3  50 

Crehore  and  Squier's  Polarizing  Photo-chronograph 8vo,  3  oo 

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Sheep,  7  50 

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Dietz's  Soldier's  First  Aid  Handbook i6mo,  morocco,  i  23 

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Hamilton's  The  Gunner's  Catechism i8mo,  i  oo 

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Ingalls's  Handbook  of  Problems  in  Direct  Fire 8vo,  4  oo 

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Peabody's  Naval  Architecture 8vo,  7  50 

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Powell's  Army  Officer's  Examiner iimo',  4  oo 

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Woodhull's  Notes  on  Military  Hygiene i6mo,  i  50 

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Low's  Technical  Methods  of  Ore  Analysis 8vo,  3  oo 

Miller's  Manual  of  Assaying i2mo,  i  oo 

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Ricketts  and  Miller's  Notes  on  Assaying 8vo,  3  oo 

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Craig's  Azimuth 4to,  3  5<> 

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Allen's  Tables  for  Iron  Analysis 8vo«  3 

Arnold's  Compendium  of  Chemistry.     (Mandel.) Small  8vo,  3 

Austen's  Notes  for  Chemical  Students I2mo'  l  5° 

Bernadou's  Smokeless  Powder. -Nitro-cellulose,  and  Theory  of  the  Cellulose 

Molecule ia™°'  a 

*  Browning's  Introduction  to  the  Rarer  Elements 8vo«  x  So 

3 


Brush  and  Penfield's  Manual  of  Determinative  Mineralogy ivo,  4  oo 

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Crafts's  Short  Course  in  Qualitative  Chemical  Analysis.   (Schaeffer.).  .  .  i2mo,  i  50 
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Ende.) i2mo,  2  50 

Drechsel's  Chemical  Reactions.     (Merrill.) i2mo,  i  25 

Duhem's  Thermodynamics  and  Chemistry.     (Burgess.) 8vo,  4  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

Effront's  Enzymes  and  their  Applications.     (Prescott.) &vo,  3  oo 

Erdmann's  Introduction  to  Chemical  Preparations.     (Dunlap.) i2mo,  i  25 

Fletcher's  Practical  Instructions  in  Quantitative  Assaying  with  the  Blowpipe. 

lamo,  morocco,  i  50 

Fowler's  Sewage  Works  Analyses i2mo,  2  oo 

Fresenius's  Manual  of  Qualitative  Chemical  Analysis.     (Wells.) 8vo,  5  oo 

Manual  of  Qualitative  Chemical  Analysis.  Part  I.  Descriptive.  (Wells.)  8vo,  3  oo 
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Fuertes's  Water  and  Public  Health i2mo,  i  50 

Furman's  Manual  of  Practical  Assaying 8vo,  3  oo 

*  Getman's  Exercises  in  Physical  Chemistry i2ino,  2  oo 

Gill's  Gas  and  Fuel  Analysis  for  Engineers i2mo,  i  25 

Grotenfelt's  Principles  of  Modern  Dairy  Practice.     (Woll.) i2rno,  2  oo 

Hammarsten's  Text-book  of  Physiological  Chemistry.     (Mandel.) 8vo,  4  oo 

Helm's  Principles  of  Mathematical  Chemistry.     (Morgan.) i2mo,  i  50 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Hind's  Inorganic  Chemistry 8vo,  3  oo 

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Holleman's  Text-book  of  Inorganic  Chemistry.     (Cooper.) 8vo,  2  50 

Text-book  of  Organic  Chemistry.     (Walker  and  Mott.) 8vo,  2  50 

*  Laboratory  Manual  of  Organic  Chemistry.     (Walker.) i2mo,  i  oo 

Hopkins's  Oil-chemists'  Handbook , 8vo,  3  oo 

Jackson's  Directions  for  Laboratory  Work  in  Physiological  Chemistry.  .8vo,  i  25 

Keep's  Cast  Iron 8vo,  2  50 

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Chemistry.  (Tingle.) i2mo,  i  oo 

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Control 8vo,  7  50 

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Lodge's  Notes  on  Assaying  and  Metallurgical  Laboratory  Experiments. ..  .8vo,  3  oo 

Low's  Technical  Method  of  Ore  Analysis 8vo,  3  oo 

Lunge's  Techno-chemical  Analysis.  (Cohn.) i2mo  i  oo 

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Mandel's  Handbook  for  Bio-chemical  Laboratory i2mo,  i  50 

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3d  Edition,  Rewritten 8vo,  4  oo 

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Matthew's  The  Textile  Fibres 8vo,  3  50 

Meyer's  Determination  of  Radicles  in  Carbon  Compounds.     (Tingle.).  .i2mo,  i  oo 

Miller's  Manual  of  Assaying i2mo,  i  oo 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.     (Waldo.) .  .  .  .  i2mo,  2  SQ 

Mixter's  Elementary  Text-book  of,  Chemistry I2mo,  i  50 

Morgan's  An  Outline  of  the  Theory  of  Solutions  and  its  Results i2mo,  i  oo 

4 


Morgan's  Elements  of  Physical  Chemistry izmo,  3  oo 

*  Physical  Chemistry  for  Electrical  Engineers ' .  .  i2mo!  i  50 

Morse's  Calculations  used  in  Cane-sugar  Factories i6mo,  morocco]  i  50 

Mulliken's  General  Method  for  the  Identification  of  Pure  Organic  Compounds.' 

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O'Brine's  Laboratory  Guide  in  Chemical  Analysis 8vo,  2  oo 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores 8vo,  2  oo 

Ostwald's  Conversations  on  Chemistry.     Part  One.     (Ramsey.) izmo,  i  50 

Part  Two.     (Turnbull.) iimo,  200 

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Pictet's  The  Alkaloids  and  their  Chemical  Constitution.     (Biddle.) 8vo,  5  oo 

Pinner's  Introduction  to  Organic  Chemistry.     (Austen.) izmo,  i  50 

Poole's  Calorific  Power  of  Fuels 8vo,  3  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
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*  Reisig's  Guide  to  Piece-dyeing 8vo,  25  oo 

Richards  and  Woodman's   Air,  Water,  and    Food  from  a  Sanitary  Stand- 
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Ricketts  and  Russell's  Skeleton  Notes  upon  Inorganic  Chemistry.     (Part  I. 

Non-metallic  Elements.) 8vo, 'morocco,        75 

Ricketts  and  Miller's  Notes  on  Assaying 8vo,  5  oo- 

Rideal's  Sewage  and  the  Bacterial  Purification  of  Sewage 8vo,  3  50 

Disinfection  and  the  Preservation  of  Food 8vo,  4  oo 

Riggs's  Elementary  Manual  for  the  Chemical  Laboratory 8vo,  i  25 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo 

Rostoski's  Serum  Diagnosis.     (Bolduan.) i2mo,  i  oo 

Ruddiman's  Incompatibilities  in  Prescriptions 8vo,  2  oo 

*  Whys  in  Pharmacy I2mo,  i  oo- 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Salkowski's  Physiological  and  Pathological  Chemistry.     (Orndorff.) 8vo,  2  50 

Schimpf's  Text-book  of  Volumetric  Analysis i2mo,  2  50 

Essentials  of  Volumetric  Analysis i2mo,  i  25 

*  Qualitative  Chemical  Analysis 8vo,  i  25 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses i6mo,  morocco,  3  oo 

Handbook  for  Cane  Sugar  Manufacturers i6mo,  morocco,  3  oo 

Stockbridge's  Rocks  and  Soils 8vo,  2  50 

*  Tillman's  Elementary  Lessons  in  Heat 8vo,  i  50 

*  Descriptive  General  Chemistry 8vo»  3  oo 

Treadwell's  Qualitative  Analysis.     (Hall.) 8vo,  300 

Quantitative  Analysis.     (Hall.) 8v°.  4  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Van  Deventer's  Physical  Chemistry  for  Beginners.     (Boltwood.) I2mo,  i 

*  Walke's  Lectures  on  Explosives 

Ware's  Beet-sugar  Manufacture  and  Refining Small  8vo,  cloth,  4 

Washington's  Manual  of  the  Chemical  Analysis  of  Rocks.  .  . 
Wassermann's  Immune  Sera :  Haemolysins,  Cytotoxins,  and  Precipitins.    (Bol- 
duan.)   12flmo'  ' 

Wells's  Laboratory  Guide  in  Qualitative'  Chemical  Analysis. .  . 

Short  Course  in  Inorganic  Qualitative  Chemical  Analysis  for  Engineering 
Students 

Text-book  of  Chemical  Arithmetic I: 

Whipple's  Microscopy  of  Drinking-water 

Wilson's  Cyanide  Processes 

I2IT1O.  I    SO 

Chlorination  Process ' 

Winton's  Microscopy  of  Vegetable  Foods.  ...  •••- 

Wulling's    Elementary    Course   in  Inorganic,  Pharmaceuhcal,  and  Medical  ^  ^ 

Chemistry 

5 


CIVIL  ENGINEERING. 

BRIDGES    AND    ROOFS        HYDRAULICS.       MATERIALS   OF    ENGINEERING. 
RAILWAY  ENGINEERING. 

Baker's  Engineers'  Surveying  Instruments i2mo,  3  oo 

Bixby's  Graphical  Computing  Table Paper  19^X24!  inches.  25 

**  Burr's  Ancient  and  Modern  Engineering  and  the  Isthmian  Cana  >.     (Postage, 

27  cents  additional.) 8vo,  3  50 

Comstock's  Field  Astronomy  for  Engineers 8vo,  2  50 

Davis's  Elevation  and  Stadia  Tables. 8vo,  i  oo 

Elliott's  Engineering  for  Land  Drainage i2mo,  i  50 

Practical  Farm  Drainage 12010,  i  oo 

*Fiebeger's  Treatise  on  Civil  Engineering 8vo,  5  00 

Flemer's  Phototopographic  Methods  and  Instruments 8vo,  5  oo 

Folwell's  Sewerage.     (Designing  and  Maintenance.) 8vo,  3  oo 

Freitag's  Architectural  Engineering.     2d  Edition,  Rewritten 8vo,  3  50 

French  and  Ives's  Stereotomy 8vo,  2  50 

Goodhue's  Municipal  Improvements i2mo,  i  75 

Goodrich's  Economic  Disposal  of  Towns'  Refuse 8vo,  3  50 

Gore's  Elements  of  Geodesy 8vo,  2  50 

Hayford's  Text-book  of  Geodetic  Astronomy 8vo,  3  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Howe's  Retaining  Walls  for  Earth i2mo,  i  25 

Johnson's  (J.  B.)  Theory  and  Practice  of  Surveying Small  8vo,  4  oo 

Johnson's  (L.  J.)  Statics  by  Algebraic  and  Graphic  Methods 8vo,  2  oo 

Laplace's  Philosophical  Essay  on  Probabilities.    (Truscott  and  Emory.) .  i2mo,  2  oo 

Mahan's  Treatise  on  Civil  Engineering.     (1873.)     (Wood.) 8vo,  5  oo 

*  Descriptive  Geometry 8vo,  i  50 

Merriman's  Elements  of  Precise  Surveying  and  Geodesy 8vo,  2  50 

Merriman  and  Brooks's  Handbook  for  Surveyors i6mo,  morocco,  2  oo 

Nugent's  Plane  Surveying 8vo,  3  50 

Ogden's  Sewer  Design • i2mo,  2  oo 

Patton's  Treatise  on  Civil  Engineering 8vo  half  leather,  7  50 

Reed's  Topographical  Drawing  and  Sketching 4*0,  5  oo 

Rideal's  Sewage  and  the  Bacterial  Purification  of  Sewage 8vo,  3  50 

Siebert  and  Biggin's  Modern  Stone-cutting  and  Masonry 8vo,  i  50 

Smith's  Manual  of  Topographical  Drawing.     (McMillan.  "> 8vo,  2  50 

Sondericker's  Graphic  Statics,  with  Applications  to  Trusses,  Beams,  and  Arches. 

8vo,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

*  Trautwine's  Civil  Engineer's  Pocket-book i6mo,  morocco,  5  oo 

Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo,  5  oo 

Sheep,  5  50 

Law  of  Contracts 8vo,  3  oo 

Warren's  Stereotomy — Problems  in  Stone-cutting X  .  8vo,  2  50 

Webb's  Problems  in  the  Use  and  Adjustment  of  Engineering  Instruments. 

i6mo,  morocco,  i  25 

Wilson's  Topographic  Surveying 8vo,  3  50 


BRIDGES  AND  ROOFS. 

Boiler's  Practical  Treatise  on  the  Construction  of  Iron  Highway  Bridges.  .8vo,    2  oo 

*       Thames  River  Bridge 4to,  paper,    5  oo 

Burr's  Course  on  the  Stresses  in  Bridges  and  Roof  Trusses,  Arched  Ribs,  and 

Suspension  Bridges 8vo,    3  50 

6 


Burr  and  Falk's  Influence  Lines  for  Bridge  and  Roof  Computations 8vo,  3  oo 

Design  and  Construction  of  Metallic  Bridges '  '  gvo[  5  oo 

Du  Bois's  Mechanics  of  Engineering.     Vol.  II .Small  4U>!  10  oo 

Foster's  Treatise  on  Wooden  Trestle  Bridges 4to>  5  QQ 

Fowler's  Ordinary  Foundations gvo'  3  g<> 

Greene's  Roof  Trusses gvo* 

Bridge  Trusses '""  'Svo'f  2  5<> 

Arches  in  Wood,  Iron,  and  Stone 8vo,  2  50 

Howe's  Treatise  on  Arches gvo,'  4  oo 

Design  of  Simple  Roof-trusses  in  Wood  and  Steel 8vo|  2  oo 

Johnson,  Bryan,  and  Turneaure's  Theory  and  Practice  in  the  Designing  of 

Modern  Framed  Structures Small  4to,  10  oo 

Merriman  and  Jacoby's  Text-book  on  Roofs  and  Bridges : 

Part  I.     Stresses  in  Simple  Trusses gVOf  2  go 

Part  II.     Graphic  Statics gvo,  2  50 

Part  III.     Bridge  Design gvo,  2  50 

Part  IV.     Higher  Structures 8vo,  2  50 

Morison's  Memphis  Bridge 4to,  10  oo 

Waddell's  De  Pontibus,  a  Pocket-book  for  Bridge  Engineers.  .  i6mo,  morocco,  2  oo 

*Specifications  for  Steel  Bridges .- i2mo,  50 

Wright's  Designing  of  Draw-spans.     Two  parts  in  one  volume 8vo,  3  50 


HYDRAULICS. 

Bazin's  Experiments  upon  the  Contraction  of  the  Liquid  Vein  Issuing  from 

an  Orifice.     (Trautwine.) 8vo,  2  oo 

Bovey's  Treatise  on  Hydraulics 8vo,  5  oo 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Diagrams  of  Mean  Velocity  of  Water  in  Open  Channels paper,  i  50 

Hydraulic  Metors 8vo,  2  oo 

Coffin's  Graphical  Solution  of  Hydraulic  Problems i6mo,  morocco,  2  50 

Flather's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo 

Folwell's  Water-supply  Engineering '. 8vo,  4  oo 

FrizelPs  Water-power 8vo,  5  oo 

Fuertes's  Water  and  Public  Health 12010,  i  50 

Water-filtration  Works i2mo,  2  50 

Ganguillet  and  Kutter's  General  Formula  for  the  Uniform  Flow  of  Water  in 

Rivers  and  Other  Channels.     (Bering  and  Trautwine.) 8vo,  4  oo 

Hazen's  Filtration  of  Public  Water-supply 8vo,  3  oo 

Hazlehurst's  Towers  and  Tanks  for  Water-works 8vo,  2  50 

Herschel's  115  Experiments  on  the  Carrying  Capacity  of  Large,  Riveted,  Metal 

Conduits 8vo,  2  oo 

Mason's  Water-supply.     (Considered  Principally  from  a  Sanitary  Standpoint.) 

8vo,  4  oo 

Merriman's  Treatise  on  Hydraulics 8vo,  5  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

Schuyler's   Reservoirs  for  Irrigation,  Water-power,  and  Domestic   Water- 
supply Large  8vo,  5  oo 

**  Thomas  and  Watt's  Improvement  of  Rivers.     (Post,  440.  additional.) . 4to,  6  oo 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5 

Wegmann's  Design  and  Construction  of  Dams 4to,  5  oo 

Water-supply  of  the  City  of  New  York  from  1658  to  1895 4to,  10  < 

Williams  and  Hazen's  Hydraulic  Tables 8vo«  l  & 

Wilson's  Irrigation  Engineering • Sma11 '  vo«  4 

Wolff's  Windmill  as  a  Prime  Mover 1Jvo»  3 

Wood's  Turbines v0'  a 

Elements  of  Analytical  Mechanics 8vo'  3  ° 

7 


MATERIALS  OF  ENGINEERING. 

Baker's  Treatise  on  Masonry  Construction 8vo,  5  oo 

Roads  and  Pavements 8vo,  5  oo 

Black's  United  States  Public  Works Oblong  4to,  5  oo 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering.  .  ....  .8vo,  7  50 

Byrne's  Highway  Construction 8vo,  5  oo 

Inspection  of  the  Materials  and  Workmanship  Employed  in  Construction. 

i6mo,  3  oo 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Du  Bois's  Mechanics  of  Engineering.     Vol.  I ' Small  4to,  7  50 

*Eckei's  Cements,  Limes,  and  Plasters 8vo,  6  oo 

Johnson's  Materials  of  Construction Large  8vo,  6  oo 

Fowler's  Ordinary  Foundations 8vo,  3  50 

*  Greene's  Structural  Mechanics 8vo,  2  50 

Keep's  Cast  Iron 8vo,  2  50 

Lanza's  Applied  Mechanics 8vo,  7  50 

Marten's  Handbook  on  Testing  Materials.     (Henning.)  -  2  vols 8vo,  7  5<> 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merrill's  Stones  for  Building  and  Decoration 8vo,  5  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

Strength  of  Materials i2tno,  i  oo 

Metcalf's  Steel.     A  Manufel  for  Steel-users i2mo,  2  oo 

Patton's  Practical  Treatise  on  Foundations 8vo,  5  oo 

Richardson's  Modern  Asphalt  Pavements 8vo,  3  oo 

Richey's  Handbook  for  Superintendents  of  Construction i6mo,  mor.,  4  oo 

Rockwell's  Roads  and  Pavements  in  France I2mo,  i  25 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Materials  of  Machines i2mo,  i  oo 

Snow's  Principal  Species  of  Wood 8vo,  3  50 

Spalding's  Hydraulic  Cement i2mo,  2  oo 

Text-book  on  Roads  and  Pavements 121110,  2  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced, 8vo,  5  oo 

Thurston's  Materials  of  Engineering.     3  Parts 8vo,  8  oo 

Part  I.     Non-metallic  Materials  of  Engineering  and  Metallurgy 8vo,  2  oe 

Part  II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Thurston's  Text-book  of  the  Materials  of  Construction 8vo,  5  oo 

Tillson's  Street  Pavements  and  Paving  Materials 8vo,  4  oo 

Waddell's  De  Pontibus.    (A  Pocket-book  for  Bridge  Engineers.).  .  i6mo,  mor.,  2  oo 

Specifications  for  Steel  Bridges i2mo,  i  25 

Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials,  and  an  Appendix  on 

the  Preservation  of  Timber 8vo,  2  oo 

Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo,  4  oo 


RAILWAY  ENGINEERING. 

Andrew's  Handbook  for  Street  Railway  Engineers 3x5  inches,  morocco,  i  25 

Berg's  Buildings  and  Structures  of  American  Railroads 4to,  5  oo 

Brook's  Handbook  of  Street  Railroad  Location i6mo,  morocco,  i  50 

Butt's  Civil  Engineer's  Field-book i6mo,  morocco,  2  50 

Crandall's  Transition  Curve i6mo,  morocco,  i  50 

Railway  and  Other  Earthwork  tables 8vo,  i  50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  .  i6mo,  morocco,  5  oo 

8 


Dredge's  History  of  the  Pennsylvania  Railroad:    (1870) Paper,  5  oo 

*  Drinker's  Tunnelling,  Explosive  Compounds,  and  Rock  Drills. 4to,  half  mor.,  25  oo 

Fisher's  Table  of  Cubic  Yards Cardboard,  25 

Godwin's  Railroad  Engineers'  Field-book  and  Explorers'  Guide.  .  .  i6mo,  mor.,  2  50 

Howard's  Transition  Curve  Field-book i6mo,  morocco,  i  50 

Hudson's  Tables  for  Calculating  the  Cubic  Contents  of  Excavations  and  Em- 
bankments  gvo,  i  oo 

Molitor  and  Beard's  Manual  for  Resident  Engineers i6mo,  i  oo 

Nagle's  Field  Manual  for  Railroad  Engineers i6mo,  morocco,  3  oo 

Philbrick's  Field  Manual  for  Engineers i6mo,  morocco,  3  oo 

Searles's  Field  Engineering i6mo,  morocco,  3  oo 

Railroad  Spiral i6mo,  merocco,  i  50 

Taylor's  Prismoidal  Formulae  and  Earthwork 8vo,  i  50 

*  Trautwine's  Method  of  Calculating  the  Cube  Contents  of  Excavations  and 

Embankments  by  the  Aid  of  Diagrams 8vo,  2  oo 

The  Field  Practice  of  Laying  Out  Circular  Curves  for  Railroads. 

1 2 mo,  morocco,  2  50 

Cross-section  Sheet Paper,  25 

Webb's  Railroad  Construction i6mo,  morocco,  5  oo 

Wellington's  Economic  Theory  of  the  Location  of  Railways Small  8vo,  5  oo 


DRAWING. 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

*  Bartlett's  Mechanical  Drawing •. .  .8vo,  3  oo 

*  "  "  "        Abridged  Ed 8vo,  150 

Coolidge's  Manual  of  Drawing 8vo,  paper  i  oo 

Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  Engi- 
neers  Oblong  4to,  2  50 

Durley's  Kinematics  of  Machines 8vo,  4  oo 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo,  2  50 

Hill's  Text-book  on  Shades  and  Shadows,  and  Perspective 8vo,  2  oo 

Jamison's  Elements  of  Mechanical  Drawing 8vo,  2  50 

Advanced  Mechanical  Drawing 8vo,  2  oo 

Jones's  Machine  Design: 

Part  I.     Kinematics  of  Machinery 8vo,  i  50 

*  Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

MacCord's  Elements  of  Descriptive  Geometry 8vo,  3  oo 

Kinematics ;  or,  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  i  50 

MacLeod's  Descriptive  Geometry .  .  .Small  8vo,  i  50 

*  Mahan's  Descriptive  Geometry  and  Stone-cutting., 8vo,  i  50 

Industrial  Drawing.     (Thompson.) 8vo,  3  50 

Moyer's  Descriptive  Geometry Svo,  2  oo 

Reed's  Topographical  Drawing  and  Sketching 4to,  500 

Reid's  Course  in  Mechanical  Drawing •  8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Robinson's  Principles  of  Mechanism 8vo,  3  o« 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  (R.  S.)  Manual  of  Topographical  Drawing.     (McMillan.) 8vo,  2  50 

Smith  (A.  W.)  and  Marx's  Machine  Design .  •  8vo,  3  oo 

Warren's  Elements  of  Plane  and  Solid  Free-hand  Geometrical  Drawing.  i2mo, 


Drafting  Instruments  and  Operations I2mo, 

Manual  of  Elementary  Projection  Drawing i2mo, 

Manual  of  Elementary  Problems  in  the  Linear  Perspective  of  Form  and 

Shadow I2rao' 

Plane  Problems  in  Elementary  Geometry 12010, 

9 


Warren's  Primary  Geometry I2mo,         75 

Elements  of  Descriptive  Geometry,  Shadows,  and  Perspective 8vo,  3  50 

General  Problems  of  Shades  and  Shadows 8vo,  3  oo 

Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Problems,  Theorems,  and  Examples  in  Descriptive  Geometry 8vo,  2  50 

Weisbach's    Kinematics  [and    Power    of    Transmission.        (Hermann    and 

Klein.) 8vo,  5  oo 

Whelpley's  Practical  Instruction  in  the  Art  of  Letter  Engraving 12 mo,  2  oo 

Wilson's  (H.  M.)  Topographic  Surveying 8vo,  3  50 

Wilson's  (V.  T.)  Free-hand  Perspective 8vo,  2  50 

Wilson's  (V.  T.)  Free-hand  Lettering 8vo,  i   oo 

Woolf's  Elementary  Course  in  Descriptive  Geometry Large  8vo,  3  oo 

ELECTRICITY  AND  PHYSICS. 

Anthony  and  Brackett's  Text-book  of  Physics.     (Magie.) Small  8vo,  3  oo 

Anthony's  Lecture-notes  on  the  Theory  of  Electrical  Measurements.  . .  .  i2mo,  i  oo 

Benjamin's  History  of  Electricity 8vo,  3  oo 

Voltaic  Cell 8vo,  3  oo 

Classen's  Quantitative  Chemical  Analysis  by  Electrolysis.     (Boltwood.).8vo,  3  oo 

Crehore  and  Squier's  Polarizing  Photo-chronograph 8vo,  3  oo 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book.  i6mo,  morocco,  5  oo 
Dolezalek's    Theory   of    the    Lead   Accumulator    (Storage    Battery).      (Von 

Ende.) 12010,  2  50 

Duhem's  Thermodynamics  and  Chemistry.     (Burgess.) 8vo,  4  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo 

Gilbert's  De  Magnete.     (Mottelay.) 8vo,  2  50 

Hanchett's  Alternating  Currents  Explained 12 mo,  i  oo 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco,  2  50 

Holman's  Precision  of  Measurements 8vo,  2  »o 

Telescopic   Mirror-scale  Method,  Adjustments,  and  Tests.  ..  .Large  8 vo,         75 

Xinzbrunner's  Testing  of  Continuous-current  Machines 8vo,  2  oo 

Landauer's  Spectrum  Analysis.     (Tingle.) 8vo,  3  oo 

Le  Chateliers  High-temperature  Measurements.  (Boudouard — Burgess.)  i2mo,  3  oo 

Lob's  Electrochemistry  of  Organic  Compounds.     (Lorenz.) 8vo,  3  oo 

*  Lyons' 3  Treatise  on  Electromagnetic  Phenomena.   Vols.  I.  and  II.  8vo,  each,  6  oo 

*  Michie's  Elements  of  Wave  Motion  Relating  to  Sound  and  Light 8vo,  4  oo 

Niaudet's  Elementary  Treatise  on  Electric  Batteries.     (Fishback.) i2mo,  2  50* 

*  Rosenberg's  Electrical  Engineering.     (Haldane  Gee — Kinzbrunner.).  .  .8vo,  i  50 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     Vol.  1 8vo,  2  50 

Thurston's  Stationary  Steam-engines 8vo,  2  50 

*  Tillman's  Elementary  Lessons  in  Heat 8vo,  i   50 

Tory  and  Pitcher's  Manual  of  Laboratory  Physics Small  8vo,  2  oo 

Ulke's  Modern  Electrolytic  Copper  Refining 8vo,  3  oo 

LAW. 

*  Davis's  Elements  of  Law 8vo,  2  50 

*  Treatise  on  the  Military  Law  of  United  States. 8vo,  7  oo 

*  Sheep,  7  50 

Manual  for  Courts-martial i6mo,  morocco,  i  50 

Wait's  Engineering  and  Architectural  Jurisprudence 8vo,  6  oo 

Sheep,  6  50 

Law  of  Operations  Preliminary  to  Construction  in  Engineering  and  Archi- 
tecture  8vo  5  oo 

Sheep,  5  50 

Law  of  Contracts 8vo,  3  oo 

Winthrop's  Abridgment  of  Military  Law 12010,  2  So 

10 


MANUFACTURES. 

Bernadou's  Smokeless  Powder— Nitro-cellulose  and  Theory  of  the  Cellulose 

Molecule I2mOf  2  5O 

Holland's  Iron  Founder i2mo,  2  50 

"  The  Iron  Founder,"  Supplement i2mo,  2  50 

Encyclopedia  of  Founding  and  Dictionary  of  Foundry  Terms  Used  in  the 

Practice  of  Moulding i2mo,  3  oo 

*  Eckel's  Cements,  Limes,  and  Plasters ] 8vo,  6  oo 

Eissler's  Modern  High  Explosives 8vo,  4  oo 

Effront's  Enzymes  and  their  Applications.     (Prescott.) 8vo,  3  oo 

Fitzgerald's  Boston  Machinist i2mo,  i  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i  oo 

Hopkin's  Oil-chemists'  Handbook 8vo,  3  oo 

Keep's  Cast  Iron 8vo,  2  50 

Leach's  The  Inspection  and  Analysis  of  Foed  with  Special  Reference  to  State 

Control Large  8vo,  7  50 

*  McKay  and  Larsen's  Principles  and  Practice  of  Butter-making 8vo,  i  50 

Matthews's  The  Textile  Fibres 8vo,  3  So 

Metcalf' s  Steel.     A  Manual  for  Steel-users i2mo,  2  oo 

Metcalf e's  Cost  of  Manufactures — And  the  Administration  of  Workshops .  8vo,  5  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oo 

Morse's  Calculations  used  in  Cane-sugar  Factories i6mo,  morocco,  i  50 

*  Reisig's  Guide  to  Piece-dyeing 8vo,  25  oo 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  oo 

Smith's  Press-working  of  Metals 8vo,  3  oo 

Spalding's  Hydraulic  Cement i2mo,  2  oo 

Spencer's  Handbook  for  Chemists  of  Beet-sugar  Houses i6mo,  morocco,  3  oo 

Handbook  for  Cane  Sugar  Manufacturers i6mo,  morocco,  3  oo 

Taylor  and  Thompson's  Treatise  on  Concrete,  Plain  and  Reinforced 8vo,  5  oo 

Thurston's  Manual  of  Steam-boilers,  their  Designs,  Construction  and  Opera- 
tion  8vo,  5  oo 

*  Walke's  Lectures  on  Explosives 8vo,  4  oo 

Ware's  Beet-sugar  Manufacture  and  Refining Small  8vo,  4  oo 

West's  American  Foundry  Practice i2mo,  2  50 

Moulder's  Text-book 12010,  2  50 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Rustless  Coatings:   Corrosion  and  Electrolysis  of  Iron  and  Steel.  .8vo,  4  oo 


MATHEMATICS. 

Baker's  Elliptic  Functions 8vo» 

*  Bass's  Elements  of  Differential  Calculus i2mo, 

Briggs's  Elements  of  Plane  Analytic  Geometry I2mo, 

Compton's  Manual  of  Logarithmic  Computations i2mo, 

Davis's  Introduction  to  the  Logic  of  Algebra 8vo, 

*  Dickson's  College  Algebra Lar«e  I2mo» 

*  Introduction  to  the  Theory  of  Algebraic  Equations Large  i2mo, 

Emch's  Introduction  to  Projective  Geometry  and  its  Applications 8vo, 

Halsted's  Elements  of  Geometry | 

Elementary  Synthetic  Geometry 8vo« 


I2H1O, 


75 


Rational  Geometry 

*  Johnson's  (J.  B.)  Three-place  Logarithmic  Tables:   Vest-pocket  size. paper, 

100  copies  for    5  oo 

*  Mounted  on  heavy  cardboard,  8  X  10  inches,        25 

10  copies  for    a  oo 

Johnson's  (W.  W.)  Elementary  Treatise  on  Differential  Calculus.  .Small  8vo,    3  oo 
Elementary -Treatise  on  the  Integral  Calculus Small  8vo,    I 


Johnson's  (W.  W.)  Curve  Tracing  in  Cartesian  Co-ordinates i2mo,     i  oo 

Johnson's  (W.  W.)  Treatise  on  Ordinary  and  Partial  Differential  Equations. 

Small  8vo,    3  50 
Johnson's  (W.  W.)  Theory  of  Errors  and  the  Method  of  Least  Squares.  i2mo,     i  50 

*  Johnson's  (W.  W.)  Theoretical  Mechanics i2mo,    3  oo 

Laplace's  Philosophical  Essay  on  Probabilities.    (Truscott  and  Emory.)  •  i2mo,    2  oo 

*  Ludlow  and  Bass.     Elements  of  Trigonometry  and  Logarithmic  and  Other 

Tables 8vo,    3  oo 

Trigonometry  and  Tables  published  separately Each,    2  oo 

*  Ludlow's  Logarithmic  and  Trigonometric  Tables 8vo,    i  oo 

Mathematical  Monographs.     Edited  by  Mansfield  Merriman  and  Robert 

S.  Woodward Octavo,  each     i  oo 

No.  i.  History  of  Modern  Mathematics,  by  David  Eugene  Smith. 
No.  2.  Synthetic  Projective  Geometry,  by  George  Bruce  Halsted. 
No.  3.  Determinants,  by  Laenas  Gifford  Weld.  No.  4.  Hyper- 
bolic Functions,  by  James  McMahon.  No.  5.  Harmonic  Func- 
tions, by  William  E.  Byerly.  No.  6.  Grassmann's  Space  Analysis, 
by  Edward  W.  Hyde.  No.  7.  Probability  and  Theory  of  Errors, 
by  Robert  S.  Woodward.  No.  8.  Vector  Analysis  and  Quaternions, 
by  Alexander  Macfarlane.  No.  9.  Differential  Equations,  by 
William  Woolsey  Johnson.  No.  10.  The  Solution  of  Equations, 
byj  Mansfield  Merriman.  No.  n.  Functions  of  a  Complex  Variable, 
by  Thomas  S.  Fiske. 

Maurer's  Technical  Mechanics 8vo,    4  oo 

Merriman's  Method  of  Least  Squares 8vo,    2  oo 

Rice  and  Johnson's  Elementary  Treatise  on  the  Differential  Calculus. .  Sm.  8vo,    3  oo 

Differential  and  Integral  Calculus.     2  vols.  in  one Small  8vo,    2  50 

Wood's  Elements  of  Co-ordinate  Geometry 8vo,    2  oo 

Trigonometry:  Analytical,  Plane,  and  Spherical i2mo,     i  oo 


MECHANICAL  ENGINEERING. 
MATERIALS  OF  ENGINEERING,  STEAM-ENGINES  AND  BOILERS. 

Bacon's  Forge  Practice I2mo,  i  50 

Baldwin's  Steam  Heating  for  Buildings i2mo,  2  50 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

*  Bartlett's  Mechanical  Drawing 8vo,  3  oo 

*  "                  "                 "        Abridged  Ed 8vo,  i  50 

Benjamin's  Wrinkles  and  Recipes i2mo,  2  oo 

Carpenter's  Experimental  Engineering 8vo,  6  oo 

Heating  and  Ventilating  Buildings 8vo,  4  oo 

Gary's  Smoke  Suppression  in  Plants  using  Bituminous  Coal.     (In  Prepara- 
tion.) 

Clerk's  Gas  and  Oil  Engine Small  8vo,  4  oo 

Coolidge's  Manual  of  Drawing 8vo,  paper,  i  oo 

Coolidge  and  Freeman's  Elements  of  General  Drafting  for  Mechanical  En- 


gineers   Oblong  4to, 

Cromwell's  Treatise  on  Toothed  Gearing i2mo, 

Treatise  on  Belts  and  Pulleys i2mo, 

Durley's  Kinematics  of  Machines 8vo, 

Flather's  Dynamometers  and  the  Measurement  of  Power i2mo, 

Rope  Driving i2mo, 

Gill's  Gas  and  Fuel  Analysis  for  Engineers i2mo, 

Hall's  Car  Lubrication i2mo, 

Bering's  Ready  Reference  Tables  (Conversion  Factors) i6mo,  morocco, 

/  12 


Button's  The  Gas  Engine 8vo,  5  ^ 

Jamison's  Mechanical  Drawing gVOf  2  5O 

Jones's  Machine  Design : 

Part  I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

Kent's  Mechanical  Engineers'  Pocket-book i6mo,  morocco,  5  oo 

Kerr's  Power  and  Power  Transmission 8vo,  2  oo 

Leonard's  Machine  Shop,  Tools,  and  Methods 8vo,  4  oo 

*  Lorenz's  Modern  Refrigerating  Machinery.    (Pope,  Haven,  and  Dean. ) . .  8vo,  4  oo 

MacCord's  Kinematics ;  or,  Practical  Mechanism 8vo,  5  oo 

Mechanical  Drawing 4to,  4  oo 

Velocity  Diagrams 8vo,  i  50 

MacFarland's  Standard  Reduction  Factors  for  Gases 8vo,  i  50 

Mahan's  Industrial  Drawing.     (Thompson.) 8vo,  3  50 

Poole's  Calorific  Power  of  Fuels 8vo,  3  oo 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Richard's  Compressed  Air i2mo,  i  50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  3  oo 

Smith's  (O.)  Press-working  of  Metals 8vo,  3  oo 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  oo 

Thurston's   Treatise   on   Friction  and   Lost  Work  in  Machinery  and   Mill 

Work 8vo,  3  oo 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Laws  of  Energetics .  12010,  i  oo 

Warren's  Elements  of  Machine  Construction  and  Drawing 8vo,  7  50 

Weisbach's    Kinematics    and    the    Power    of    Transmission.     (Herrmann — 

Klein.) 8vo,  5  oo 

Machinery  of  Transmission  and  Governors.     (Herrmann — Klein.).  .Sro,  5  oo 

Wolff's  Windmill  as  a  Prime  Mover 8vo,  3  oo 

Wood's  Turbines 8vo,  2  50 


MATERIALS  OP  ENGINEERING. 

*  Bovey's  Strength  of  Materials  and  Theory  of  Structures 8vo,  7  50 

Burr's  Elasticity  and  Resistance  of  the  Materials  of  Engineering.    6th  Edition. 

Reset , 8vo»  7  5<> 

Church's  Mechanics  of  Engineering •  8vo,  6  oo 

*  Greene's  Structural  Mechanics 8vo»  2  So 

Johnson's  Materials  of  Construction 8vo,  6  oo 

Keep's  Cast  Iron 8vo»  2  So 

Lanza's  Applied  Mechanics 8vo»  7 

Martens's  Handbook  on  Testing  Materials.     (Henning.) 8vo,  7  5' 

Maurer's  Technical  Mechanics 8vo>  4  oo 

Merriman's  Mechanics  of  Materials 8v°.  5 

Strength  of  Materials I2mo«  I 

Metcalf's  Steel.     A  manual  for  Steel-users 12010,  2 

Sabin's  Industrial  and  Artistic  Technology  of  Paints  and  Varnish 8vo,  3  o< 

Smith's  Materials  of  Machines I2mo»  ' 

Thurston's  Materials  of  -Engineering 3  vols.,  8vo,  8 

Part  II.     Iron  and  Steel 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents v 8vo-  a 

Text-book  of  the  Materials  of  Construction 

Wood's  (De  V.)  Treatise  on  the  Resistance  of  Materials  and  an  Appendix  on 

the  Preservation  of  Timber '. 8vo-  2  °° 

13 


Wood's  (De  V.)  Elements  of  Analytical  Mechanics 8vo,  3  oo 

Wood's  (M.  P.)  Rustless  Coatings:    Corrosion  and  Electrolysis  of  Iron  and 

Steel 8vo.  4  oo 

STEAM-ENGINES  AND  BOILERS. 

Berry's  Temperature-entropy  Diagram I2mo,  i  25 

Carnot's  Reflections  on  the  Motive  Power  of  Heat.     (Thurston.) i2mo,  i  50 

Dawson's  "Engineering"  and  Electric  Traction  Pocket-book i6mo,  mor.,  5  oo 

Ford's  Boiler  Making  for  Boiler  Makers i8mo,  i  oo 

Goss's  Locomotive  Sparks 8vo,  2  oo 

Hemenway's  Indicator  Practice  and  Steam-engine  Economy i2mo,  2  oo 

Button's  Mechanical  Engineering  of  Power  Plants 8vo,  5  oo 

Heat  and  Heat-engines 8vo,  5  oo 

Kent's  Steam  boiler  Economy 8vo,  4  oo 

Kneass's  Practice  and  Theory  of  the  Injector 8vo,  i  50 

MacCord's  Slide-valves 8vo,  2  oo 

Meyer's  Modern  Locomotive  Construction 4to,  10  oc 

Peabody's  Manual  of  the  Steam-engine  Indicator i2mo.  i  50 

Tables  of  the  Properties  of  Saturated  Steam  and  Other  Vapors   8vo,  i  oo 

Thermodynamics  of  the  Steam-engine  and  Other  Heat-engines 8vo,  5  oo 

Valve-gears  for  Steam-engines 8vo,  2  50 

Peabody  and  Miller's  Steam-boilers 8vo,  4  oo 

Pray's  Twenty  Years  with  the  Indicator Large  8vo,  2  50 

Pupin's  Thermodynamics  of  Reversible  Cycles  in  Gases  and  Saturated  Vapors. 

(Osterberg.) i2mo,  i  25 

Reagan's  Locomotives:   Simple   Compound,  and  Electric i2mo,  2  50 

Rontgen's  Principles  of  Thermodynamics.     (Du  Bois.) 8vo,  5  oo 

Sinclair's  Locomotive  Engine  Running  and  Management i2mo,  2  oo 

Smart's  Handbook  of  Engineering  Laboratory  Practice I2mo,  2  50 

Snow's  Steam-boiler  Practice 8vo,  3  oo 

Spangler's  Valve-gears 8vo,  2  50 

Notes  on  Thermodynamics i2mo,  i  oo 

Spangler,  Greene,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thomas's  Steam-turbines : 8vo,  3  50 

Thurston's  Handy  Tables 8vo,  i  50 

Manual  of  the  Steam-engine 2  vols.,  8vo,  10  oo 

Part  I.     History,  Structure,  and  Theory 8vo,  6  oo 

Part  II.     Design,  Construction,  and  Operation 8vo,  6  oo 

Handbook  of  Engine  and  Boiler  Trials,  and  the  Use  of  the  Indicator  and 

the  Prony  Brake 8vo,  5  oo 

Stationary  Steam-engines 8vo,  2  50 

Steam-boiler  Explosions  in  Theory  and  in  Practice i2mo,  i  50 

Manual  of  Steam-boilers,  their  Designs,  Construction,  and  Operation 8vo,  5  oo 

Weisbach's  Heat,  Steam,  and  Steam-engines.     (Du  Bois.) 8vo,  5  oo 

Whitham's  Steam-engine  Design 8vo,  5  oo 

Wood's  Thermodynamics,  Heat  Motors,  and  Refrigerating  Machines.  .  .8vo,  4  oo 

MECHANICS  AND  MACHINERY. 

Barr's  Kinematics  of  Machinery 8vo,  2  50 

*,Bovey's  Strength  of  Materials  and  Theory  of  Structures   .  * 8vo,  7  50 

Chase's  The  Art  of  Pattern-making I2mo,  2  50 

Church's  Mechanics  of  Engineering 8vo,  6  oo 

Notes  and  Examples  in  Mechanics » 8vo,  2  po 

Compton's  First  Lessons  in  Metal-working I2mo,  I  50 

Compton  and  De  Groodt's  The  Speed/Lathe I2mo  i  50 

14 


Cromwell's  Treatise  on  Toothed  Gearing i2mo,  i  50 

Treatise  on  Belts  and  Pulleys .  .  i2mo,'  -  50 

Dana's  Text-book  of  Elementary  Mechanics  for  Colleges  and  Schools! '.  i2mo,  i  50 

Dingey's  Machinery  Pattern  Making 12010,  2  oo 

Dredge's  Record  of  the  Transportation  Exhibits  Building  of  the  World's' 

Columbian  Exposition  of  1893 4to  half  morocco,  5  oo 

Du  Bois's  Elementary  Principles  of  Mechanics: 

Vol.      I.     Kinematics 8vo>  3  5O 

Vol.    II.     Statics 8vo,  400 

Mechanics  of  Engineering.     Vol.    I Small  4to,  7  50 

Vol.  II Small  4to,  10  oo 

Durley's  Kinematics  of  Machines .8vo,  4  oo 

Fitzgerald's  Boston  Machinist i6mo,  i  oo 

Flather's  Dynamometers,  and  the  Measurement  of  Power i2mo,  3  oo 

Rope  Driving i2mo,  2  oo 

Goss's  Locomotive  Sparks 8vo,  2  oo 

*  Greene's  Structural  Mechanics 8vo,  2  50 

Hall's  Car  Lubrication i2mo,  i  oo 

Holly's  Art  of  Saw  Filing i8mo,  75 

James's  Kinematics  of  a  Point  and  the  Rational  Mechanics  of  a  Particle. 

Small  8vo,  2  oo 

*  Johnson's  (W.  W.)  Theoretical  Mechanics i2»o,  3  oo 

Johnson's  (L.  J.)  Statics  by  Graphic  and  Algebraic  Methods 8vo,  2  oo 

Jones's  Machine  Design: 

Part    I.     Kinematics  of  Machinery 8vo,  i  50 

Part  II.     Form,  Strength,  and  Proportions  of  Parts 8vo,  3  oo 

Kerr's  Power  and  Power  Transmission 8vo,  2  oo 

Lanza's  Applied  Mechanics 8vo,  7  50 

Leonard's  Machine  Shop,  Tools,  and  Methods 8vo,  4  oo 

*  Lorenz's  Modern  Refrigerating  Machinery.     (Pope,  Haven,  and  Dean.). 8vo,  4  oo 
MacCord's  Kinematics;  or,  Practical  Mechanism 8vo,  5  oo 

Velocity  Diagrams 8vo,  i  50 

Maurer's  Technical  Mechanics 8vo,  4  oo 

Merriman's  Mechanics  of  Materials 8vo,  5  oo 

*  Elements  of  Mechanics I2mo,  i  oo 

*  Michie's  Elements  of  Analytical  Mechanics 8vo,  4  oo 

Reagan's  Locomotives:  Simple,  Compound,  and  Electric 12 mo,  2  50 

Reid's  Course  in  Mechanical  Drawing 8vo,  2  oo 

Text-book  of  Mechanical  Drawing  and  Elementary  Machine  Design. 8vo,  3  oo 

Richards's  Compressed  Air i2mo,  i  50 

Robinson's  Principles  of  Mechanism 8vo,  3  oo 

Ryan,  Norris,  and  Hoxie's  Electrical  Machinery.     Vol.  1 8vo,  2  50 

Schwamb  and  Merrill's  Elements  of  Mechanism 8vo,  300 

Sinclair's  Locomotive-engine  Running  and  Management I2mo,  2  oo 

Smith's  (0.)  Press-working  of  Metals 8vo,  3  oo 

Smith's  (A.  W.)  Materials  of  Machines izmo,  i  oo 

Smith  (A.  W.)  and  Marx's  Machine  Design 8vo,  3  oo 

Spangler,  Green«,  and  Marshall's  Elements  of  Steam-engineering 8vo,  3  oo 

Thurston's  Treatise  on  Friction  and  Lost  Work  in    Machinery  and    Mill 

Work 8vo-  3  °° 

Animal  as  a  Machine  and  Prime  Motor,  and  the  Lawc  of  Energetics. 

12010,      I    00 

Warren's  Elements  of  Machine  Construction  and  Drawing 

Weisbach's  Kinematics  and  Power  of  Transmission.    (Herrmann— Klein.  ).8vo,    5  oo 

Machinery  of  Transmission  and  Governors.      (Herrmann— Klein. ).8vo,    5 
Wood's  Elements  of  Analytical  Mechanics 

Principles  of  Elementary  Mechanics lamo,    i  25 

.        Turbines 8vo'    2  5° 

The  World's  Columbian  Exposition  of  1893 4to«    i  o< 

15 


METALLURGY. 

Egleston's  Metallurgy  of  Silver,  Gold,  and  Mercury: 

Vol.    I.     Silver 8vo,  7  50 

Vol.  II.     Gold  and  Mercury 8vo,  7  50 

**  Iles's  Lead-smelting.     (Postage  9  cents  additional.) I2mo,  2  50 

Keep's  Cast  Iron 8vo,  2  50 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe 8vo,  i  50 

Le  Chatelier's  High-temperature  Measurements.  (Boudouard — Burgess. )i2ino.  3  oo 

Metcalf's  Steel.     A  Manual  for  Steel-users.  .* i2mo,  2  oo 

Minet's  Production  of  Aluminum  and  its  Industrial  Use.     (Waldo.). . .  .  i2mo,  2  50 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) 8vo,  4  oo 

Smith's  Materials  of  Machines I2mo,  i  oo 

Thurston's  Materials  of  Engineering.     In  Three  Parts 8vo,  8  oo 

Part    II.     Iron  and  Steel 8vo,  3  50 

Part  III.     A  Treatise  on  Brasses,  Bronzes,  and  Other  Alloys  and  their 

Constituents 8vo,  2  50 

Hike's  Modern  Electrolytic  Copper  Refining 8vo»  3  oo 


MINERALOGY. 

Barringer's  Description  of  Minerals  of  Commercial  Value.    Oblong,  morocco,  2  50 

Boyd's  Resources  of  Southwest  Virginia 8vo,  3  oo 

Map  of  Southwest  Virignia Pocket-book  form.  2  oo 

Brush's  Manual  of  Determinative  Mineralogy.     (Penfield.) 8vo,  4  oo 

Chester's  Catalogue  of  Minerals 8vo,  paper,  i  oo 

Cloth,  i  25 

Dictionary  of  the  Names  of  Minerals 8vo,  3  50 

Dana's  System  of  Mineralogy Large  8vo,  half  leather,  12  50 

First  Appendix  to  Dana's  New  "  System  of  Mineralogy." Large  8vo,  i  oo 

Text-book  of  Mineralogy 8vo,  4  oo 

Minerals  and  How  to  Study  Them I2mo,  i  50 

Catalogue  of  American  Localities  of  Minerals Large  8vo,  i  oo 

Manual  of  Mineralogy  and  Petrography 12010,  2  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects I2mo,  i  oo 

Eakle's  Mineral  Tables 8vo,  i  25 

Egleston's  Catalogue  of  Minerals  and  Synonyms 8vo,  2  50 

Hussak's  The  Determination  of  Rock-forming  Minerals.    ( Smith.). Small  8vo,  2  oo 

Merrill's  Non-metallic  Minerals:  Their  Occurrence  and  Uses 8vo,  4  oo 

*  Penfield's  Notes  on  Determinative  Mineralogy  and  Record  of  Mineral  Tests. 

8vo,  paper,  50 
Rosenbusch's   Microscopical  Physiography   of   the   Rock-making  Minerals. 

(Iddings.) 8vo,  5  oo 

*  Tillman's  Text-book  of  Important  Minerals  and  Rocks 8vo,  2  oo 


MINING. 

Beard's  Ventilation  of  Mines 1 2mo,  2  50 

Boyd's  Resources  of  Southwest  Virginia f  vo,  3  oo 

Map  of  Southwest -Virginia Pocket-book  form  2  oo 

Douglas's  Untechnical  Addresses  on  Technical  Subjects i2mo.  i  oo 

*  Drinker's  Tunneling,  Explosive  Compounds,  and  Rocx  Drills.   4to,hf.  mor.,  25  oo 

Eissler's  Modern  High  Explosives.  . ./ 8vo,  4  oo 

16 


Goodyear's  Coal-mines  of  the  Western  Coast  of  the  United  States i2mo,  2  50 

Ihlseng's  Manual  of  Mining .- gvo>'  g  ^ 

**  Iles's  Lead-smelting.     (Postage  oc.  additional.) i2mo!  2  50 

Kunhardt's  Practice  of  Ore  Dressing  in  Europe 8vo,  i  50 

O'Driscoll's  Notes  on  the  Treatment  of  Gold  Ores .Svc,  2  oo 

Robine  and  Lenglen's  Cyanide  Industry.     (Le  Clerc.) '.'.  .8vo,  4  oo 

*  Walke's  Lectures  on  Explosives gvo>  4  <,<, 

Wilson's  Cyanide  Processes I2mo,  i  50 

Chlorination  Process I2mo,  i  50 

Hydraulic  and  Placer  Mining i2mo!  2  oo 

Treatise  on  Practical  and  Theoretical  Mine  Ventilation T2mo,  I  25 


SANITARY  SCIENCE. 

Bashore's  Sanitation  ®f  a  Country  House I2mo,  i  oo 

Folwell's  Sewerage.     (Designing,  Construction,  and  Maintenance.) 8vo,  3  oo 

Water-supply  Engineering 8vo,  4  oo 

Fowler's  Sewage  Works  Analyses I2mo,  2  oo 

Fuertes's  Water  and  Public  Health I2mo,  i  50 

Water-filtration  Works i2mo,  2  50 

Gerhard's  Guide  to  Sanitary  House-inspection i6mo,  i  oo 

Goodrich's  Economic  Disposal  of  Town's  Refuse Demy  8vo,  3  50 

Hazen's  Filtration  of  Public  Water-supplies 8vo,  3  oo 

Leach's  The  Inspection  and  Analysis  of  Food  with  Special  Reference  to  State 

Control 8vo,  7  50 

Mason's  Water-supply.  (Considered  principally  from  a  Sanitary  Standpoint)  8vo,  4  oo 

Examination  of  Water.     (Chemical  and  Bacteriological.) I2mo,  i  25 

Ogden's  Sewer  Design I2mo,  2  oo 

Prescott  and  Winslow's  Elements  of  Water  Bacteriology,  with  Special  Refer- 
ence to  Sanitary  Water  Analysis 1 2mo,  i  25 

*  Price's  Handbook  on  Sanitation I2mo,  I  50 

Richards's  Cost  of  Food.     A  Study  in  Dietaries i2mo,  i  oo 

Cost  of  Living  as  Modified  by  Sanitary  Science i2mo,  i  oo 

Cost  of  Shelter : i2mo,  i  oo 

Richards  and  Woodman's  Air,  Water,  and  Food  from  a  Sanitary  Stand- 
point  , 8vo,  2  oo 

*  Richards  and  Williams's  The  Dietary  Computer 8vo,  i  50 

Rideal's  Sewage  and  Bacterial  Purification  of  Sewage 8vo,  3  50 

Turneaure  and  Russell's  Public  Water-supplies 8vo,  5  oo 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) i2mo,  i  oo 

Whipple's  Microscopy  of  Drinking-water 8vo,  3  50 

Winton's  Microscopy  of  Vegetable  Foods 8vo,  7  5<> 

Woodhull's  Notes  on  Military  Hygiene i6mo,  i  50 

*  Personal  H/giene i2mo,  i  oo 


MISCELLANEOUS. 

De  Fursac's  Manual  of  Psychiatry.     (Rosanoff  and  Collins.) Large  i2mo,    2  50 

Emmons's  Geological  Guide-took  of  the  Rocky  Mountain  Excursion  of  the 

International  Congress  of  Geologists Large  £vo,     i  5' 

Ferrel's  Popular  Treatise  on  the  Winds 

Raines's  American  Railway  Management I2mo,    2 

Mott's  Fallacy  of  the  Present  Theory  of  Sound .  •  i6mo,     * 

Ricketts's  History  of  Rensselaer  Polytechnic  Institute,  1824-1894.  -Small  8vo,    3 

Rostoski's  Serum  Diagnosis.     (Bolduan.) 

Rotherham's  Emphasized  New  Testament Large  8vo,    2  o 

17 


Steel's  Treatise  on  the  Diseases  of  the  Dog 8vo,  3  50 

The  World's  Columbian  Exposition  of  1893 4to,  i  oo 

Von  Behring's  Suppression  of  Tuberculosis.     (Bolduan.) i2mo,  i  oo 

Winslow's  Elements  of  Applied  Microscopy i2mo,  i  50 

Worcester  and  Atkinson.     Small  Hospitals,  Establishment  and  Maintenance; 

Suggestions  for  Hospital  Architecture :  Plans  for  Small  Hospital .  1 2  mo ,  125 


HEBREW  AND  CHALDEE  TEXT-BOOKS. 

Green's  Elementary  Hebrew  Grammar i2mo,  i  25 

Hebrew  Chrestomathy 8vo,  2  oo 

Gesenius's  Hebrew  and  Chaldee  Lexicon  to  the  Old  Testament  Scriptures. 

(Tregelles.) Small  4to,  half  morocco,  5  oo 

Letteris's  Hebrew  Bible. 8vo,  2  25 

18 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
.     jfljflj),^  j,pTJ]7 1 H |  (I,,  last  date  stt 


OCT    17  1947 


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LD  21-100m-12,'46(A2012sl6)4120 


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UN1VERS1TY  OF  CALIFORNIA  UBRARY 


